comparable → comparable → comparable.
#T1; #T2; napply (mk_comparable (ProdT T1 T2));
##[ napply (pair … (zeroc T1) (zeroc T2))
- ##| napply (λx.false)
+ ##| napply (λP.(forallc T1)
+ (λe1.(forallc T2)
+ (λe2.P (pair … e1 e2))))
##| napply (eq_pair … (eqc T1) (eqc T2))
##| napply (eqpair_to_eq … (eqc T1) (eqc T2));
##[ napply (eqc_to_eq T1)
comparable → comparable → comparable → comparable.
#T1; #T2; #T3; napply (mk_comparable (Prod3T T1 T2 T3));
##[ napply (triple … (zeroc T1) (zeroc T2) (zeroc T3))
- ##| napply (λx.false)
+ ##| napply (λP.(forallc T1)
+ (λe1.(forallc T2)
+ (λe2.(forallc T3)
+ (λe3.P (triple … e1 e2 e3)))))
##| napply (eq_triple … (eqc T1) (eqc T2) (eqc T3))
##| napply (eqtriple_to_eq … (eqc T1) (eqc T2) (eqc T3));
##[ napply (eqc_to_eq T1)
comparable → comparable → comparable → comparable → comparable.
#T1; #T2; #T3; #T4; napply (mk_comparable (Prod4T T1 T2 T3 T4));
##[ napply (quadruple … (zeroc T1) (zeroc T2) (zeroc T3) (zeroc T4))
- ##| napply (λx.false)
+ ##| napply (λP.(forallc T1)
+ (λe1.(forallc T2)
+ (λe2.(forallc T3)
+ (λe3.(forallc T4)
+ (λe4.P (quadruple … e1 e2 e3 e4))))))
##| napply (eq_quadruple … (eqc T1) (eqc T2) (eqc T3) (eqc T4))
##| napply (eqquadruple_to_eq … (eqc T1) (eqc T2) (eqc T3) (eqc T4));
##[ napply (eqc_to_eq T1)
comparable → comparable → comparable → comparable → comparable → comparable.
#T1; #T2; #T3; #T4; #T5; napply (mk_comparable (Prod5T T1 T2 T3 T4 T5));
##[ napply (quintuple … (zeroc T1) (zeroc T2) (zeroc T3) (zeroc T4) (zeroc T5))
- ##| napply (λx.false)
+ ##| napply (λP.(forallc T1)
+ (λe1.(forallc T2)
+ (λe2.(forallc T3)
+ (λe3.(forallc T4)
+ (λe4.(forallc T5)
+ (λe5.P (quintuple … e1 e2 e3 e4 e5)))))))
##| napply (eq_quintuple … (eqc T1) (eqc T2) (eqc T3) (eqc T4) (eqc T5))
##| napply (eqquintuple_to_eq … (eqc T1) (eqc T2) (eqc T3) (eqc T4) (eqc T5));
##[ napply (eqc_to_eq T1)
+emulator/status/status_base.ma emulator/memory/memory_abs.ma emulator/opcodes/pseudo.ma emulator/status/HC05_status.ma emulator/status/HC08_status.ma emulator/status/IP2022_status.ma emulator/status/RS08_status.ma
+common/nelist.ma common/list.ma
+emulator/opcodes/HC05_table_tests.ma emulator/opcodes/HC05_table.ma emulator/opcodes/pseudo.ma
+emulator/opcodes/IP2022_instr_mode_base.ma num/bitrigesim.ma num/oct.ma
+num/bool.ma common/theory.ma
compiler/preast_tree.ma common/string.ma compiler/ast_type.ma num/word32.ma
-num/word32.ma num/word16.ma
+emulator/status/HC08_status.ma emulator/status/HC08_status_base.ma
+compiler/ast_base_type_base.ma num/bool.ma
common/nat.ma common/comp.ma num/bool_lemmas.ma
-common/ascii_base.ma num/bool.ma
-emulator/opcodes/HCS08_table.ma common/list.ma emulator/opcodes/Freescale_instr_mode.ma emulator/opcodes/Freescale_pseudo.ma emulator/opcodes/byte_or_word.ma
-num/bitrigesim.ma common/comp.ma num/bool_lemmas.ma
+emulator/opcodes/IP2022_pseudo.ma common/comp.ma emulator/opcodes/IP2022_pseudo_base.ma num/bool_lemmas.ma
+num/exadecim.ma num/bool_lemmas.ma num/comp_ext.ma num/oct.ma
+emulator/memory/memory_struct_base.ma num/byte8.ma
+emulator/status/status.ma emulator/status/status_base.ma
+num/byte8.ma num/bitrigesim.ma num/comp_num.ma num/exadecim.ma
+emulator/opcodes/HC08_table.ma common/list.ma emulator/opcodes/Freescale_instr_mode.ma emulator/opcodes/Freescale_pseudo.ma emulator/opcodes/byte_or_word.ma
+emulator/memory/memory_base.ma common/comp.ma num/bool_lemmas.ma
emulator/opcodes/HC05_table.ma common/list.ma emulator/opcodes/Freescale_instr_mode.ma emulator/opcodes/Freescale_pseudo.ma emulator/opcodes/byte_or_word.ma
-emulator/opcodes/byte_or_word.ma num/word16.ma
-emulator/opcodes/Freescale_pseudo_base.ma num/bool.ma
+emulator/status/HC08_status_base.ma num/word16.ma
+common/comp.ma common/hints_declaration.ma num/bool.ma
+emulator/memory/memory_trees.ma common/list.ma emulator/memory/memory_base.ma emulator/memory/memory_struct.ma num/word32.ma
+emulator/opcodes/Freescale_pseudo.ma common/comp.ma emulator/opcodes/Freescale_pseudo_base.ma num/bool_lemmas.ma
+emulator/status/HC05_status_base.ma num/word16.ma
common/pts.ma
-compiler/ast_type_base.ma common/nelist.ma compiler/ast_base_type.ma
+num/comp_ext.ma common/comp.ma common/prod.ma
+common/ascii_base.ma num/bool.ma
+emulator/opcodes/RS08_table_tests.ma emulator/opcodes/RS08_table.ma emulator/opcodes/pseudo.ma
+compiler/environment.ma common/string.ma compiler/ast_type.ma
+emulator/translation/translation_base.ma common/option.ma emulator/opcodes/HC05_table.ma emulator/opcodes/HC08_table.ma emulator/opcodes/HCS08_table.ma emulator/opcodes/IP2022_table.ma emulator/opcodes/RS08_table.ma emulator/opcodes/pseudo.ma
+compiler/ast_base_type.ma common/comp.ma compiler/ast_base_type_base.ma num/bool_lemmas.ma
+emulator/opcodes/IP2022_table.ma common/list.ma emulator/opcodes/IP2022_instr_mode.ma emulator/opcodes/IP2022_pseudo.ma emulator/opcodes/byte_or_word.ma
+emulator/status/HC05_status.ma emulator/status/HC05_status_base.ma
+emulator/memory/memory_bits.ma emulator/memory/memory_trees.ma
+common/string.ma common/ascii.ma common/list.ma
+common/theory.ma common/pts.ma
+emulator/opcodes/byte_or_word.ma num/word16.ma
+compiler/ast_type.ma compiler/ast_type_base.ma
+num/word16.ma common/nat.ma num/byte8.ma
+emulator/opcodes/IP2022_instr_mode.ma emulator/opcodes/IP2022_instr_mode_base.ma
common/prod.ma common/comp.ma common/prod_base.ma num/bool_lemmas.ma
-common/prod_base.ma num/bool.ma
-universe/universe.ma common/nelist.ma common/prod.ma
-num/bool_lemmas.ma num/bool.ma
-emulator/opcodes/Freescale_instr_mode.ma common/comp.ma emulator/opcodes/Freescale_instr_mode_base.ma num/bool_lemmas.ma
-num/exadecim.ma num/bool_lemmas.ma num/comp_ext.ma num/oct.ma
-common/comp.ma common/hints_declaration.ma num/bool.ma
num/word24.ma num/byte8.ma
-emulator/opcodes/IP2022_pseudo.ma common/comp.ma emulator/opcodes/IP2022_pseudo_base.ma num/bool_lemmas.ma
-common/theory.ma common/pts.ma
-emulator/opcodes/Freescale_pseudo.ma common/comp.ma emulator/opcodes/Freescale_pseudo_base.ma num/bool_lemmas.ma
-emulator/opcodes/HC08_table.ma common/list.ma emulator/opcodes/Freescale_instr_mode.ma emulator/opcodes/Freescale_pseudo.ma emulator/opcodes/byte_or_word.ma
-emulator/opcodes/Freescale_instr_mode_base.ma num/bitrigesim.ma num/exadecim.ma
+num/bool_lemmas.ma common/comp.ma num/bool.ma
+emulator/memory/memory_abs.ma emulator/memory/memory_bits.ma emulator/memory/memory_func.ma emulator/memory/memory_trees.ma
+emulator/status/IP2022_status_base.ma emulator/memory/memory_struct.ma num/word16.ma num/word24.ma
+emulator/memory/memory_struct.ma emulator/memory/memory_struct_base.ma
+num/word32.ma num/word16.ma
+common/ascii.ma common/ascii_base.ma common/comp.ma num/bool_lemmas.ma
+emulator/opcodes/HCS08_table_tests.ma emulator/opcodes/HCS08_table.ma emulator/opcodes/pseudo.ma
+emulator/opcodes/IP2022_table_tests.ma emulator/opcodes/IP2022_table.ma emulator/opcodes/pseudo.ma
+emulator/status/IP2022_status.ma emulator/status/IP2022_status_base.ma
+emulator/translation/Freescale_translation.ma emulator/translation/translation_base.ma
+emulator/memory/memory_func.ma common/list.ma emulator/memory/memory_base.ma num/word16.ma
+emulator/opcodes/Freescale_instr_mode.ma common/comp.ma emulator/opcodes/Freescale_instr_mode_base.ma num/bool_lemmas.ma
+emulator/status/RS08_status_base.ma num/word16.ma
+emulator/status/RS08_status.ma emulator/status/RS08_status_base.ma
+compiler/ast_type_base.ma common/nelist.ma compiler/ast_base_type.ma
+common/prod_base.ma num/bool.ma
+common/option_base.ma num/bool.ma
+common/option.ma common/comp.ma common/option_base.ma num/bool_lemmas.ma
emulator/opcodes/RS08_table.ma common/list.ma emulator/opcodes/Freescale_instr_mode.ma emulator/opcodes/Freescale_pseudo.ma emulator/opcodes/byte_or_word.ma
+num/comp_num.ma num/bool_lemmas.ma num/comp_ext.ma
common/sigma.ma common/theory.ma
-num/oct.ma common/comp.ma num/bool_lemmas.ma
-compiler/ast_base_type.ma common/comp.ma compiler/ast_base_type_base.ma num/bool_lemmas.ma
-num/byte8.ma num/bitrigesim.ma num/comp_num.ma num/exadecim.ma
+emulator/opcodes/HCS08_table.ma common/list.ma emulator/opcodes/Freescale_instr_mode.ma emulator/opcodes/Freescale_pseudo.ma emulator/opcodes/byte_or_word.ma
+emulator/translation/IP2022_translation.ma emulator/translation/translation_base.ma
+universe/universe.ma common/nelist.ma common/prod.ma
+num/bitrigesim.ma common/comp.ma num/bool_lemmas.ma
common/hints_declaration.ma common/pts.ma
-common/option.ma common/comp.ma common/option_base.ma num/bool_lemmas.ma
-num/bool.ma common/theory.ma
-common/option_base.ma num/bool.ma
-emulator/opcodes/IP2022_instr_mode_base.ma num/bitrigesim.ma num/oct.ma
-compiler/ast_base_type_base.ma num/bool.ma
-num/word16.ma common/nat.ma num/byte8.ma
-compiler/environment.ma common/string.ma compiler/ast_type.ma
-common/ascii.ma common/ascii_base.ma common/comp.ma num/bool_lemmas.ma
emulator/opcodes/pseudo.ma common/list.ma emulator/opcodes/Freescale_instr_mode.ma emulator/opcodes/Freescale_pseudo.ma emulator/opcodes/IP2022_instr_mode.ma emulator/opcodes/IP2022_pseudo.ma emulator/opcodes/byte_or_word.ma
-common/string.ma common/ascii.ma common/list.ma
-common/list.ma common/comp.ma common/nat.ma common/option.ma
-compiler/ast_type.ma compiler/ast_type_base.ma
-num/comp_num.ma num/bool_lemmas.ma num/comp_ext.ma
-emulator/opcodes/IP2022_table.ma common/list.ma emulator/opcodes/IP2022_instr_mode.ma emulator/opcodes/IP2022_pseudo.ma emulator/opcodes/byte_or_word.ma
-num/comp_ext.ma common/comp.ma common/prod.ma
-emulator/opcodes/IP2022_instr_mode.ma emulator/opcodes/IP2022_instr_mode_base.ma
-common/nelist.ma common/list.ma
+emulator/opcodes/Freescale_pseudo_base.ma num/bool.ma
+emulator/translation/translation.ma emulator/translation/Freescale_translation.ma emulator/translation/IP2022_translation.ma
+num/oct.ma common/comp.ma num/bool_lemmas.ma
emulator/opcodes/IP2022_pseudo_base.ma num/bool.ma
+common/list.ma common/comp.ma common/nat.ma common/option.ma
+emulator/opcodes/Freescale_instr_mode_base.ma num/bitrigesim.ma num/exadecim.ma
+emulator/opcodes/HC08_table_tests.ma emulator/opcodes/HC08_table.ma emulator/opcodes/pseudo.ma
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/memory/memory_func.ma".
+include "emulator/memory/memory_trees.ma".
+include "emulator/memory/memory_bits.ma".
+
+(* ********************************************* *)
+(* ASTRAZIONE DALL'IMPLEMENTAZIONE DELLA MEMORIA *)
+(* ********************************************* *)
+
+(* se si disattiva l'implementazione a funzione
+ la memoria diventa un'oggetto confrontabile! *)
+
+(* tipi di implementazione della memoria *)
+ninductive memory_impl : Type ≝
+ (*MEM_FUNC: memory_impl
+|*) MEM_TREE: memory_impl
+| MEM_BITS: memory_impl.
+
+(* ausiliario per il tipo della memoria *)
+ndefinition aux_mem_type ≝
+λt:memory_impl.match t with
+ [ (*MEM_FUNC ⇒ oct → word16 → byte8
+ |*) MEM_TREE ⇒ aux_20B_type byte8
+ | MEM_BITS ⇒ aux_20B_type (Array8T bool)
+ ].
+
+(* ausiliario per il tipo del checker *)
+ndefinition aux_chk_type ≝
+λt:memory_impl.match t with
+ [ (*MEM_FUNC ⇒ oct → word16 → memory_type
+ |*) MEM_TREE ⇒ aux_20B_type memory_type
+ | MEM_BITS ⇒ aux_20B_type (Array8T memory_type)
+ ].
+
+(* unificazione di out_of_bound_memory *)
+ndefinition out_of_bound_memory ≝
+λt:memory_impl.
+ match t
+ return λt.aux_chk_type t
+ with
+ [ (*MEM_FUNC ⇒ mf_out_of_bound_memory
+ |*) MEM_TREE ⇒ mt_out_of_bound_memory
+ | MEM_BITS ⇒ mb_out_of_bound_memory
+ ].
+
+(* unificazione di zero_memory *)
+ndefinition zero_memory ≝
+λt:memory_impl.
+ match t
+ return λt.aux_mem_type t
+ with
+ [ (*MEM_FUNC ⇒ mf_zero_memory
+ |*) MEM_TREE ⇒ mt_zero_memory
+ | MEM_BITS ⇒ mb_zero_memory
+ ].
+
+(* unificazione della lettura senza chk: mem_read_abs mem addr *)
+ndefinition mem_read_abs ≝
+λt:memory_impl.
+ match t
+ return λt.aux_mem_type t → oct → word16 → byte8
+ with
+ [ (*MEM_FUNC ⇒ λm:aux_mem_type MEM_FUNC.
+ m
+ |*) MEM_TREE ⇒ λm:aux_mem_type MEM_TREE.
+ mt_visit ? m
+ | MEM_BITS ⇒ λm:aux_mem_type MEM_BITS.
+ λsel:oct.λaddr:word16.
+ byte8_of_bits (mt_visit ? m sel addr)
+ ].
+
+(* unificazione del chk *)
+ndefinition chk_get ≝
+λt:memory_impl.
+ match t
+ return λt.aux_chk_type t → oct → word16 → Array8T memory_type
+ with
+ [ (*MEM_FUNC ⇒ λc:aux_chk_type MEM_FUNC.λsel:oct.λaddr:word16.
+ match c sel addr with
+ [ MEM_READ_ONLY ⇒ mk_Array8T ? MEM_READ_ONLY MEM_READ_ONLY MEM_READ_ONLY MEM_READ_ONLY MEM_READ_ONLY MEM_READ_ONLY MEM_READ_ONLY MEM_READ_ONLY
+ | MEM_READ_WRITE ⇒ mk_Array8T ? MEM_READ_WRITE MEM_READ_WRITE MEM_READ_WRITE MEM_READ_WRITE MEM_READ_WRITE MEM_READ_WRITE MEM_READ_WRITE MEM_READ_WRITE
+ | MEM_OUT_OF_BOUND ⇒ mk_Array8T ? MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND
+ ]
+ |*) MEM_TREE ⇒ λc:aux_chk_type MEM_TREE.λsel:oct.λaddr:word16.
+ match mt_visit ? c sel addr with
+ [ MEM_READ_ONLY ⇒ mk_Array8T ? MEM_READ_ONLY MEM_READ_ONLY MEM_READ_ONLY MEM_READ_ONLY MEM_READ_ONLY MEM_READ_ONLY MEM_READ_ONLY MEM_READ_ONLY
+ | MEM_READ_WRITE ⇒ mk_Array8T ? MEM_READ_WRITE MEM_READ_WRITE MEM_READ_WRITE MEM_READ_WRITE MEM_READ_WRITE MEM_READ_WRITE MEM_READ_WRITE MEM_READ_WRITE
+ | MEM_OUT_OF_BOUND ⇒ mk_Array8T ? MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND
+ ]
+ | MEM_BITS ⇒ mt_visit ?
+ ].
+
+(* unificazione della lettura con chk: mem_read mem chk addr *)
+ndefinition mem_read ≝
+λt:memory_impl.
+ match t
+ return λt.aux_mem_type t → aux_chk_type t → oct → word16 → option byte8
+ with
+ [ (*MEM_FUNC ⇒ mf_mem_read
+ |*) MEM_TREE ⇒ mt_mem_read
+ | MEM_BITS ⇒ mb_mem_read
+ ].
+
+(* unificazione della lettura di bit con chk: mem_read mem chk addr sub *)
+ndefinition mem_read_bit ≝
+λt:memory_impl.
+ match t
+ return λt.aux_mem_type t → aux_chk_type t → oct → word16 → oct → option bool
+ with
+ [ (*MEM_FUNC ⇒ λm:aux_mem_type MEM_FUNC.
+ λc:aux_chk_type MEM_FUNC.
+ λsel:oct.λaddr:word16.
+ λo:oct.
+ opt_map … (mf_mem_read m c sel addr)
+ (λb.Some ? (getn_array8T o bool (bits_of_byte8 b)))
+ |*) MEM_TREE ⇒ λm:aux_mem_type MEM_TREE.
+ λc:aux_chk_type MEM_TREE.
+ λsel:oct.λaddr:word16.
+ λo:oct.
+ opt_map … (mt_mem_read m c sel addr)
+ (λb.Some ? (getn_array8T o bool (bits_of_byte8 b)))
+ | MEM_BITS ⇒ mb_mem_read_bit
+ ].
+
+(* unificazione della scrittura con chk: mem_update mem chk addr val *)
+ndefinition mem_update ≝
+λt:memory_impl.
+ match t
+ return λt.aux_mem_type t → aux_chk_type t → oct → word16 → byte8 → option (aux_mem_type t)
+ with
+ [ (*MEM_FUNC ⇒ mf_mem_update
+ |*) MEM_TREE ⇒ mt_mem_update
+ | MEM_BITS ⇒ mb_mem_update
+ ].
+
+(* unificazione della scrittura di bit con chk: mem_update mem chk addr sub val *)
+ndefinition mem_update_bit ≝
+λt:memory_impl.
+ match t
+ return λt.aux_mem_type t → aux_chk_type t → oct → word16 → oct → bool → option (aux_mem_type t)
+ with
+ [ (*MEM_FUNC ⇒ λm:aux_mem_type MEM_FUNC.
+ λc:aux_chk_type MEM_FUNC.
+ λsel:oct.λaddr:word16.
+ λo:oct.
+ λv:bool.
+ mf_mem_update m c sel addr (byte8_of_bits (setn_array8T o bool (bits_of_byte8 (m addr)) v))
+ |*) MEM_TREE ⇒ λm:aux_mem_type MEM_TREE.
+ λc:aux_chk_type MEM_TREE.
+ λsel:oct.λaddr:word16.
+ λo:oct.
+ λv:bool.
+ mt_mem_update m c sel addr (byte8_of_bits (setn_array8T o bool (bits_of_byte8 (mt_visit ? m sel addr)) v))
+ | MEM_BITS ⇒ mb_mem_update_bit
+ ].
+
+(* unificazione del caricamento: load_from_source_at old_mem source addr *)
+ndefinition load_from_source_at ≝
+λt:memory_impl.
+ match t
+ return λt.aux_mem_type t → list byte8 → oct → word16 → aux_mem_type t
+ with
+ [ (*MEM_FUNC ⇒ mf_load_from_source_at
+ |*) MEM_TREE ⇒ mt_load_from_source_at
+ | MEM_BITS ⇒ mb_load_from_source_at
+ ].
+
+(* unificazione dell'impostazione della memoria: chk_update_ranged chk inf sup v *)
+ndefinition check_update_ranged ≝
+λt:memory_impl.
+ match t
+ return λt.aux_chk_type t → oct → word16 → word16 → memory_type → aux_chk_type t
+ with
+ [ (*MEM_FUNC ⇒ mf_check_update_ranged
+ |*) MEM_TREE ⇒ λc:aux_chk_type MEM_TREE.
+ λsel:oct.λaddr:word16.
+ λrange:word16.
+ mt_update_ranged ? c sel addr ? (w16_to_recw16 range)
+ | MEM_BITS ⇒ λc:aux_chk_type MEM_BITS.
+ λsel:oct.λaddr:word16.
+ λrange:word16.
+ λv:memory_type.
+ mt_update_ranged ? c sel addr ? (w16_to_recw16 range) (mk_Array8T ? v v v v v v v v)
+ ].
+
+(* unificazione dell'impostazione dei bit: chk_update_bit chk addr sub v *)
+(* NB: dove non esiste la granularita' del bit, lascio inalterato *)
+ndefinition check_update_bit ≝
+λt:memory_impl.
+ match t
+ return λt.aux_chk_type t → oct → word16 → oct → memory_type → aux_chk_type t
+ with
+ [ (*MEM_FUNC ⇒ λc:aux_chk_type MEM_FUNC.
+ λsel:oct.λaddr:word16.
+ λo:oct.
+ λv:memory_type.
+ c
+ |*) MEM_TREE ⇒ λc:aux_chk_type MEM_TREE.
+ λsel:oct.λaddr:word16.
+ λo:oct.
+ λv:memory_type.
+ c
+ | MEM_BITS ⇒ mb_chk_update_bit
+ ].
+
+ndefinition mem_is_comparable: memory_impl → comparable.
+ #m; @ (aux_mem_type m)
+ ##[ nelim m;
+ ##[ napply mt_zero_memory
+ ##| napply mb_zero_memory ##]
+ ##| nelim m;
+ ##[ napply (forallc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable byte8_is_comparable))))))
+ ##| napply (forallc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable bool_is_comparable))))))) ##]
+ ##| nelim m;
+ ##[ napply (eqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable byte8_is_comparable))))))
+ ##| napply (eqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable bool_is_comparable))))))) ##]
+ ##| nelim m;
+ ##[ napply (eqc_to_eq (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable byte8_is_comparable))))))
+ ##| napply (eqc_to_eq (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable bool_is_comparable))))))) ##]
+ ##| nelim m;
+ ##[ napply (eq_to_eqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable byte8_is_comparable))))))
+ ##| napply (eq_to_eqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable bool_is_comparable))))))) ##]
+ ##| nelim m;
+ ##[ napply (neqc_to_neq (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable byte8_is_comparable))))))
+ ##| napply (neqc_to_neq (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable bool_is_comparable))))))) ##]
+ ##| nelim m;
+ ##[ napply (neq_to_neqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable byte8_is_comparable))))))
+ ##| napply (neq_to_neqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable bool_is_comparable))))))) ##]
+ ##| nelim m;
+ ##[ napply (decidable_c (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable byte8_is_comparable))))))
+ ##| napply (decidable_c (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable bool_is_comparable))))))) ##]
+ ##| nelim m;
+ ##[ napply (symmetric_eqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable byte8_is_comparable))))))
+ ##| napply (symmetric_eqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable bool_is_comparable))))))) ##]
+ ##]
+nqed.
+
+unification hint 0 ≔ M:memory_impl ⊢ carr (mem_is_comparable M) ≡ aux_mem_type M.
+
+ndefinition chk_is_comparable: memory_impl → comparable.
+ #m; @ (aux_chk_type m)
+ ##[ nelim m;
+ ##[ napply mt_out_of_bound_memory
+ ##| napply mb_out_of_bound_memory ##]
+ ##| nelim m;
+ ##[ napply (forallc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable memorytype_is_comparable))))))
+ ##| napply (forallc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable memorytype_is_comparable))))))) ##]
+ ##| nelim m;
+ ##[ napply (eqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable memorytype_is_comparable))))))
+ ##| napply (eqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable memorytype_is_comparable))))))) ##]
+ ##| nelim m;
+ ##[ napply (eqc_to_eq (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable memorytype_is_comparable))))))
+ ##| napply (eqc_to_eq (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable memorytype_is_comparable))))))) ##]
+ ##| nelim m;
+ ##[ napply (eq_to_eqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable memorytype_is_comparable))))))
+ ##| napply (eq_to_eqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable memorytype_is_comparable))))))) ##]
+ ##| nelim m;
+ ##[ napply (neqc_to_neq (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable memorytype_is_comparable))))))
+ ##| napply (neqc_to_neq (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable memorytype_is_comparable))))))) ##]
+ ##| nelim m;
+ ##[ napply (neq_to_neqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable memorytype_is_comparable))))))
+ ##| napply (neq_to_neqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable memorytype_is_comparable))))))) ##]
+ ##| nelim m;
+ ##[ napply (decidable_c (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable memorytype_is_comparable))))))
+ ##| napply (decidable_c (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable memorytype_is_comparable))))))) ##]
+ ##| nelim m;
+ ##[ napply (symmetric_eqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable memorytype_is_comparable))))))
+ ##| napply (symmetric_eqc (ar8_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar16_is_comparable (ar8_is_comparable memorytype_is_comparable))))))) ##]
+ ##]
+nqed.
+
+unification hint 0 ≔ M:memory_impl ⊢ carr (chk_is_comparable M) ≡ aux_chk_type M.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "common/comp.ma".
+include "num/bool_lemmas.ma".
+
+(* **************************** *)
+(* TIPI PER I MODULI DI MEMORIA *)
+(* **************************** *)
+
+(* tipi di memoria:RAM/ROM/non installata *)
+ninductive memory_type : Type ≝
+ MEM_READ_ONLY: memory_type
+| MEM_READ_WRITE: memory_type
+| MEM_OUT_OF_BOUND: memory_type.
+
+(* iteratore sugli ottali *)
+ndefinition forall_memory_type ≝ λP.
+ P MEM_READ_ONLY ⊗ P MEM_READ_WRITE ⊗ P MEM_OUT_OF_BOUND.
+
+(* operatore = *)
+ndefinition eq_memorytype ≝
+λm1,m2.match m1 with
+ [ MEM_READ_ONLY ⇒ match m2 with [ MEM_READ_ONLY ⇒ true | _ ⇒ false ]
+ | MEM_READ_WRITE ⇒ match m2 with [ MEM_READ_WRITE ⇒ true | _ ⇒ false ]
+ | MEM_OUT_OF_BOUND ⇒ match m2 with [ MEM_OUT_OF_BOUND ⇒ true | _ ⇒ false ]
+ ].
+
+ndefinition memorytype_destruct_aux ≝
+Πn1,n2:memory_type.ΠP:Prop.n1 = n2 →
+ match eq_memorytype n1 n2 with [ true ⇒ P → P | false ⇒ P ].
+
+ndefinition memorytype_destruct : memorytype_destruct_aux.
+ #n1; #n2; #P; #H;
+ nrewrite < H;
+ nelim n1;
+ nnormalize;
+ napply (λx.x).
+nqed.
+
+nlemma eq_to_eqmemorytype : ∀n1,n2.n1 = n2 → eq_memorytype n1 n2 = true.
+ #n1; #n2; #H;
+ nrewrite > H;
+ nelim n2;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma neqmemorytype_to_neq : ∀n1,n2.eq_memorytype n1 n2 = false → n1 ≠ n2.
+ #n1; #n2; #H;
+ napply (not_to_not (n1 = n2) (eq_memorytype n1 n2 = true) …);
+ ##[ ##1: napply (eq_to_eqmemorytype n1 n2)
+ ##| ##2: napply (eqfalse_to_neqtrue … H)
+ ##]
+nqed.
+
+nlemma eqmemorytype_to_eq : ∀n1,n2.eq_memorytype n1 n2 = true → n1 = n2.
+ #n1; #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,5,9: #H; napply refl_eq
+ ##| ##*: #H; ndestruct (*napply (bool_destruct … H)*)
+ ##]
+nqed.
+
+nlemma neq_to_neqmemorytype : ∀n1,n2.n1 ≠ n2 → eq_memorytype n1 n2 = false.
+ #n1; #n2; #H;
+ napply (neqtrue_to_eqfalse (eq_memorytype n1 n2));
+ napply (not_to_not (eq_memorytype n1 n2 = true) (n1 = n2) ? H);
+ napply (eqmemorytype_to_eq n1 n2).
+nqed.
+
+nlemma decidable_memorytype : ∀x,y:memory_type.decidable (x = y).
+ #x; #y; nnormalize;
+ napply (or2_elim (eq_memorytype x y = true) (eq_memorytype x y = false) ? (decidable_bexpr ?));
+ ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqmemorytype_to_eq … H))
+ ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqmemorytype_to_neq … H))
+ ##]
+nqed.
+
+nlemma symmetric_eqmemorytype : symmetricT memory_type bool eq_memorytype.
+ #n1; #n2;
+ napply (or2_elim (n1 = n2) (n1 ≠ n2) ? (decidable_memorytype n1 n2));
+ ##[ ##1: #H; nrewrite > H; napply refl_eq
+ ##| ##2: #H; nrewrite > (neq_to_neqmemorytype n1 n2 H);
+ napply (symmetric_eq ? (eq_memorytype n2 n1) false);
+ napply (neq_to_neqmemorytype n2 n1 (symmetric_neq ? n1 n2 H))
+ ##]
+nqed.
+
+nlemma memorytype_is_comparable : comparable.
+ @ memory_type
+ ##[ napply MEM_READ_ONLY
+ ##| napply forall_memory_type
+ ##| napply eq_memorytype
+ ##| napply eqmemorytype_to_eq
+ ##| napply eq_to_eqmemorytype
+ ##| napply neqmemorytype_to_neq
+ ##| napply neq_to_neqmemorytype
+ ##| napply decidable_memorytype
+ ##| napply symmetric_eqmemorytype
+ ##]
+nqed.
+
+unification hint 0 ≔ ⊢ carr memorytype_is_comparable ≡ memory_type.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/memory/memory_trees.ma".
+
+(* ********************* *)
+(* MEMORIA E DESCRITTORE *)
+(* ********************* *)
+
+(* tutta la memoria non installata *)
+ndefinition mb_out_of_bound_memory ≝
+ aux_20B_filler ?
+ (mk_Array8T ? MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND
+ MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND MEM_OUT_OF_BOUND).
+
+(* tutta la memoria a 0 *)
+ndefinition mb_zero_memory ≝
+ aux_20B_filler ? (mk_Array8T ? false false false false false false false false).
+
+(* scrivi bit controllando il tipo di memoria *)
+ndefinition mb_mem_update_bit ≝
+λmem:aux_20B_type (Array8T bool).
+λchk:aux_20B_type (Array8T memory_type).
+λsel:oct.λaddr:word16.λsub:oct.λv:bool.
+ match getn_array8T sub ? (mt_visit ? chk sel addr) with
+ (* ROM? ok, ma il valore viene perso *)
+ [ MEM_READ_ONLY ⇒ Some ? mem
+ (* RAM? ok *)
+ | MEM_READ_WRITE ⇒ Some ? (mt_update ? mem sel addr (setn_array8T sub ? (mt_visit ? mem sel addr) v))
+ (* NON INSTALLATA? no *)
+ | MEM_OUT_OF_BOUND ⇒ None ? ].
+
+ndefinition mb_mem_update ≝
+λmem:aux_20B_type (Array8T bool).
+λchk:aux_20B_type (Array8T memory_type).
+λsel:oct.λaddr:word16.λv:byte8.
+let old_value ≝ mt_visit (Array8T bool) mem sel addr in
+let new_value ≝ bits_of_byte8 v in
+let memtypes ≝ mt_visit (Array8T memory_type) chk sel addr in
+let newbit0 ≝ match getn_array8T o0 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o0 bool old_value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o0 bool new_value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+let newbit1 ≝ match getn_array8T o1 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o1 bool old_value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o1 bool new_value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+let newbit2 ≝ match getn_array8T o2 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o2 bool old_value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o2 bool new_value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+let newbit3 ≝ match getn_array8T o3 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o3 bool old_value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o3 bool new_value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+let newbit4 ≝ match getn_array8T o4 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o4 bool old_value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o4 bool new_value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+let newbit5 ≝ match getn_array8T o5 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o5 bool old_value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o5 bool new_value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+let newbit6 ≝ match getn_array8T o6 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o6 bool old_value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o6 bool new_value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+let newbit7 ≝ match getn_array8T o7 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o7 bool old_value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o7 bool new_value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+ opt_map … newbit0
+ (λnb0.opt_map … newbit1
+ (λnb1.opt_map … newbit2
+ (λnb2.opt_map … newbit3
+ (λnb3.opt_map … newbit4
+ (λnb4.opt_map … newbit5
+ (λnb5.opt_map … newbit6
+ (λnb6.opt_map … newbit7
+ (λnb7.Some ? (mt_update ? mem sel addr (mk_Array8T bool nb7 nb6 nb5 nb4 nb3 nb2 nb1 nb0)))))))))).
+
+(* scrivi tipo di bit *)
+ndefinition mb_chk_update_bit ≝
+λchk:aux_20B_type (Array8T memory_type).
+λsel:oct.λaddr:word16.λsub:oct.λv:memory_type.
+ mt_update ? chk sel addr (setn_array8T sub ? (mt_visit ? chk sel addr) v).
+
+(* leggi bit controllando il tipo di memoria *)
+ndefinition mb_mem_read_bit ≝
+λmem:aux_20B_type (Array8T bool).
+λchk:aux_20B_type (Array8T memory_type).
+λsel:oct.λaddr:word16.λsub:oct.
+ match getn_array8T sub ? (mt_visit ? chk sel addr) with
+ (* ROM? ok, ma il valore viene perso *)
+ [ MEM_READ_ONLY ⇒ Some ? (getn_array8T sub ? (mt_visit ? mem sel addr))
+ (* RAM? ok *)
+ | MEM_READ_WRITE ⇒ Some ? (getn_array8T sub ? (mt_visit ? mem sel addr))
+ (* NON INSTALLATA? no *)
+ | MEM_OUT_OF_BOUND ⇒ None ? ].
+
+(* leggi controllando il tipo di memoria *)
+(* NB: devono esistere tutti i bit *)
+ndefinition mb_mem_read ≝
+λmem:aux_20B_type (Array8T bool).
+λchk:aux_20B_type (Array8T memory_type).
+λsel:oct.λaddr:word16.
+let value ≝ mt_visit (Array8T bool) mem sel addr in
+let memtypes ≝ mt_visit (Array8T memory_type) chk sel addr in
+let newbit0 ≝ match getn_array8T o0 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o0 bool value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o0 bool value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+let newbit1 ≝ match getn_array8T o1 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o1 bool value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o1 bool value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+let newbit2 ≝ match getn_array8T o2 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o2 bool value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o2 bool value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+let newbit3 ≝ match getn_array8T o3 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o3 bool value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o3 bool value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+let newbit4 ≝ match getn_array8T o4 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o4 bool value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o4 bool value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+let newbit5 ≝ match getn_array8T o5 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o5 bool value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o5 bool value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+let newbit6 ≝ match getn_array8T o6 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o6 bool value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o6 bool value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+let newbit7 ≝ match getn_array8T o7 memory_type memtypes with
+ [ MEM_READ_ONLY ⇒ Some bool (getn_array8T o7 bool value)
+ | MEM_READ_WRITE ⇒ Some bool (getn_array8T o7 bool value)
+ | MEM_OUT_OF_BOUND ⇒ None bool ] in
+ opt_map … newbit0
+ (λnb0.opt_map … newbit1
+ (λnb1.opt_map … newbit2
+ (λnb2.opt_map … newbit3
+ (λnb3.opt_map … newbit4
+ (λnb4.opt_map … newbit5
+ (λnb5.opt_map … newbit6
+ (λnb6.opt_map … newbit7
+ (λnb7.Some ? (byte8_of_bits (mk_Array8T bool nb7 nb6 nb5 nb4 nb3 nb2 nb1 nb0)))))))))).
+
+(* ************************** *)
+(* CARICAMENTO PROGRAMMA/DATI *)
+(* ************************** *)
+
+(* carica a paratire da addr, scartando source (pescando da old_mem) se si supera 0xFFFF... *)
+nlet rec mb_load_from_source_at (old_mem:aux_20B_type (Array8T bool))
+ (src:list byte8) (sel:oct) (addr:word16) on src ≝
+ match src with
+ (* fine di source: carica da old_mem *)
+ [ nil ⇒ old_mem
+ | cons hd tl ⇒ mb_load_from_source_at (mt_update ? old_mem sel addr (bits_of_byte8 hd))
+ tl sel (succc ? addr)
+ ].
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/memory/memory_base.ma".
+include "num/word16.ma".
+include "common/list.ma".
+
+(* ************************** *)
+(* 8 segmenti da 64Kb → 512Kb *)
+(* ************************** *)
+
+(* ********************* *)
+(* MEMORIA E DESCRITTORE *)
+(* ********************* *)
+
+(* (mf_check_update_ranged chk inf sup mode) = setta tipo memoria *)
+ndefinition mf_check_update_ranged ≝
+λf:oct → word16 → memory_type.λsel:oct.λaddr:word16.λrange:word16.λv.
+ λx,y.
+ match (eqc ? sel x)⊗(inrangec ? y addr (plusc_d_d ? addr range)) with
+ [ true ⇒ v
+ | false ⇒ f x y ].
+
+(* tutta la memoria non installata *)
+ndefinition mf_out_of_bound_memory ≝ λ_:oct.λ_:word16.MEM_OUT_OF_BOUND.
+
+(* (mf_mem_update mem checked addr val) = scrivi controllando il tipo di memoria *)
+ndefinition mf_mem_update ≝
+λf:oct → word16 → byte8.λc:oct → word16 → memory_type.λsel:oct.λa:word16.λv:byte8.
+ match c sel a with
+ (* ROM? ok, ma il valore viene perso *)
+ [ MEM_READ_ONLY ⇒ Some ? f
+ (* RAM? ok *)
+ | MEM_READ_WRITE ⇒ Some ? (λx,y.match (eqc ? sel x)⊗(eqc ? a y) with [ true ⇒ v | false ⇒ f x y ])
+ (* NON INSTALLATA? no *)
+ | MEM_OUT_OF_BOUND ⇒ None ? ].
+
+(* tutta la memoria a 0 *)
+ndefinition mf_zero_memory ≝ λ_:oct.λ_:word16.〈x0,x0〉.
+
+(* (mf_mem_read mem check addr) = leggi controllando il tipo di memoria *)
+ndefinition mf_mem_read ≝
+λf:oct → word16 → byte8.λc:oct → word16 → memory_type.λsel:oct.λa:word16.
+ match c sel a with
+ [ MEM_READ_ONLY ⇒ Some ? (f sel a)
+ | MEM_READ_WRITE ⇒ Some ? (f sel a)
+ | MEM_OUT_OF_BOUND ⇒ None ? ].
+
+(* ************************** *)
+(* CARICAMENTO PROGRAMMA/DATI *)
+(* ************************** *)
+
+(* carica a paratire da addr, overflow se si supera 0xFFFF... *)
+nlet rec mf_load_from_source_at (old_mem:oct → word16 → byte8) (src:list byte8) (sel:oct) (addr:word16) on src ≝
+ match src with
+ (* fine di source: carica da old_mem *)
+ [ nil ⇒ old_mem
+ | cons hd tl ⇒ λx,y.match (eqc ? sel x)⊗(eqc ? addr y) with
+ (* la locazione corrisponde al punto corrente di source *)
+ [ true ⇒ hd
+ (* la locazione e' piu' avanti? ricorsione *)
+ | false ⇒ (mf_load_from_source_at old_mem tl sel (succc ? addr)) x y
+ ]
+ ].
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/memory/memory_struct_base.ma".
+
+(* **************** *)
+(* TIPO ARRAY DA 16 *)
+(* **************** *)
+
+nlemma ar16_destruct_1 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x1 = y1.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T a _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x1 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_2 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x2 = y2.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ a _ _ _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x2 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_3 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x3 = y3.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ _ a _ _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x3 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_4 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x4 = y4.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ _ _ a _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x4 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_5 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x5 = y5.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ _ _ _ a _ _ _ _ _ _ _ _ _ _ _ ⇒ x5 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_6 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x6 = y6.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ _ _ _ _ a _ _ _ _ _ _ _ _ _ _ ⇒ x6 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_7 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x7 = y7.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ _ _ _ _ _ a _ _ _ _ _ _ _ _ _ ⇒ x7 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_8 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x8 = y8.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ _ _ _ _ _ _ a _ _ _ _ _ _ _ _ ⇒ x8 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_9 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x9 = y9.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ _ _ _ _ _ _ _ a _ _ _ _ _ _ _ ⇒ x9 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_10 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x10 = y10.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ _ _ _ _ _ _ _ _ a _ _ _ _ _ _ ⇒ x10 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_11 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x11 = y11.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ _ _ _ _ _ _ _ _ _ a _ _ _ _ _ ⇒ x11 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_12 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x12 = y12.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ _ _ _ _ _ _ _ _ _ _ a _ _ _ _ ⇒ x12 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_13 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x13 = y13.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ _ _ _ _ _ _ _ _ _ _ _ a _ _ _ ⇒ x13 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_14 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x14 = y14.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ _ _ _ _ _ _ _ _ _ _ _ _ a _ _ ⇒ x14 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_15 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x15 = y15.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ _ _ _ _ _ _ _ _ _ _ _ _ _ a _ ⇒ x15 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar16_destruct_16 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x16 = y16.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_Array16T _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ a ⇒ x16 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma symmetric_eqar16 :
+∀T.∀f:T → T → bool.
+ (symmetricT T bool f) →
+ (symmetricT (Array16T T) bool (eq_ar16 T f)).
+ #T; #f; #H;
+ #alu1; ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #alu2; ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nchange with (
+ ((f x1 y1) ⊗ (f x2 y2) ⊗ (f x3 y3) ⊗ (f x4 y4) ⊗
+ (f x5 y5) ⊗ (f x6 y6) ⊗ (f x7 y7) ⊗ (f x8 y8) ⊗
+ (f x9 y9) ⊗ (f x10 y10) ⊗ (f x11 y11) ⊗ (f x12 y12) ⊗
+ (f x13 y13) ⊗ (f x14 y14) ⊗ (f x15 y15) ⊗ (f x16 y16)) =
+ ((f y1 x1) ⊗ (f y2 x2) ⊗ (f y3 x3) ⊗ (f y4 x4) ⊗
+ (f y5 x5) ⊗ (f y6 x6) ⊗ (f y7 x7) ⊗ (f y8 x8) ⊗
+ (f y9 x9) ⊗ (f y10 x10) ⊗ (f y11 x11) ⊗ (f y12 x12) ⊗
+ (f y13 x13) ⊗ (f y14 x14) ⊗ (f y15 x15) ⊗ (f y16 x16)));
+ nrewrite > (H x1 y1);
+ nrewrite > (H x2 y2);
+ nrewrite > (H x3 y3);
+ nrewrite > (H x4 y4);
+ nrewrite > (H x5 y5);
+ nrewrite > (H x6 y6);
+ nrewrite > (H x7 y7);
+ nrewrite > (H x8 y8);
+ nrewrite > (H x9 y9);
+ nrewrite > (H x10 y10);
+ nrewrite > (H x11 y11);
+ nrewrite > (H x12 y12);
+ nrewrite > (H x13 y13);
+ nrewrite > (H x14 y14);
+ nrewrite > (H x15 y15);
+ nrewrite > (H x16 y16);
+ napply refl_eq.
+nqed.
+
+nlemma eqar16_to_eq :
+∀T.∀f:T → T → bool.
+ (∀x,y.(f x y = true) → (x = y)) →
+ (∀a1,a2:Array16T T.(eq_ar16 T f a1 a2 = true) → (a1 = a2)).
+ #T; #f; #H;
+ #alu1; ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #alu2; ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H1;
+ nchange in H1:(%) with (
+ ((f x1 y1) ⊗ (f x2 y2) ⊗ (f x3 y3) ⊗ (f x4 y4) ⊗
+ (f x5 y5) ⊗ (f x6 y6) ⊗ (f x7 y7) ⊗ (f x8 y8) ⊗
+ (f x9 y9) ⊗ (f x10 y10) ⊗ (f x11 y11) ⊗ (f x12 y12) ⊗
+ (f x13 y13) ⊗ (f x14 y14) ⊗ (f x15 y15) ⊗ (f x16 y16)) = true);
+ nrewrite > (H … (andb_true_true_r … H1));
+ nletin H2 ≝ (andb_true_true_l … H1);
+ nrewrite > (H … (andb_true_true_r … H2));
+ nletin H3 ≝ (andb_true_true_l … H2);
+ nrewrite > (H … (andb_true_true_r … H3));
+ nletin H4 ≝ (andb_true_true_l … H3);
+ nrewrite > (H … (andb_true_true_r … H4));
+ nletin H5 ≝ (andb_true_true_l … H4);
+ nrewrite > (H … (andb_true_true_r … H5));
+ nletin H6 ≝ (andb_true_true_l … H5);
+ nrewrite > (H … (andb_true_true_r … H6));
+ nletin H7 ≝ (andb_true_true_l … H6);
+ nrewrite > (H … (andb_true_true_r … H7));
+ nletin H8 ≝ (andb_true_true_l … H7);
+ nrewrite > (H … (andb_true_true_r … H8));
+ nletin H9 ≝ (andb_true_true_l … H8);
+ nrewrite > (H … (andb_true_true_r … H9));
+ nletin H10 ≝ (andb_true_true_l … H9);
+ nrewrite > (H … (andb_true_true_r … H10));
+ nletin H11 ≝ (andb_true_true_l … H10);
+ nrewrite > (H … (andb_true_true_r … H11));
+ nletin H12 ≝ (andb_true_true_l … H11);
+ nrewrite > (H … (andb_true_true_r … H12));
+ nletin H13 ≝ (andb_true_true_l … H12);
+ nrewrite > (H … (andb_true_true_r … H13));
+ nletin H14 ≝ (andb_true_true_l … H13);
+ nrewrite > (H … (andb_true_true_r … H14));
+ nletin H15 ≝ (andb_true_true_l … H14);
+ nrewrite > (H … (andb_true_true_r … H15));
+ nrewrite > (H … (andb_true_true_l … H15));
+ napply refl_eq.
+nqed.
+
+nlemma eq_to_eqar16 :
+∀T.∀f:T → T → bool.
+ (∀x,y.(x = y) → (f x y = true)) →
+ (∀a1,a2:Array16T T.(a1 = a2) → (eq_ar16 T f a1 a2 = true)).
+ #T; #f; #H;
+ #alu1; ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #alu2; ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H1;
+ nrewrite > (ar16_destruct_1 … H1);
+ nrewrite > (ar16_destruct_2 … H1);
+ nrewrite > (ar16_destruct_3 … H1);
+ nrewrite > (ar16_destruct_4 … H1);
+ nrewrite > (ar16_destruct_5 … H1);
+ nrewrite > (ar16_destruct_6 … H1);
+ nrewrite > (ar16_destruct_7 … H1);
+ nrewrite > (ar16_destruct_8 … H1);
+ nrewrite > (ar16_destruct_9 … H1);
+ nrewrite > (ar16_destruct_10 … H1);
+ nrewrite > (ar16_destruct_11 … H1);
+ nrewrite > (ar16_destruct_12 … H1);
+ nrewrite > (ar16_destruct_13 … H1);
+ nrewrite > (ar16_destruct_14 … H1);
+ nrewrite > (ar16_destruct_15 … H1);
+ nrewrite > (ar16_destruct_16 … H1);
+ nchange with (
+ ((f y1 y1) ⊗ (f y2 y2) ⊗ (f y3 y3) ⊗ (f y4 y4) ⊗
+ (f y5 y5) ⊗ (f y6 y6) ⊗ (f y7 y7) ⊗ (f y8 y8) ⊗
+ (f y9 y9) ⊗ (f y10 y10) ⊗ (f y11 y11) ⊗ (f y12 y12) ⊗
+ (f y13 y13) ⊗ (f y14 y14) ⊗ (f y15 y15) ⊗ (f y16 y16)) = true);
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ napply refl_eq.
+nqed.
+
+nlemma decidable_ar16_aux1 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x1 ≠ y1) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_1 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux2 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x2 ≠ y2) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_2 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux3 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x3 ≠ y3) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_3 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux4 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x4 ≠ y4) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_4 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux5 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x5 ≠ y5) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_5 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux6 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x6 ≠ y6) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_6 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux7 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x7 ≠ y7) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_7 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux8 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x8 ≠ y8) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_8 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux9 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x9 ≠ y9) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_9 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux10 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x10 ≠ y10) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_10 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux11 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x11 ≠ y11) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_11 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux12 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x12 ≠ y12) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_12 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux13 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x13 ≠ y13) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_13 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux14 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x14 ≠ y14) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_14 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux15 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x15 ≠ y15) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_15 … H1)).
+nqed.
+
+nlemma decidable_ar16_aux16 :
+∀T.
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16:T.
+∀y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16:T.
+ (x16 ≠ y16) →
+ (mk_Array16T T x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_Array16T T y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (ar16_destruct_16 … H1)).
+nqed.
+
+nlemma decidable_ar16 :
+∀T.(∀x,y:T.decidable (x = y)) →
+ (∀a1,a2:Array16T T.decidable (a1 = a2)).
+ #T; #H;
+ #x; nelim x; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y; nelim y; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize;
+ napply (or2_elim (? = ?) (? ≠ ?) ? (H x1 y1) …);
+ ##[ ##2: #H1; napply (or2_intro2 … (decidable_ar16_aux1 T … H1))
+ ##| ##1: #H1; napply (or2_elim (? = ?) (? ≠ ?) ? (H x2 y2) …);
+ ##[ ##2: #H2; napply (or2_intro2 … (decidable_ar16_aux2 T … H2))
+ ##| ##1: #H2; napply (or2_elim (? = ?) (? ≠ ?) ? (H x3 y3) …);
+ ##[ ##2: #H3; napply (or2_intro2 … (decidable_ar16_aux3 T … H3))
+ ##| ##1: #H3; napply (or2_elim (? = ?) (? ≠ ?) ? (H x4 y4) …);
+ ##[ ##2: #H4; napply (or2_intro2 … (decidable_ar16_aux4 T … H4))
+ ##| ##1: #H4; napply (or2_elim (? = ?) (? ≠ ?) ? (H x5 y5) …);
+ ##[ ##2: #H5; napply (or2_intro2 … (decidable_ar16_aux5 T … H5))
+ ##| ##1: #H5; napply (or2_elim (? = ?) (? ≠ ?) ? (H x6 y6) …);
+ ##[ ##2: #H6; napply (or2_intro2 … (decidable_ar16_aux6 T … H6))
+ ##| ##1: #H6; napply (or2_elim (? = ?) (? ≠ ?) ? (H x7 y7) …);
+ ##[ ##2: #H7; napply (or2_intro2 … (decidable_ar16_aux7 T … H7))
+ ##| ##1: #H7; napply (or2_elim (? = ?) (? ≠ ?) ? (H x8 y8) …);
+ ##[ ##2: #H8; napply (or2_intro2 … (decidable_ar16_aux8 T … H8))
+ ##| ##1: #H8; napply (or2_elim (? = ?) (? ≠ ?) ? (H x9 y9) …);
+ ##[ ##2: #H9; napply (or2_intro2 … (decidable_ar16_aux9 T … H9))
+ ##| ##1: #H9; napply (or2_elim (? = ?) (? ≠ ?) ? (H x10 y10) …);
+ ##[ ##2: #H10; napply (or2_intro2 … (decidable_ar16_aux10 T … H10))
+ ##| ##1: #H10; napply (or2_elim (? = ?) (? ≠ ?) ? (H x11 y11) …);
+ ##[ ##2: #H11; napply (or2_intro2 … (decidable_ar16_aux11 T … H11))
+ ##| ##1: #H11; napply (or2_elim (? = ?) (? ≠ ?) ? (H x12 y12) …);
+ ##[ ##2: #H12; napply (or2_intro2 … (decidable_ar16_aux12 T … H12))
+ ##| ##1: #H12; napply (or2_elim (? = ?) (? ≠ ?) ? (H x13 y13) …);
+ ##[ ##2: #H13; napply (or2_intro2 … (decidable_ar16_aux13 T … H13))
+ ##| ##1: #H13; napply (or2_elim (? = ?) (? ≠ ?) ? (H x14 y14) …);
+ ##[ ##2: #H14; napply (or2_intro2 … (decidable_ar16_aux14 T … H14))
+ ##| ##1: #H14; napply (or2_elim (? = ?) (? ≠ ?) ? (H x15 y15) …);
+ ##[ ##2: #H15; napply (or2_intro2 … (decidable_ar16_aux15 T … H15))
+ ##| ##1: #H15; napply (or2_elim (? = ?) (? ≠ ?) ? (H x16 y16) …);
+ ##[ ##2: #H16; napply (or2_intro2 … (decidable_ar16_aux16 T … H16))
+ ##| ##1: #H16; nrewrite > H1; nrewrite > H2; nrewrite > H3; nrewrite > H4;
+ nrewrite > H5; nrewrite > H6; nrewrite > H7; nrewrite > H8;
+ nrewrite > H9; nrewrite > H10; nrewrite > H11; nrewrite > H12;
+ nrewrite > H13; nrewrite > H14; nrewrite > H15; nrewrite > H16;
+ napply (or2_intro1 (? = ?) (? ≠ ?) (refl_eq …))
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+nqed.
+
+(* !!! per brevita *)
+naxiom neqar16_to_neq :
+∀T.∀f:T → T → bool.
+ (∀x,y:T.f x y = false → x ≠ y) →
+ (∀p1,p2:Array16T T.(eq_ar16 T f p1 p2 = false → p1 ≠ p2)).
+
+(* !!! per brevita *)
+naxiom neq_to_neqar16 :
+∀T.∀f:T → T → bool.
+ (∀x,y:T.decidable (x = y)) →
+ (∀x,y:T.x ≠ y → f x y = false) →
+ (∀p1,p2:Array16T T.(p1 ≠ p2 → eq_ar16 T f p1 p2 = false)).
+
+nlemma ar16_is_comparable : comparable → comparable.
+ #T; @ (Array16T T)
+ ##[ napply (mk_Array16T ? (zeroc T) (zeroc T) (zeroc T) (zeroc T)
+ (zeroc T) (zeroc T) (zeroc T) (zeroc T)
+ (zeroc T) (zeroc T) (zeroc T) (zeroc T)
+ (zeroc T) (zeroc T) (zeroc T) (zeroc T))
+ ##| napply (λP.(forallc T)
+ (λe1.(forallc T)
+ (λe2.(forallc T)
+ (λe3.(forallc T)
+ (λe4.(forallc T)
+ (λe5.(forallc T)
+ (λe6.(forallc T)
+ (λe7.(forallc T)
+ (λe8.(forallc T)
+ (λe9.(forallc T)
+ (λe10.(forallc T)
+ (λe11.(forallc T)
+ (λe12.(forallc T)
+ (λe13.(forallc T)
+ (λe14.(forallc T)
+ (λe15.(forallc T)
+ (λe16.P (mk_Array16T T e1 e2 e3 e4 e5 e6 e7 e8 e9 e10 e11 e12 e13 e14 e15 e16))))))))))))))))))
+ ##| napply (eq_ar16 … (eqc T))
+ ##| napply eqar16_to_eq;
+ napply (eqc_to_eq T)
+ ##| napply eq_to_eqar16;
+ napply (eq_to_eqc T)
+ ##| napply neqar16_to_neq;
+ napply (neqc_to_neq T)
+ ##| napply neq_to_neqar16;
+ ##[ napply (decidable_c T)
+ ##| napply (neq_to_neqc T) ##]
+ ##| napply decidable_ar16;
+ napply (decidable_c T)
+ ##| napply symmetric_eqar16;
+ napply (symmetric_eqc T)
+ ##]
+nqed.
+
+unification hint 0 ≔ S: comparable ;
+ T ≟ (carr S),
+ X ≟ (ar16_is_comparable S)
+ (*********************************************) ⊢
+ carr X ≡ Array16T T.
+
+(* *************** *)
+(* TIPO ARRAY DA 8 *)
+(* *************** *)
+
+nlemma ar8_destruct_1 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8:T.∀y1,y2,y3,y4,y5,y6,y7,y8:T.
+ mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8 = mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8 →
+ x1 = y1.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_Array8T a _ _ _ _ _ _ _ ⇒ x1 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar8_destruct_2 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8:T.∀y1,y2,y3,y4,y5,y6,y7,y8:T.
+ mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8 = mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8 →
+ x2 = y2.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_Array8T _ a _ _ _ _ _ _ ⇒ x2 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar8_destruct_3 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8:T.∀y1,y2,y3,y4,y5,y6,y7,y8:T.
+ mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8 = mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8 →
+ x3 = y3.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_Array8T _ _ a _ _ _ _ _ ⇒ x3 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar8_destruct_4 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8:T.∀y1,y2,y3,y4,y5,y6,y7,y8:T.
+ mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8 = mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8 →
+ x4 = y4.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_Array8T _ _ _ a _ _ _ _ ⇒ x4 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar8_destruct_5 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8:T.∀y1,y2,y3,y4,y5,y6,y7,y8:T.
+ mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8 = mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8 →
+ x5 = y5.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_Array8T _ _ _ _ a _ _ _ ⇒ x5 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar8_destruct_6 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8:T.∀y1,y2,y3,y4,y5,y6,y7,y8:T.
+ mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8 = mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8 →
+ x6 = y6.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_Array8T _ _ _ _ _ a _ _ ⇒ x6 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar8_destruct_7 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8:T.∀y1,y2,y3,y4,y5,y6,y7,y8:T.
+ mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8 = mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8 →
+ x7 = y7.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_Array8T _ _ _ _ _ _ a _ ⇒ x7 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma ar8_destruct_8 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8:T.∀y1,y2,y3,y4,y5,y6,y7,y8:T.
+ mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8 = mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8 →
+ x8 = y8.
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_Array8T _ _ _ _ _ _ _ a ⇒ x8 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma symmetric_eqar8 :
+∀T.∀f:T → T → bool.
+ (symmetricT T bool f) →
+ (symmetricT (Array8T T) bool (eq_ar8 T f)).
+ #T; #f; #H;
+ #alu1; ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #alu2; ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nchange with (
+ ((f x1 y1) ⊗ (f x2 y2) ⊗ (f x3 y3) ⊗ (f x4 y4) ⊗
+ (f x5 y5) ⊗ (f x6 y6) ⊗ (f x7 y7) ⊗ (f x8 y8)) =
+ ((f y1 x1) ⊗ (f y2 x2) ⊗ (f y3 x3) ⊗ (f y4 x4) ⊗
+ (f y5 x5) ⊗ (f y6 x6) ⊗ (f y7 x7) ⊗ (f y8 x8)));
+ nrewrite > (H x1 y1);
+ nrewrite > (H x2 y2);
+ nrewrite > (H x3 y3);
+ nrewrite > (H x4 y4);
+ nrewrite > (H x5 y5);
+ nrewrite > (H x6 y6);
+ nrewrite > (H x7 y7);
+ nrewrite > (H x8 y8);
+ napply refl_eq.
+nqed.
+
+nlemma eqar8_to_eq :
+∀T.∀f:T → T → bool.
+ (∀x,y.(f x y = true) → (x = y)) →
+ (∀a1,a2:Array8T T.(eq_ar8 T f a1 a2 = true) → (a1 = a2)).
+ #T; #f; #H;
+ #alu1; ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #alu2; ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H1;
+ nchange in H1:(%) with (
+ ((f x1 y1) ⊗ (f x2 y2) ⊗ (f x3 y3) ⊗ (f x4 y4) ⊗
+ (f x5 y5) ⊗ (f x6 y6) ⊗ (f x7 y7) ⊗ (f x8 y8)) = true);
+ nrewrite > (H … (andb_true_true_r … H1));
+ nletin H2 ≝ (andb_true_true_l … H1);
+ nrewrite > (H … (andb_true_true_r … H2));
+ nletin H3 ≝ (andb_true_true_l … H2);
+ nrewrite > (H … (andb_true_true_r … H3));
+ nletin H4 ≝ (andb_true_true_l … H3);
+ nrewrite > (H … (andb_true_true_r … H4));
+ nletin H5 ≝ (andb_true_true_l … H4);
+ nrewrite > (H … (andb_true_true_r … H5));
+ nletin H6 ≝ (andb_true_true_l … H5);
+ nrewrite > (H … (andb_true_true_r … H6));
+ nletin H7 ≝ (andb_true_true_l … H6);
+ nrewrite > (H … (andb_true_true_r … H7));
+ nrewrite > (H … (andb_true_true_l … H7));
+ napply refl_eq.
+nqed.
+
+nlemma eq_to_eqar8 :
+∀T.∀f:T → T → bool.
+ (∀x,y.(x = y) → (f x y = true)) →
+ (∀a1,a2:Array8T T.(a1 = a2) → (eq_ar8 T f a1 a2 = true)).
+ #T; #f; #H;
+ #alu1; ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #alu2; ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H1;
+ nrewrite > (ar8_destruct_1 … H1);
+ nrewrite > (ar8_destruct_2 … H1);
+ nrewrite > (ar8_destruct_3 … H1);
+ nrewrite > (ar8_destruct_4 … H1);
+ nrewrite > (ar8_destruct_5 … H1);
+ nrewrite > (ar8_destruct_6 … H1);
+ nrewrite > (ar8_destruct_7 … H1);
+ nrewrite > (ar8_destruct_8 … H1);
+ nchange with (
+ ((f y1 y1) ⊗ (f y2 y2) ⊗ (f y3 y3) ⊗ (f y4 y4) ⊗
+ (f y5 y5) ⊗ (f y6 y6) ⊗ (f y7 y7) ⊗ (f y8 y8)) = true);
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ nrewrite > (H … (refl_eq …));
+ napply refl_eq.
+nqed.
+
+nlemma decidable_ar8_aux1 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8:T.
+ (x1 ≠ y1) →
+ (mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8) ≠ (mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (ar8_destruct_1 … H1)).
+nqed.
+
+nlemma decidable_ar8_aux2 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8:T.
+ (x2 ≠ y2) →
+ (mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8) ≠ (mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (ar8_destruct_2 … H1)).
+nqed.
+
+nlemma decidable_ar8_aux3 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8:T.
+ (x3 ≠ y3) →
+ (mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8) ≠ (mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (ar8_destruct_3 … H1)).
+nqed.
+
+nlemma decidable_ar8_aux4 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8:T.
+ (x4 ≠ y4) →
+ (mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8) ≠ (mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (ar8_destruct_4 … H1)).
+nqed.
+
+nlemma decidable_ar8_aux5 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8:T.
+ (x5 ≠ y5) →
+ (mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8) ≠ (mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (ar8_destruct_5 … H1)).
+nqed.
+
+nlemma decidable_ar8_aux6 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8:T.
+ (x6 ≠ y6) →
+ (mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8) ≠ (mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (ar8_destruct_6 … H1)).
+nqed.
+
+nlemma decidable_ar8_aux7 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8:T.
+ (x7 ≠ y7) →
+ (mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8) ≠ (mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (ar8_destruct_7 … H1)).
+nqed.
+
+nlemma decidable_ar8_aux8 :
+∀T.∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8:T.
+ (x8 ≠ y8) →
+ (mk_Array8T T x1 x2 x3 x4 x5 x6 x7 x8) ≠ (mk_Array8T T y1 y2 y3 y4 y5 y6 y7 y8).
+ #T; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (ar8_destruct_8 … H1)).
+nqed.
+
+nlemma decidable_ar8 :
+∀T.(∀x,y:T.decidable (x = y)) →
+ (∀a1,a2:Array8T T.decidable (a1 = a2)).
+ #T; #H;
+ #x; nelim x; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y; nelim y; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize;
+ napply (or2_elim (? = ?) (? ≠ ?) ? (H x1 y1) …);
+ ##[ ##2: #H1; napply (or2_intro2 … (decidable_ar8_aux1 T … H1))
+ ##| ##1: #H1; napply (or2_elim (? = ?) (? ≠ ?) ? (H x2 y2) …);
+ ##[ ##2: #H2; napply (or2_intro2 … (decidable_ar8_aux2 T … H2))
+ ##| ##1: #H2; napply (or2_elim (? = ?) (? ≠ ?) ? (H x3 y3) …);
+ ##[ ##2: #H3; napply (or2_intro2 … (decidable_ar8_aux3 T … H3))
+ ##| ##1: #H3; napply (or2_elim (? = ?) (? ≠ ?) ? (H x4 y4) …);
+ ##[ ##2: #H4; napply (or2_intro2 … (decidable_ar8_aux4 T … H4))
+ ##| ##1: #H4; napply (or2_elim (? = ?) (? ≠ ?) ? (H x5 y5) …);
+ ##[ ##2: #H5; napply (or2_intro2 … (decidable_ar8_aux5 T … H5))
+ ##| ##1: #H5; napply (or2_elim (? = ?) (? ≠ ?) ? (H x6 y6) …);
+ ##[ ##2: #H6; napply (or2_intro2 … (decidable_ar8_aux6 T … H6))
+ ##| ##1: #H6; napply (or2_elim (? = ?) (? ≠ ?) ? (H x7 y7) …);
+ ##[ ##2: #H7; napply (or2_intro2 … (decidable_ar8_aux7 T … H7))
+ ##| ##1: #H7; napply (or2_elim (? = ?) (? ≠ ?) ? (H x8 y8) …);
+ ##[ ##2: #H8; napply (or2_intro2 … (decidable_ar8_aux8 T … H8))
+ ##| ##1: #H8; nrewrite > H1; nrewrite > H2; nrewrite > H3; nrewrite > H4;
+ nrewrite > H5; nrewrite > H6; nrewrite > H7; nrewrite > H8;
+ napply (or2_intro1 (? = ?) (? ≠ ?) (refl_eq …))
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+nqed.
+
+(* !!! per brevita *)
+naxiom neqar8_to_neq :
+∀T.∀f:T → T → bool.
+ (∀x,y:T.f x y = false → x ≠ y) →
+ (∀p1,p2:Array8T T.(eq_ar8 T f p1 p2 = false → p1 ≠ p2)).
+
+(* !!! per brevita *)
+naxiom neq_to_neqar8 :
+∀T.∀f:T → T → bool.
+ (∀x,y:T.decidable (x = y)) →
+ (∀x,y:T.x ≠ y → f x y = false) →
+ (∀p1,p2:Array8T T.(p1 ≠ p2 → eq_ar8 T f p1 p2 = false)).
+
+nlemma ar8_is_comparable : comparable → comparable.
+ #T; @ (Array8T T)
+ ##[ napply (mk_Array8T ? (zeroc T) (zeroc T) (zeroc T) (zeroc T)
+ (zeroc T) (zeroc T) (zeroc T) (zeroc T))
+ ##| napply (λP.(forallc T)
+ (λe1.(forallc T)
+ (λe2.(forallc T)
+ (λe3.(forallc T)
+ (λe4.(forallc T)
+ (λe5.(forallc T)
+ (λe6.(forallc T)
+ (λe7.(forallc T)
+ (λe8.P (mk_Array8T T e1 e2 e3 e4 e5 e6 e7 e8))))))))))
+ ##| napply (eq_ar8 … (eqc T))
+ ##| napply eqar8_to_eq;
+ napply (eqc_to_eq T)
+ ##| napply eq_to_eqar8;
+ napply (eq_to_eqc T)
+ ##| napply neqar8_to_neq;
+ napply (neqc_to_neq T)
+ ##| napply neq_to_neqar8;
+ ##[ napply (decidable_c T)
+ ##| napply (neq_to_neqc T) ##]
+ ##| napply decidable_ar8;
+ napply (decidable_c T)
+ ##| napply symmetric_eqar8;
+ napply (symmetric_eqc T)
+ ##]
+nqed.
+
+unification hint 0 ≔ S: comparable ;
+ T ≟ (carr S),
+ X ≟ (ar8_is_comparable S)
+ (*********************************************) ⊢
+ carr X ≡ Array8T T.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "num/byte8.ma".
+
+(* **************** *)
+(* TIPO ARRAY DA 16 *)
+(* **************** *)
+
+(* definizione di un array omogeneo di dimensione 16 *)
+nrecord Array16T (T:Type) : Type ≝
+{ a16_1 : T ; a16_2 : T ; a16_3 : T ; a16_4 : T
+; a16_5 : T ; a16_6 : T ; a16_7 : T ; a16_8 : T
+; a16_9 : T ; a16_10 : T ; a16_11 : T ; a16_12 : T
+; a16_13 : T ; a16_14 : T ; a16_15 : T ; a16_16 : T }.
+
+(* operatore uguaglianza *)
+ndefinition eq_ar16 ≝
+λT.λf:T → T → bool.λa1,a2:Array16T T.
+ (f (a16_1 ? a1) (a16_1 ? a2)) ⊗ (f (a16_2 ? a1) (a16_2 ? a2)) ⊗
+ (f (a16_3 ? a1) (a16_3 ? a2)) ⊗ (f (a16_4 ? a1) (a16_4 ? a2)) ⊗
+ (f (a16_5 ? a1) (a16_5 ? a2)) ⊗ (f (a16_6 ? a1) (a16_6 ? a2)) ⊗
+ (f (a16_7 ? a1) (a16_7 ? a2)) ⊗ (f (a16_8 ? a1) (a16_8 ? a2)) ⊗
+ (f (a16_9 ? a1) (a16_9 ? a2)) ⊗ (f (a16_10 ? a1) (a16_10 ? a2)) ⊗
+ (f (a16_11 ? a1) (a16_11 ? a2)) ⊗ (f (a16_12 ? a1) (a16_12 ? a2)) ⊗
+ (f (a16_13 ? a1) (a16_13 ? a2)) ⊗ (f (a16_14 ? a1) (a16_14 ? a2)) ⊗
+ (f (a16_15 ? a1) (a16_15 ? a2)) ⊗ (f (a16_16 ? a1) (a16_16 ? a2)).
+
+(* abbiamo gia' gli esadecimali come tipo induttivo quindi: *)
+(* posso definire un getter a matrice sull'array *)
+
+ndefinition getn_array16T ≝
+λn:exadecim.λT:Type.λp:Array16T T.
+ match n return λn.(Array16T T) → T with
+ [ x0 ⇒ a16_1 T | x1 ⇒ a16_2 T | x2 ⇒ a16_3 T | x3 ⇒ a16_4 T
+ | x4 ⇒ a16_5 T | x5 ⇒ a16_6 T | x6 ⇒ a16_7 T | x7 ⇒ a16_8 T
+ | x8 ⇒ a16_9 T | x9 ⇒ a16_10 T | xA ⇒ a16_11 T | xB ⇒ a16_12 T
+ | xC ⇒ a16_13 T | xD ⇒ a16_14 T | xE ⇒ a16_15 T | xF ⇒ a16_16 T
+ ] p.
+
+(* abbiamo gia' gli esadecimali come tipo induttivo quindi: *)
+(* posso definire un setter a matrice sull'array *)
+ndefinition setn_array16T ≝
+λn:exadecim.λT:Type.λp:Array16T T.λv:T.
+let e00 ≝ (a16_1 T p) in
+let e01 ≝ (a16_2 T p) in
+let e02 ≝ (a16_3 T p) in
+let e03 ≝ (a16_4 T p) in
+let e04 ≝ (a16_5 T p) in
+let e05 ≝ (a16_6 T p) in
+let e06 ≝ (a16_7 T p) in
+let e07 ≝ (a16_8 T p) in
+let e08 ≝ (a16_9 T p) in
+let e09 ≝ (a16_10 T p) in
+let e10 ≝ (a16_11 T p) in
+let e11 ≝ (a16_12 T p) in
+let e12 ≝ (a16_13 T p) in
+let e13 ≝ (a16_14 T p) in
+let e14 ≝ (a16_15 T p) in
+let e15 ≝ (a16_16 T p) in
+ match n with
+ [ x0 ⇒ mk_Array16T T v e01 e02 e03 e04 e05 e06 e07 e08 e09 e10 e11 e12 e13 e14 e15
+ | x1 ⇒ mk_Array16T T e00 v e02 e03 e04 e05 e06 e07 e08 e09 e10 e11 e12 e13 e14 e15
+ | x2 ⇒ mk_Array16T T e00 e01 v e03 e04 e05 e06 e07 e08 e09 e10 e11 e12 e13 e14 e15
+ | x3 ⇒ mk_Array16T T e00 e01 e02 v e04 e05 e06 e07 e08 e09 e10 e11 e12 e13 e14 e15
+ | x4 ⇒ mk_Array16T T e00 e01 e02 e03 v e05 e06 e07 e08 e09 e10 e11 e12 e13 e14 e15
+ | x5 ⇒ mk_Array16T T e00 e01 e02 e03 e04 v e06 e07 e08 e09 e10 e11 e12 e13 e14 e15
+ | x6 ⇒ mk_Array16T T e00 e01 e02 e03 e04 e05 v e07 e08 e09 e10 e11 e12 e13 e14 e15
+ | x7 ⇒ mk_Array16T T e00 e01 e02 e03 e04 e05 e06 v e08 e09 e10 e11 e12 e13 e14 e15
+ | x8 ⇒ mk_Array16T T e00 e01 e02 e03 e04 e05 e06 e07 v e09 e10 e11 e12 e13 e14 e15
+ | x9 ⇒ mk_Array16T T e00 e01 e02 e03 e04 e05 e06 e07 e08 v e10 e11 e12 e13 e14 e15
+ | xA ⇒ mk_Array16T T e00 e01 e02 e03 e04 e05 e06 e07 e08 e09 v e11 e12 e13 e14 e15
+ | xB ⇒ mk_Array16T T e00 e01 e02 e03 e04 e05 e06 e07 e08 e09 e10 v e12 e13 e14 e15
+ | xC ⇒ mk_Array16T T e00 e01 e02 e03 e04 e05 e06 e07 e08 e09 e10 e11 v e13 e14 e15
+ | xD ⇒ mk_Array16T T e00 e01 e02 e03 e04 e05 e06 e07 e08 e09 e10 e11 e12 v e14 e15
+ | xE ⇒ mk_Array16T T e00 e01 e02 e03 e04 e05 e06 e07 e08 e09 e10 e11 e12 e13 v e15
+ | xF ⇒ mk_Array16T T e00 e01 e02 e03 e04 e05 e06 e07 e08 e09 e10 e11 e12 e13 e14 v
+ ].
+
+(* ************************** *)
+(* TIPO BYTE COME INSIEME BIT *)
+(* ************************** *)
+
+(* definizione di un byte come 8 bit *)
+nrecord Array8T (T:Type) : Type ≝
+{ a8_1 : T ; a8_2 : T ; a8_3 : T ; a8_4 : T
+; a8_5 : T ; a8_6 : T ; a8_7 : T ; a8_8 : T }.
+
+(* operatore uguaglianza *)
+ndefinition eq_ar8 ≝
+λT.λf:T → T → bool.λa1,a2:Array8T T.
+ (f (a8_1 ? a1) (a8_1 ? a2)) ⊗ (f (a8_2 ? a1) (a8_2 ? a2)) ⊗
+ (f (a8_3 ? a1) (a8_3 ? a2)) ⊗ (f (a8_4 ? a1) (a8_4 ? a2)) ⊗
+ (f (a8_5 ? a1) (a8_5 ? a2)) ⊗ (f (a8_6 ? a1) (a8_6 ? a2)) ⊗
+ (f (a8_7 ? a1) (a8_7 ? a2)) ⊗ (f (a8_8 ? a1) (a8_8 ? a2)).
+
+(* abbiamo gia' gli ottali come tipo induttivo quindi: *)
+(* posso definire un getter a matrice sull'array *)
+ndefinition getn_array8T ≝
+λn:oct.λT:Type.λp:Array8T T.
+ match n return λn.(Array8T T) → T with
+ [ o0 ⇒ a8_1 T | o1 ⇒ a8_2 T | o2 ⇒ a8_3 T | o3 ⇒ a8_4 T
+ | o4 ⇒ a8_5 T | o5 ⇒ a8_6 T | o6 ⇒ a8_7 T | o7 ⇒ a8_8 T
+ ] p.
+
+(* abbiamo gia' gli ottali come tipo induttivo quindi: *)
+(* posso definire un setter a matrice sull'array *)
+ndefinition setn_array8T ≝
+λn:oct.λT:Type.λp:Array8T T.λv:T.
+let e00 ≝ (a8_1 T p) in
+let e01 ≝ (a8_2 T p) in
+let e02 ≝ (a8_3 T p) in
+let e03 ≝ (a8_4 T p) in
+let e04 ≝ (a8_5 T p) in
+let e05 ≝ (a8_6 T p) in
+let e06 ≝ (a8_7 T p) in
+let e07 ≝ (a8_8 T p) in
+ match n with
+ [ o0 ⇒ mk_Array8T T v e01 e02 e03 e04 e05 e06 e07
+ | o1 ⇒ mk_Array8T T e00 v e02 e03 e04 e05 e06 e07
+ | o2 ⇒ mk_Array8T T e00 e01 v e03 e04 e05 e06 e07
+ | o3 ⇒ mk_Array8T T e00 e01 e02 v e04 e05 e06 e07
+ | o4 ⇒ mk_Array8T T e00 e01 e02 e03 v e05 e06 e07
+ | o5 ⇒ mk_Array8T T e00 e01 e02 e03 e04 v e06 e07
+ | o6 ⇒ mk_Array8T T e00 e01 e02 e03 e04 e05 v e07
+ | o7 ⇒ mk_Array8T T e00 e01 e02 e03 e04 e05 e06 v
+ ].
+
+(* lettura byte *)
+ndefinition byte8_of_bits ≝
+λp:Array8T bool.
+ mk_byte8
+ (orc ? (match a8_1 ? p with [ true ⇒ x8 | false ⇒ x0 ])
+ (orc ? (match a8_2 ? p with [ true ⇒ x4 | false ⇒ x0 ])
+ (orc ? (match a8_3 ? p with [ true ⇒ x2 | false ⇒ x0 ])
+ (match a8_4 ? p with [ true ⇒ x1 | false ⇒ x0 ]))))
+ (orc ? (match a8_5 ? p with [ true ⇒ x8 | false ⇒ x0 ])
+ (orc ? (match a8_6 ? p with [ true ⇒ x4 | false ⇒ x0 ])
+ (orc ? (match a8_7 ? p with [ true ⇒ x2 | false ⇒ x0 ])
+ (match a8_8 ? p with [ true ⇒ x1 | false ⇒ x0 ])))).
+
+(* scrittura byte *)
+ndefinition bits_of_exadecim ≝
+λe:exadecim.match e with
+ [ x0 ⇒ quadruple … false false false false
+ | x1 ⇒ quadruple … false false false true
+ | x2 ⇒ quadruple … false false true false
+ | x3 ⇒ quadruple … false false true true
+ | x4 ⇒ quadruple … false true false false
+ | x5 ⇒ quadruple … false true false true
+ | x6 ⇒ quadruple … false true true false
+ | x7 ⇒ quadruple … false true true true
+ | x8 ⇒ quadruple … true false false false
+ | x9 ⇒ quadruple … true false false true
+ | xA ⇒ quadruple … true false true false
+ | xB ⇒ quadruple … true false true true
+ | xC ⇒ quadruple … true true false false
+ | xD ⇒ quadruple … true true false true
+ | xE ⇒ quadruple … true true true false
+ | xF ⇒ quadruple … true true true true
+ ].
+
+ndefinition bits_of_byte8 ≝
+λb:byte8.
+ mk_Array8T ? (fst4T … (bits_of_exadecim (cnH ? b)))
+ (snd4T … (bits_of_exadecim (cnH ? b)))
+ (thd4T … (bits_of_exadecim (cnH ? b)))
+ (fth4T … (bits_of_exadecim (cnH ? b)))
+ (fst4T … (bits_of_exadecim (cnL ? b)))
+ (snd4T … (bits_of_exadecim (cnL ? b)))
+ (thd4T … (bits_of_exadecim (cnL ? b)))
+ (fth4T … (bits_of_exadecim (cnL ? b))).
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/memory/memory_base.ma".
+include "emulator/memory/memory_struct.ma".
+include "num/word32.ma".
+include "common/list.ma".
+
+(* ************************** *)
+(* 8 segmenti da 64Kb → 512Kb *)
+(* 4 + 16 bit indirizzo *)
+(* ************************** *)
+
+(* ********************* *)
+(* MEMORIA E DESCRITTORE *)
+(* ********************* *)
+
+ndefinition aux_20B_filler ≝
+λT:Type.λel:T.
+let lev4 ≝ mk_Array16T T el el el el el el el el el el el el el el el el in
+let lev3 ≝ mk_Array16T ?
+ lev4 lev4 lev4 lev4 lev4 lev4 lev4 lev4
+ lev4 lev4 lev4 lev4 lev4 lev4 lev4 lev4 in
+let lev2 ≝ mk_Array16T ?
+ lev3 lev3 lev3 lev3 lev3 lev3 lev3 lev3
+ lev3 lev3 lev3 lev3 lev3 lev3 lev3 lev3 in
+let lev1 ≝ mk_Array16T ?
+ lev2 lev2 lev2 lev2 lev2 lev2 lev2 lev2
+ lev2 lev2 lev2 lev2 lev2 lev2 lev2 lev2 in
+let lev0 ≝ mk_Array8T ?
+ lev1 lev1 lev1 lev1 lev1 lev1 lev1 lev1
+ in
+lev0.
+
+ndefinition aux_20B_type ≝
+λT:Type.Array8T (Array16T (Array16T (Array16T (Array16T T)))).
+
+(* tutta la memoria non installata *)
+ndefinition mt_out_of_bound_memory ≝ aux_20B_filler ? MEM_OUT_OF_BOUND.
+
+(* tutta la memoria a 0 *)
+ndefinition mt_zero_memory ≝ aux_20B_filler ? 〈x0,x0〉.
+
+(* visita di un albero da 512Kb di elementi: ln16(512Kb)=5 passaggi *)
+ndefinition mt_visit ≝
+λT:Type.λdata:aux_20B_type T.λsel:oct.λaddr:word16.
+ getn_array16T (cnL ? (cnL ? addr)) ?
+ (getn_array16T (cnH ? (cnL ? addr)) ?
+ (getn_array16T (cnL ? (cnH ? addr)) ?
+ (getn_array16T (cnH ? (cnH ? addr)) ?
+ (getn_array8T sel ? data)))).
+
+(* scrittura di un elemento in un albero da 512Kb *)
+ndefinition mt_update ≝
+λT:Type.λdata:aux_20B_type T.λsel:oct.λaddr:word16.λv:T.
+ let lev1 ≝ getn_array8T sel ? data in
+ let lev2 ≝ getn_array16T (cnH ? (cnH ? addr)) ? lev1 in
+ let lev3 ≝ getn_array16T (cnL ? (cnH ? addr)) ? lev2 in
+ let lev4 ≝ getn_array16T (cnH ? (cnL ? addr)) ? lev3 in
+ setn_array8T sel ? data
+ (setn_array16T (cnH ? (cnH ? addr)) ? lev1
+ (setn_array16T (cnL ? (cnH ? addr)) ? lev2
+ (setn_array16T (cnH ? (cnL ? addr)) ? lev3
+ (setn_array16T (cnL ? (cnL ? addr)) T lev4 v)))).
+
+(* scrittura di un segmento (max 64Kb) degli otto disponibili *)
+nlet rec mt_update_ranged (T:Type) (data:aux_20B_type T) (sel:oct) (addr:word16) (w:word16) (rw:rec_word16 w) (v:T) on rw ≝
+ match rw with
+ [ w16_O ⇒ data
+ | w16_S w' rw' ⇒ mt_update_ranged T (mt_update T data sel addr v)
+ sel (succc ? addr) w' rw' v
+ ].
+
+(* scrivi controllando il tipo di memoria *)
+ndefinition mt_mem_update ≝
+λmem:aux_20B_type byte8.
+λchk:aux_20B_type memory_type.
+λsel:oct.λaddr:word16.λv:byte8.
+ match mt_visit ? chk sel addr with
+ (* ROM? ok, ma il valore viene perso *)
+ [ MEM_READ_ONLY ⇒ Some ? mem
+ (* RAM? ok *)
+ | MEM_READ_WRITE ⇒ Some ? (mt_update ? mem sel addr v)
+ (* NON INSTALLATA? no *)
+ | MEM_OUT_OF_BOUND ⇒ None ? ].
+
+(* leggi controllando il tipo di memoria *)
+ndefinition mt_mem_read ≝
+λmem:aux_20B_type byte8.
+λchk:aux_20B_type memory_type.
+λsel:oct.λaddr:word16.
+ match mt_visit ? chk sel addr with
+ [ MEM_READ_ONLY ⇒ Some ? (mt_visit ? mem sel addr)
+ | MEM_READ_WRITE ⇒ Some ? (mt_visit ? mem sel addr)
+ | MEM_OUT_OF_BOUND ⇒ None ? ].
+
+(* ************************** *)
+(* CARICAMENTO PROGRAMMA/DATI *)
+(* ************************** *)
+
+(* carica a paratire da addr, overflow se si supera 0xFFFF... *)
+nlet rec mt_load_from_source_at (old_mem:aux_20B_type byte8)
+ (src:list byte8) (sel:oct) (addr:word16) on src ≝
+ match src with
+ (* fine di source: carica da old_mem *)
+ [ nil ⇒ old_mem
+ | cons hd tl ⇒ mt_load_from_source_at (mt_update ? old_mem sel addr hd)
+ tl sel (succc ? addr)
+ ].
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/opcodes/pseudo.ma".
+include "emulator/opcodes/HC05_table.ma".
+
+(* ***************** *)
+(* TABELLA DELL'HC05 *)
+(* ***************** *)
+
+(* HC05: opcode non implementati come da manuale *)
+ndefinition HC05_not_impl_byte ≝
+ [〈x3,x1〉;〈x3,x2〉;〈x3,x5〉;〈x3,xB〉;〈x3,xE〉
+ ;〈x4,x1〉;〈x4,x5〉;〈x4,xB〉;〈x4,xE〉
+ ;〈x5,x1〉;〈x5,x2〉;〈x5,x5〉;〈x5,xB〉;〈x5,xE〉
+ ;〈x6,x1〉;〈x6,x2〉;〈x6,x5〉;〈x6,xB〉;〈x6,xE〉
+ ;〈x7,x1〉;〈x7,x2〉;〈x7,x5〉;〈x7,xB〉;〈x7,xE〉
+ ;〈x8,x2〉;〈x8,x4〉;〈x8,x5〉;〈x8,x6〉;〈x8,x7〉;〈x8,x8〉;〈x8,x9〉;〈x8,xA〉;〈x8,xB〉;〈x8,xC〉;〈x8,xD〉
+ ;〈x9,x0〉;〈x9,x1〉;〈x9,x2〉;〈x9,x3〉;〈x9,x4〉;〈x9,x5〉;〈x9,x6〉;〈x9,xE〉
+ ;〈xA,x7〉;〈xA,xC〉;〈xA,xF〉
+ ].
+
+nlemma ok_byte_table_HC05 : forallc ? (λb.
+ (test_not_impl_byte b HC05_not_impl_byte ⊙ eqc ? (get_byte_count HC05 b 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC05) 〈〈x0,x0〉:〈x0,x1〉〉) ⊗
+ (⊖ (test_not_impl_byte b HC05_not_impl_byte) ⊙ eqc ? (get_byte_count HC05 b 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC05) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+(* HC05: pseudocodici non implementati come da manuale *)
+ndefinition HC05_not_impl_pseudo ≝
+ [ AIS ; AIX ; BGE ; BGND ; BGT ; BLE ; BLT ; CBEQA ; CBEQX ; CPHX ; DAA
+ ; DBNZ ; DIV ; LDHX ; MOV ; NSA ; PSHA ; PSHH ; PSHX ; PULA ; PULH ; PULX
+ ; SHA ; SLA ; STHX ; TAP ; TPA ; TSX ; TXS ].
+
+nlemma ok_pseudo_table_HC05 : forallc ? (λo.
+ (test_not_impl_pseudo HC05 o HC05_not_impl_pseudo ⊙ lec ? 〈〈x0,x0〉:〈x0,x1〉〉 (get_pseudo_count HC05 o 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC05)) ⊗
+ (⊖ (test_not_impl_pseudo HC05 o HC05_not_impl_pseudo) ⊙ eqc ? (get_pseudo_count HC05 o 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC05) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+(* HC05: modalita' non implementate come da manuale *)
+ndefinition HC05_not_impl_mode ≝
+ [ MODE_INHH ; MODE_SP1 ; MODE_SP2 ; MODE_DIR1_to_DIR1
+ ; MODE_IMM1_to_DIR1 ; MODE_IX0p_to_DIR1 ; MODE_DIR1_to_IX0p
+ ; MODE_INHA_and_IMM1 ; MODE_INHX_and_IMM1 ; MODE_IMM1_and_IMM1
+ ; MODE_DIR1_and_IMM1 ; MODE_IX0_and_IMM1 ; MODE_IX0p_and_IMM1
+ ; MODE_IX1_and_IMM1 ; MODE_IX1p_and_IMM1 ; MODE_SP1_and_IMM1
+ ; MODE_TNY x0 ; MODE_TNY x1 ; MODE_TNY x2 ; MODE_TNY x3
+ ; MODE_TNY x4 ; MODE_TNY x5 ; MODE_TNY x6 ; MODE_TNY x7
+ ; MODE_TNY x8 ; MODE_TNY x9 ; MODE_TNY xA ; MODE_TNY xB
+ ; MODE_TNY xC ; MODE_TNY xD ; MODE_TNY xE ; MODE_TNY xF
+ ; MODE_SRT t00 ; MODE_SRT t01 ; MODE_SRT t02 ; MODE_SRT t03
+ ; MODE_SRT t04 ; MODE_SRT t05 ; MODE_SRT t06 ; MODE_SRT t07
+ ; MODE_SRT t08 ; MODE_SRT t09 ; MODE_SRT t0A ; MODE_SRT t0B
+ ; MODE_SRT t0C ; MODE_SRT t0D ; MODE_SRT t0E ; MODE_SRT t0F
+ ; MODE_SRT t10 ; MODE_SRT t11 ; MODE_SRT t12 ; MODE_SRT t13
+ ; MODE_SRT t14 ; MODE_SRT t15 ; MODE_SRT t16 ; MODE_SRT t17
+ ; MODE_SRT t18 ; MODE_SRT t19 ; MODE_SRT t1A ; MODE_SRT t1B
+ ; MODE_SRT t1C ; MODE_SRT t1D ; MODE_SRT t1E ; MODE_SRT t1F ].
+
+nlemma ok_mode_table_HC05 : forallc ? (λi.
+ (test_not_impl_mode HC05 i HC05_not_impl_mode ⊙ lec ? 〈〈x0,x0〉:〈x0,x1〉〉 (get_mode_count HC05 i 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC05)) ⊗
+ (⊖ (test_not_impl_mode HC05 i HC05_not_impl_mode) ⊙ eqc ? (get_mode_count HC05 i 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC05) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+nlemma ok_PsIm_table_HC05 :
+ forallc ? (λi.
+ forallc ? (λps.
+ lec ? (get_PsIm_count HC05 ps i 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC05) 〈〈x0,x0〉:〈x0,x1〉〉)) = true.
+ napply refl_eq.
+nqed.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/opcodes/pseudo.ma".
+include "emulator/opcodes/HC08_table.ma".
+
+(* ***************** *)
+(* TABELLA DELL'HC08 *)
+(* ***************** *)
+
+(* HC08: opcode non implementati come da manuale (byte) *)
+ndefinition HC08_not_impl_byte ≝
+ [〈x3,x2〉;〈x3,xE〉
+ ;〈x8,x2〉;〈x8,xD〉
+ ;〈x9,x6〉;〈x9,xE〉
+ ;〈xA,xC〉
+ ].
+
+nlemma ok_byte_table_HC08 : forallc ? (λb.
+ (test_not_impl_byte b HC08_not_impl_byte ⊙ eqc ? (get_byte_count HC08 b 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC08) 〈〈x0,x0〉:〈x0,x1〉〉) ⊗
+ (⊖ (test_not_impl_byte b HC08_not_impl_byte) ⊙ eqc ? (get_byte_count HC08 b 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC08) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+(* HC08: opcode non implementati come da manuale (0x9E+byte) *)
+ndefinition HC08_not_impl_word ≝
+ [〈x0,x0〉;〈x0,x1〉;〈x0,x2〉;〈x0,x3〉;〈x0,x4〉;〈x0,x5〉;〈x0,x6〉;〈x0,x7〉
+ ;〈x0,x8〉;〈x0,x9〉;〈x0,xA〉;〈x0,xB〉;〈x0,xC〉;〈x0,xD〉;〈x0,xE〉;〈x0,xF〉
+ ;〈x1,x0〉;〈x1,x1〉;〈x1,x2〉;〈x1,x3〉;〈x1,x4〉;〈x1,x5〉;〈x1,x6〉;〈x1,x7〉
+ ;〈x1,x8〉;〈x1,x9〉;〈x1,xA〉;〈x1,xB〉;〈x1,xC〉;〈x1,xD〉;〈x1,xE〉;〈x1,xF〉
+ ;〈x2,x0〉;〈x2,x1〉;〈x2,x2〉;〈x2,x3〉;〈x2,x4〉;〈x2,x5〉;〈x2,x6〉;〈x2,x7〉
+ ;〈x2,x8〉;〈x2,x9〉;〈x2,xA〉;〈x2,xB〉;〈x2,xC〉;〈x2,xD〉;〈x2,xE〉;〈x2,xF〉
+ ;〈x3,x0〉;〈x3,x1〉;〈x3,x2〉;〈x3,x3〉;〈x3,x4〉;〈x3,x5〉;〈x3,x6〉;〈x3,x7〉
+ ;〈x3,x8〉;〈x3,x9〉;〈x3,xA〉;〈x3,xB〉;〈x3,xC〉;〈x3,xD〉;〈x3,xE〉;〈x3,xF〉
+ ;〈x4,x0〉;〈x4,x1〉;〈x4,x2〉;〈x4,x3〉;〈x4,x4〉;〈x4,x5〉;〈x4,x6〉;〈x4,x7〉
+ ;〈x4,x8〉;〈x4,x9〉;〈x4,xA〉;〈x4,xB〉;〈x4,xC〉;〈x4,xD〉;〈x4,xE〉;〈x4,xF〉
+ ;〈x5,x0〉;〈x5,x1〉;〈x5,x2〉;〈x5,x3〉;〈x5,x4〉;〈x5,x5〉;〈x5,x6〉;〈x5,x7〉
+ ;〈x5,x8〉;〈x5,x9〉;〈x5,xA〉;〈x5,xB〉;〈x5,xC〉;〈x5,xD〉;〈x5,xE〉;〈x5,xF〉
+ ;〈x6,x2〉;〈x6,x5〉;〈x6,xE〉
+ ;〈x7,x0〉;〈x7,x1〉;〈x7,x2〉;〈x7,x3〉;〈x7,x4〉;〈x7,x5〉;〈x7,x6〉;〈x7,x7〉
+ ;〈x7,x8〉;〈x7,x9〉;〈x7,xA〉;〈x7,xB〉;〈x7,xC〉;〈x7,xD〉;〈x7,xE〉;〈x7,xF〉
+ ;〈x8,x0〉;〈x8,x1〉;〈x8,x2〉;〈x8,x3〉;〈x8,x4〉;〈x8,x5〉;〈x8,x6〉;〈x8,x7〉
+ ;〈x8,x8〉;〈x8,x9〉;〈x8,xA〉;〈x8,xB〉;〈x8,xC〉;〈x8,xD〉;〈x8,xE〉;〈x8,xF〉
+ ;〈x9,x0〉;〈x9,x1〉;〈x9,x2〉;〈x9,x3〉;〈x9,x4〉;〈x9,x5〉;〈x9,x6〉;〈x9,x7〉
+ ;〈x9,x8〉;〈x9,x9〉;〈x9,xA〉;〈x9,xB〉;〈x9,xC〉;〈x9,xD〉;〈x9,xE〉;〈x9,xF〉
+ ;〈xA,x0〉;〈xA,x1〉;〈xA,x2〉;〈xA,x3〉;〈xA,x4〉;〈xA,x5〉;〈xA,x6〉;〈xA,x7〉
+ ;〈xA,x8〉;〈xA,x9〉;〈xA,xA〉;〈xA,xB〉;〈xA,xC〉;〈xA,xD〉;〈xA,xE〉;〈xA,xF〉
+ ;〈xB,x0〉;〈xB,x1〉;〈xB,x2〉;〈xB,x3〉;〈xB,x4〉;〈xB,x5〉;〈xB,x6〉;〈xB,x7〉
+ ;〈xB,x8〉;〈xB,x9〉;〈xB,xA〉;〈xB,xB〉;〈xB,xC〉;〈xB,xD〉;〈xB,xE〉;〈xB,xF〉
+ ;〈xC,x0〉;〈xC,x1〉;〈xC,x2〉;〈xC,x3〉;〈xC,x4〉;〈xC,x5〉;〈xC,x6〉;〈xC,x7〉
+ ;〈xC,x8〉;〈xC,x9〉;〈xC,xA〉;〈xC,xB〉;〈xC,xC〉;〈xC,xD〉;〈xC,xE〉;〈xC,xF〉
+ ;〈xD,xC〉;〈xD,xD〉
+ ;〈xE,xC〉;〈xE,xD〉
+ ;〈xF,x0〉;〈xF,x1〉;〈xF,x2〉;〈xF,x3〉;〈xF,x4〉;〈xF,x5〉;〈xF,x6〉;〈xF,x7〉
+ ;〈xF,x8〉;〈xF,x9〉;〈xF,xA〉;〈xF,xB〉;〈xF,xC〉;〈xF,xD〉;〈xF,xE〉;〈xF,xF〉
+ ].
+
+nlemma ok_word_table_HC08 : forallc ? (λb.
+ (test_not_impl_byte b HC08_not_impl_word ⊙ eqc ? (get_word_count HC08 〈〈x9,xE〉:b〉 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC08) 〈〈x0,x0〉:〈x0,x1〉〉) ⊗
+ (⊖ (test_not_impl_byte b HC08_not_impl_word) ⊙ eqc ? (get_word_count HC08 〈〈x9,xE〉:b〉 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC08) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+(* HC08: pseudocodici non implementati come da manuale *)
+ndefinition HC08_not_impl_pseudo ≝
+ [ BGND ; SHA ; SLA ].
+
+nlemma ok_pseudo_table_HC08 : forallc ? (λo.
+ (test_not_impl_pseudo HC08 o HC08_not_impl_pseudo ⊙ lec ? 〈〈x0,x0〉:〈x0,x1〉〉 (get_pseudo_count HC08 o 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC08)) ⊗
+ (⊖ (test_not_impl_pseudo HC08 o HC08_not_impl_pseudo) ⊙ eqc ? (get_pseudo_count HC08 o 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC08) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+(* HC08: modalita' non implementate come da manuale *)
+ndefinition HC08_not_impl_mode ≝
+ [ MODE_TNY x0 ; MODE_TNY x1 ; MODE_TNY x2 ; MODE_TNY x3
+ ; MODE_TNY x4 ; MODE_TNY x5 ; MODE_TNY x6 ; MODE_TNY x7
+ ; MODE_TNY x8 ; MODE_TNY x9 ; MODE_TNY xA ; MODE_TNY xB
+ ; MODE_TNY xC ; MODE_TNY xD ; MODE_TNY xE ; MODE_TNY xF
+ ; MODE_SRT t00 ; MODE_SRT t01 ; MODE_SRT t02 ; MODE_SRT t03
+ ; MODE_SRT t04 ; MODE_SRT t05 ; MODE_SRT t06 ; MODE_SRT t07
+ ; MODE_SRT t08 ; MODE_SRT t09 ; MODE_SRT t0A ; MODE_SRT t0B
+ ; MODE_SRT t0C ; MODE_SRT t0D ; MODE_SRT t0E ; MODE_SRT t0F
+ ; MODE_SRT t10 ; MODE_SRT t11 ; MODE_SRT t12 ; MODE_SRT t13
+ ; MODE_SRT t14 ; MODE_SRT t15 ; MODE_SRT t16 ; MODE_SRT t17
+ ; MODE_SRT t18 ; MODE_SRT t19 ; MODE_SRT t1A ; MODE_SRT t1B
+ ; MODE_SRT t1C ; MODE_SRT t1D ; MODE_SRT t1E ; MODE_SRT t1F ].
+
+nlemma ok_mode_table_HC08 : forallc ? (λi.
+ (test_not_impl_mode HC08 i HC08_not_impl_mode ⊙ lec ? 〈〈x0,x0〉:〈x0,x1〉〉 (get_mode_count HC08 i 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC08)) ⊗
+ (⊖ (test_not_impl_mode HC08 i HC08_not_impl_mode) ⊙ eqc ? (get_mode_count HC08 i 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC08) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+nlemma ok_PsIm_table_HC08 :
+ forallc ? (λi.
+ forallc ? (λps.
+ lec ? (get_PsIm_count HC08 ps i 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HC08) 〈〈x0,x0〉:〈x0,x1〉〉)) = true.
+ napply refl_eq.
+nqed.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/opcodes/pseudo.ma".
+include "emulator/opcodes/HCS08_table.ma".
+
+(* ****************** *)
+(* TABELLA DELL'HCS08 *)
+(* ****************** *)
+
+(* HCS08: opcode non implementati come da manuale (byte) *)
+ndefinition HCS08_not_impl_byte ≝
+ [〈x8,xD〉
+ ;〈x9,xE〉
+ ;〈xA,xC〉
+ ].
+
+nlemma ok_byte_table_HCS08 : forallc ? (λb.
+ (test_not_impl_byte b HCS08_not_impl_byte ⊙ eqc ? (get_byte_count HCS08 b 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HCS08) 〈〈x0,x0〉:〈x0,x1〉〉) ⊗
+ (⊖ (test_not_impl_byte b HCS08_not_impl_byte) ⊙ eqc ? (get_byte_count HCS08 b 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HCS08) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+(* HCS08: opcode non implementati come da manuale (0x9E+byte) *)
+ndefinition HCS08_not_impl_word ≝
+ [〈x0,x0〉;〈x0,x1〉;〈x0,x2〉;〈x0,x3〉;〈x0,x4〉;〈x0,x5〉;〈x0,x6〉;〈x0,x7〉
+ ;〈x0,x8〉;〈x0,x9〉;〈x0,xA〉;〈x0,xB〉;〈x0,xC〉;〈x0,xD〉;〈x0,xE〉;〈x0,xF〉
+ ;〈x1,x0〉;〈x1,x1〉;〈x1,x2〉;〈x1,x3〉;〈x1,x4〉;〈x1,x5〉;〈x1,x6〉;〈x1,x7〉
+ ;〈x1,x8〉;〈x1,x9〉;〈x1,xA〉;〈x1,xB〉;〈x1,xC〉;〈x1,xD〉;〈x1,xE〉;〈x1,xF〉
+ ;〈x2,x0〉;〈x2,x1〉;〈x2,x2〉;〈x2,x3〉;〈x2,x4〉;〈x2,x5〉;〈x2,x6〉;〈x2,x7〉
+ ;〈x2,x8〉;〈x2,x9〉;〈x2,xA〉;〈x2,xB〉;〈x2,xC〉;〈x2,xD〉;〈x2,xE〉;〈x2,xF〉
+ ;〈x3,x0〉;〈x3,x1〉;〈x3,x2〉;〈x3,x3〉;〈x3,x4〉;〈x3,x5〉;〈x3,x6〉;〈x3,x7〉
+ ;〈x3,x8〉;〈x3,x9〉;〈x3,xA〉;〈x3,xB〉;〈x3,xC〉;〈x3,xD〉;〈x3,xE〉;〈x3,xF〉
+ ;〈x4,x0〉;〈x4,x1〉;〈x4,x2〉;〈x4,x3〉;〈x4,x4〉;〈x4,x5〉;〈x4,x6〉;〈x4,x7〉
+ ;〈x4,x8〉;〈x4,x9〉;〈x4,xA〉;〈x4,xB〉;〈x4,xC〉;〈x4,xD〉;〈x4,xE〉;〈x4,xF〉
+ ;〈x5,x0〉;〈x5,x1〉;〈x5,x2〉;〈x5,x3〉;〈x5,x4〉;〈x5,x5〉;〈x5,x6〉;〈x5,x7〉
+ ;〈x5,x8〉;〈x5,x9〉;〈x5,xA〉;〈x5,xB〉;〈x5,xC〉;〈x5,xD〉;〈x5,xE〉;〈x5,xF〉
+ ;〈x6,x2〉;〈x6,x5〉;〈x6,xE〉
+ ;〈x7,x0〉;〈x7,x1〉;〈x7,x2〉;〈x7,x3〉;〈x7,x4〉;〈x7,x5〉;〈x7,x6〉;〈x7,x7〉
+ ;〈x7,x8〉;〈x7,x9〉;〈x7,xA〉;〈x7,xB〉;〈x7,xC〉;〈x7,xD〉;〈x7,xE〉;〈x7,xF〉
+ ;〈x8,x0〉;〈x8,x1〉;〈x8,x2〉;〈x8,x3〉;〈x8,x4〉;〈x8,x5〉;〈x8,x6〉;〈x8,x7〉
+ ;〈x8,x8〉;〈x8,x9〉;〈x8,xA〉;〈x8,xB〉;〈x8,xC〉;〈x8,xD〉;〈x8,xE〉;〈x8,xF〉
+ ;〈x9,x0〉;〈x9,x1〉;〈x9,x2〉;〈x9,x3〉;〈x9,x4〉;〈x9,x5〉;〈x9,x6〉;〈x9,x7〉
+ ;〈x9,x8〉;〈x9,x9〉;〈x9,xA〉;〈x9,xB〉;〈x9,xC〉;〈x9,xD〉;〈x9,xE〉;〈x9,xF〉
+ ;〈xA,x0〉;〈xA,x1〉;〈xA,x2〉;〈xA,x3〉;〈xA,x4〉;〈xA,x5〉;〈xA,x6〉;〈xA,x7〉;〈xA,x8〉;〈xA,x9〉;〈xA,xA〉;〈xA,xB〉;〈xA,xC〉;〈xA,xD〉;〈xA,xF〉
+ ;〈xB,x0〉;〈xB,x1〉;〈xB,x2〉;〈xB,x3〉;〈xB,x4〉;〈xB,x5〉;〈xB,x6〉;〈xB,x7〉;〈xB,x8〉;〈xB,x9〉;〈xB,xA〉;〈xB,xB〉;〈xB,xC〉;〈xB,xD〉;〈xB,xF〉
+ ;〈xC,x0〉;〈xC,x1〉;〈xC,x2〉;〈xC,x3〉;〈xC,x4〉;〈xC,x5〉;〈xC,x6〉;〈xC,x7〉;〈xC,x8〉;〈xC,x9〉;〈xC,xA〉;〈xC,xB〉;〈xC,xC〉;〈xC,xD〉;〈xC,xF〉
+ ;〈xD,xC〉;〈xD,xD〉
+ ;〈xE,xC〉;〈xE,xD〉
+ ;〈xF,x0〉;〈xF,x1〉;〈xF,x2〉;〈xF,x4〉;〈xF,x5〉;〈xF,x6〉;〈xF,x7〉;〈xF,x8〉;〈xF,x9〉;〈xF,xA〉;〈xF,xB〉;〈xF,xC〉;〈xF,xD〉
+ ].
+
+nlemma ok_word_table_HCS08 : forallc ? (λb.
+ (test_not_impl_byte b HCS08_not_impl_word ⊙ eqc ? (get_word_count HCS08 〈〈x9,xE〉:b〉 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HCS08) 〈〈x0,x0〉:〈x0,x1〉〉) ⊗
+ (⊖ (test_not_impl_byte b HCS08_not_impl_word) ⊙ eqc ? (get_word_count HCS08 〈〈x9,xE〉:b〉 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HCS08) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+(* HCS08: pseudocodici non implementati come da manuale *)
+ndefinition HCS08_not_impl_pseudo ≝
+ [ SHA ; SLA ].
+
+nlemma ok_pseudo_table_HCS08 : forallc ? (λo.
+ (test_not_impl_pseudo HCS08 o HCS08_not_impl_pseudo ⊙ lec ? 〈〈x0,x0〉:〈x0,x1〉〉 (get_pseudo_count HCS08 o 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HCS08)) ⊗
+ (⊖ (test_not_impl_pseudo HCS08 o HCS08_not_impl_pseudo) ⊙ eqc ? (get_pseudo_count HCS08 o 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HCS08) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+(* HCS08: modalita' non implementate come da manuale *)
+ndefinition HCS08_not_impl_mode ≝
+ [ MODE_TNY x0 ; MODE_TNY x1 ; MODE_TNY x2 ; MODE_TNY x3
+ ; MODE_TNY x4 ; MODE_TNY x5 ; MODE_TNY x6 ; MODE_TNY x7
+ ; MODE_TNY x8 ; MODE_TNY x9 ; MODE_TNY xA ; MODE_TNY xB
+ ; MODE_TNY xC ; MODE_TNY xD ; MODE_TNY xE ; MODE_TNY xF
+ ; MODE_SRT t00 ; MODE_SRT t01 ; MODE_SRT t02 ; MODE_SRT t03
+ ; MODE_SRT t04 ; MODE_SRT t05 ; MODE_SRT t06 ; MODE_SRT t07
+ ; MODE_SRT t08 ; MODE_SRT t09 ; MODE_SRT t0A ; MODE_SRT t0B
+ ; MODE_SRT t0C ; MODE_SRT t0D ; MODE_SRT t0E ; MODE_SRT t0F
+ ; MODE_SRT t10 ; MODE_SRT t11 ; MODE_SRT t12 ; MODE_SRT t13
+ ; MODE_SRT t14 ; MODE_SRT t15 ; MODE_SRT t16 ; MODE_SRT t17
+ ; MODE_SRT t18 ; MODE_SRT t19 ; MODE_SRT t1A ; MODE_SRT t1B
+ ; MODE_SRT t1C ; MODE_SRT t1D ; MODE_SRT t1E ; MODE_SRT t1F ].
+
+nlemma ok_mode_table_HCS08 : forallc ? (λi.
+ (test_not_impl_mode HCS08 i HCS08_not_impl_mode ⊙ lec ? 〈〈x0,x0〉:〈x0,x1〉〉 (get_mode_count HCS08 i 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HCS08)) ⊗
+ (⊖ (test_not_impl_mode HCS08 i HCS08_not_impl_mode) ⊙ eqc ? (get_mode_count HCS08 i 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HCS08) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+nlemma ok_PsIm_table_HCS08 :
+ forallc ? (λi.
+ forallc ? (λps.
+ lec ? (get_PsIm_count HCS08 ps i 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_HCS08) 〈〈x0,x0〉:〈x0,x1〉〉)) = true.
+ napply refl_eq.
+nqed.
napply (neq_to_neqIP2022im n2 n1 (symmetric_neq ? n1 n2 H))
##]
nqed.
+
+nlemma IP2022im_is_comparable : comparable.
+ @ IP2022_instr_mode
+ ##[ napply MODE_INH
+ ##| napply forall_IP2022_im
+ ##| napply eq_IP2022_im
+ ##| napply eqIP2022im_to_eq
+ ##| napply eq_to_eqIP2022im
+ ##| napply neqIP2022im_to_neq
+ ##| napply neq_to_neqIP2022im
+ ##| napply decidable_IP2022im
+ ##| napply symmetric_eqIP2022im
+ ##]
+nqed.
+
+unification hint 0 ≔ ⊢ carr IP2022im_is_comparable ≡ IP2022_instr_mode.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/opcodes/pseudo.ma".
+include "emulator/opcodes/IP2022_table.ma".
+
+(* ******************* *)
+(* TABELLA DELL'IP2022 *)
+(* ******************* *)
+
+(* IP2022: opcode non implementati come da manuale (byte) *)
+ndefinition IP2022_not_impl_byte ≝
+ [〈x0,x0〉;〈x5,x2〉;〈x5,x3〉;〈x5,x6〉;〈x5,x7〉;〈x6,x0〉;〈x6,x1〉;〈x6,x2〉
+ ;〈x6,x3〉;〈x6,x4〉;〈x6,x5〉;〈x6,x6〉;〈x6,x7〉;〈x6,x8〉;〈x6,x9〉;〈x6,xA〉
+ ;〈x6,xB〉;〈x6,xC〉;〈x6,xD〉;〈x6,xE〉;〈x6,xF〉;〈x7,x5〉 ].
+
+(*nlemma ok_byte_table_IP2022 : forallc ? (λb.
+ (test_not_impl_byte b IP2022_not_impl_byte ⊙ eqc ? (get_byte_count IP2022 b 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_IP2022) 〈〈x0,x0〉:〈x0,x1〉〉) ⊗
+ (⊖ (test_not_impl_byte b IP2022_not_impl_byte) ⊙ eqc ? (get_byte_count IP2022 b 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_IP2022) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.*)
+
+(* IP2022: opcode non implementati come da manuale (0x00+byte) *)
+ndefinition IP2022_not_impl_word ≝
+ [〈x1,xE〉;〈x1,xF〉
+ ;〈x2,x0〉;〈x2,x1〉;〈x2,x2〉;〈x2,x3〉;〈x2,x4〉;〈x2,x5〉;〈x2,x6〉;〈x2,x7〉
+ ;〈x2,x8〉;〈x2,x9〉;〈x2,xA〉;〈x2,xB〉;〈x2,xC〉;〈x2,xD〉;〈x2,xE〉;〈x2,xF〉
+ ;〈x3,x0〉;〈x3,x1〉;〈x3,x2〉;〈x3,x3〉;〈x3,x4〉;〈x3,x5〉;〈x3,x6〉;〈x3,x7〉
+ ;〈x3,x8〉;〈x3,x9〉;〈x3,xA〉;〈x3,xB〉;〈x3,xC〉;〈x3,xD〉;〈x3,xE〉;〈x3,xF〉
+ ;〈x4,x0〉;〈x4,x1〉;〈x4,x2〉;〈x4,x3〉;〈x4,x4〉;〈x4,x5〉;〈x4,x6〉;〈x4,x7〉
+ ;〈x4,x8〉;〈x4,x9〉;〈x4,xA〉;〈x4,xB〉;〈x4,xC〉;〈x4,xD〉;〈x4,xE〉;〈x4,xF〉
+ ;〈x5,x0〉;〈x5,x1〉;〈x5,x2〉;〈x5,x3〉;〈x5,x4〉;〈x5,x5〉;〈x5,x6〉;〈x5,x7〉
+ ;〈x5,x8〉;〈x5,x9〉;〈x5,xA〉;〈x5,xB〉;〈x5,xC〉;〈x5,xD〉;〈x5,xE〉;〈x5,xF〉
+ ;〈x6,x0〉;〈x6,x1〉;〈x6,x2〉;〈x6,x3〉;〈x6,x4〉;〈x6,x5〉;〈x6,x6〉;〈x6,x7〉
+ ;〈x6,x8〉;〈x6,x9〉;〈x6,xA〉;〈x6,xB〉;〈x6,xC〉;〈x6,xD〉;〈x6,xE〉;〈x6,xF〉
+ ;〈x7,x0〉;〈x7,x1〉;〈x7,x2〉;〈x7,x3〉;〈x7,x4〉;〈x7,x5〉;〈x7,x6〉;〈x7,x7〉
+ ;〈x7,x8〉;〈x7,x9〉;〈x7,xA〉;〈x7,xB〉;〈x7,xC〉;〈x7,xD〉;〈x7,xE〉;〈x7,xF〉
+ ;〈x8,x0〉;〈x8,x1〉;〈x8,x2〉;〈x8,x3〉;〈x8,x4〉;〈x8,x5〉;〈x8,x6〉;〈x8,x7〉
+ ;〈x8,x8〉;〈x8,x9〉;〈x8,xA〉;〈x8,xB〉;〈x8,xC〉;〈x8,xD〉;〈x8,xE〉;〈x8,xF〉
+ ;〈x9,x0〉;〈x9,x1〉;〈x9,x2〉;〈x9,x3〉;〈x9,x4〉;〈x9,x5〉;〈x9,x6〉;〈x9,x7〉
+ ;〈x9,x8〉;〈x9,x9〉;〈x9,xA〉;〈x9,xB〉;〈x9,xC〉;〈x9,xD〉;〈x9,xE〉;〈x9,xF〉
+ ;〈xA,x0〉;〈xA,x1〉;〈xA,x2〉;〈xA,x3〉;〈xA,x4〉;〈xA,x5〉;〈xA,x6〉;〈xA,x7〉
+ ;〈xA,x8〉;〈xA,x9〉;〈xA,xA〉;〈xA,xB〉;〈xA,xC〉;〈xA,xD〉;〈xA,xE〉;〈xA,xF〉
+ ;〈xB,x0〉;〈xB,x1〉;〈xB,x2〉;〈xB,x3〉;〈xB,x4〉;〈xB,x5〉;〈xB,x6〉;〈xB,x7〉
+ ;〈xB,x8〉;〈xB,x9〉;〈xB,xA〉;〈xB,xB〉;〈xB,xC〉;〈xB,xD〉;〈xB,xE〉;〈xB,xF〉
+ ;〈xC,x0〉;〈xC,x1〉;〈xC,x2〉;〈xC,x3〉;〈xC,x4〉;〈xC,x5〉;〈xC,x6〉;〈xC,x7〉
+ ;〈xC,x8〉;〈xC,x9〉;〈xC,xA〉;〈xC,xB〉;〈xC,xC〉;〈xC,xD〉;〈xC,xE〉;〈xC,xF〉
+ ;〈xD,x0〉;〈xD,x1〉;〈xD,x2〉;〈xD,x3〉;〈xD,x4〉;〈xD,x5〉;〈xD,x6〉;〈xD,x7〉
+ ;〈xD,x8〉;〈xD,x9〉;〈xD,xA〉;〈xD,xB〉;〈xD,xC〉;〈xD,xD〉;〈xD,xE〉;〈xD,xF〉
+ ;〈xE,x0〉;〈xE,x1〉;〈xE,x2〉;〈xE,x3〉;〈xE,x4〉;〈xE,x5〉;〈xE,x6〉;〈xE,x7〉
+ ;〈xE,x8〉;〈xE,x9〉;〈xE,xA〉;〈xE,xB〉;〈xE,xC〉;〈xE,xD〉;〈xE,xE〉;〈xE,xF〉
+ ;〈xF,x0〉;〈xF,x1〉;〈xF,x2〉;〈xF,x3〉;〈xF,x4〉;〈xF,x5〉;〈xF,x6〉;〈xF,x7〉
+ ;〈xF,x8〉;〈xF,x9〉;〈xF,xA〉;〈xF,xB〉;〈xF,xC〉;〈xF,xD〉;〈xF,xE〉;〈xF,xF〉
+ ].
+
+nlemma ok_word_table_IP2022 : forallc ? (λb.
+ (test_not_impl_byte b IP2022_not_impl_word ⊙ eqc ? (get_word_count IP2022 〈〈x0,x0〉:b〉 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_IP2022) 〈〈x0,x0〉:〈x0,x1〉〉) ⊗
+ (⊖ (test_not_impl_byte b IP2022_not_impl_word) ⊙ eqc ? (get_word_count IP2022 〈〈x0,x0〉:b〉 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_IP2022) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+(* tutti gli pseudo implementati *)
+nlemma ok_pseudo_table_IP2022 :
+ forallc ? (λo.
+ lec ? 〈〈x0,x0〉:〈x0,x1〉〉 (get_pseudo_count IP2022 o 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_IP2022)) = true.
+ napply refl_eq.
+nqed.
+
+(* tutte le modalita' implementate *)
+nlemma ok_mode_table_IP2022 :
+ forallc ? (λi.
+ lec ? 〈〈x0,x0〉:〈x0,x1〉〉 (get_mode_count IP2022 i 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_IP2022)) = true.
+ napply refl_eq.
+nqed.
+
+nlemma ok_PsIm_table_IP2022 :
+ forallc ? (λi.
+ forallc ? (λps.
+ lec ? (get_PsIm_count IP2022 ps i 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_IP2022) 〈〈x0,x0〉:〈x0,x1〉〉)) = true.
+ napply refl_eq.
+nqed.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/opcodes/pseudo.ma".
+include "emulator/opcodes/RS08_table.ma".
+
+(* ***************** *)
+(* TABELLA DELL'RS08 *)
+(* ***************** *)
+
+(* RS08: opcode non implementati come da manuale *)
+ndefinition RS08_not_impl_byte ≝
+ [〈x3,x2〉;〈x3,x3〉;〈x3,xD〉
+ ;〈x4,x0〉;〈x4,x7〉;〈x4,xD〉
+ ;〈xA,x3〉;〈xA,x5〉;〈xA,x7〉
+ ;〈xB,x3〉;〈xB,x5〉
+ ].
+
+nlemma ok_byte_table_RS08 : forallc ? (λb.
+ (test_not_impl_byte b RS08_not_impl_byte ⊙ eqc ? (get_byte_count RS08 b 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_RS08) 〈〈x0,x0〉:〈x0,x1〉〉) ⊗
+ (⊖ (test_not_impl_byte b RS08_not_impl_byte) ⊙ eqc ? (get_byte_count RS08 b 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_RS08) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+(* RS08: pseudocodici non implementati come da manuale *)
+ndefinition RS08_not_impl_pseudo ≝
+ [ AIS ; AIX ; ASR ; BGE ; BGT ; BHCC ; BHCS ; BHI ; BIH ; BIL ; BIT ; BLE ; BLS
+ ; BLT ; BMC ; BMI ; BMS ; BPL ; BRN ; CBEQX ; CLI ; CPHX ; CPX ; DAA ; DIV
+ ; LDHX ; LDX ; MUL ; NEG ; NSA ; PSHA ; PSHH ; PSHX ; PULA ; PULH ; PULX ; RSP
+ ; RTI ; SEI ; STHX ; STX ; SWI ; TAP ; TAX ; TPA ; TST ; TSX ; TXA ; TXS ].
+
+nlemma ok_pseudo_table_RS08 : forallc ? (λo.
+ (test_not_impl_pseudo RS08 o RS08_not_impl_pseudo ⊙ lec ? 〈〈x0,x0〉:〈x0,x1〉〉 (get_pseudo_count RS08 o 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_RS08)) ⊗
+ (⊖ (test_not_impl_pseudo RS08 o RS08_not_impl_pseudo) ⊙ eqc ? (get_pseudo_count RS08 o 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_RS08) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+(* RS08: modalita' non implementate come da manuale *)
+ndefinition RS08_not_impl_mode ≝
+ [ MODE_INHX ; MODE_INHH ; MODE_INHX0ADD ; MODE_INHX1ADD ; MODE_INHX2ADD ; MODE_IMM1EXT
+ ; MODE_DIR2 ; MODE_IX0 ; MODE_IX1 ; MODE_IX2 ; MODE_SP1 ; MODE_SP2
+ ; MODE_IX0p_to_DIR1 ; MODE_DIR1_to_IX0p ; MODE_INHX_and_IMM1 ; MODE_IX0_and_IMM1
+ ; MODE_IX0p_and_IMM1 ; MODE_IX1_and_IMM1 ; MODE_IX1p_and_IMM1 ; MODE_SP1_and_IMM1 ].
+
+nlemma ok_mode_table_RS08 : forallc ? (λi.
+ (test_not_impl_mode RS08 i RS08_not_impl_mode ⊙ lec ? 〈〈x0,x0〉:〈x0,x1〉〉 (get_mode_count RS08 i 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_RS08)) ⊗
+ (⊖ (test_not_impl_mode RS08 i RS08_not_impl_mode) ⊙ eqc ? (get_mode_count RS08 i 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_RS08) 〈〈x0,x0〉:〈x0,x0〉〉))
+ = true.
+ napply refl_eq.
+nqed.
+
+nlemma ok_PsIm_table_RS08 :
+ forallc ? (λi.
+ forallc ? (λps.
+ lec ? (get_PsIm_count RS08 ps i 〈〈x0,x0〉:〈x0,x0〉〉 opcode_table_RS08) 〈〈x0,x0〉:〈x0,x1〉〉)) = true.
+ napply refl_eq.
+nqed.
| IP2022 ⇒ IP2022_pseudo
].
+ndefinition pseudo_is_comparable: mcu_type → comparable.
+ #mcu; @ (aux_pseudo_type mcu)
+ ##[ nelim mcu;
+ ##[ ##1,2,3,4: napply (zeroc Freescalepseudo_is_comparable)
+ ##| ##5: napply (zeroc IP2022pseudo_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (forallc Freescalepseudo_is_comparable)
+ ##| ##5: napply (forallc IP2022pseudo_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (eqc Freescalepseudo_is_comparable)
+ ##| ##5: napply (eqc IP2022pseudo_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (eqc_to_eq Freescalepseudo_is_comparable)
+ ##| ##5: napply (eqc_to_eq IP2022pseudo_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (eq_to_eqc Freescalepseudo_is_comparable)
+ ##| ##5: napply (eq_to_eqc IP2022pseudo_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (neqc_to_neq Freescalepseudo_is_comparable)
+ ##| ##5: napply (neqc_to_neq IP2022pseudo_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (neq_to_neqc Freescalepseudo_is_comparable)
+ ##| ##5: napply (neq_to_neqc IP2022pseudo_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (decidable_c Freescalepseudo_is_comparable)
+ ##| ##5: napply (decidable_c IP2022pseudo_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (symmetric_eqc Freescalepseudo_is_comparable)
+ ##| ##5: napply (symmetric_eqc IP2022pseudo_is_comparable) ##]
+ ##]
+nqed.
+
+unification hint 0 ≔ M:mcu_type ⊢ carr (pseudo_is_comparable M) ≡ aux_pseudo_type M.
+
ndefinition aux_im_type ≝
λmcu:mcu_type.match mcu with
[ HC05 ⇒ Freescale_instr_mode
| IP2022 ⇒ IP2022_instr_mode
].
+ndefinition im_is_comparable: mcu_type → comparable.
+ #mcu; @ (aux_im_type mcu)
+ ##[ nelim mcu;
+ ##[ ##1,2,3,4: napply (zeroc Freescaleim_is_comparable)
+ ##| ##5: napply (zeroc IP2022im_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (forallc Freescaleim_is_comparable)
+ ##| ##5: napply (forallc IP2022im_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (eqc Freescaleim_is_comparable)
+ ##| ##5: napply (eqc IP2022im_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (eqc_to_eq Freescaleim_is_comparable)
+ ##| ##5: napply (eqc_to_eq IP2022im_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (eq_to_eqc Freescaleim_is_comparable)
+ ##| ##5: napply (eq_to_eqc IP2022im_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (neqc_to_neq Freescaleim_is_comparable)
+ ##| ##5: napply (neqc_to_neq IP2022im_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (neq_to_neqc Freescaleim_is_comparable)
+ ##| ##5: napply (neq_to_neqc IP2022im_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (decidable_c Freescaleim_is_comparable)
+ ##| ##5: napply (decidable_c IP2022im_is_comparable) ##]
+ ##| nelim mcu;
+ ##[ ##1,2,3,4: napply (symmetric_eqc Freescaleim_is_comparable)
+ ##| ##5: napply (symmetric_eqc IP2022im_is_comparable) ##]
+ ##]
+nqed.
+
+unification hint 0 ≔ M:mcu_type ⊢ carr (im_is_comparable M) ≡ aux_im_type M.
+
(* ********************************************* *)
(* STRUMENTI PER LE DIMOSTRAZIONI DI CORRETTEZZA *)
(* ********************************************* *)
ndefinition aux_table_type ≝ λmcu:mcu_type.Prod4T (aux_pseudo_type mcu) (aux_im_type mcu) byte8_or_word16 byte8.
-naxiom daemon: False.
-
-ndefinition pseudo_is_comparable: mcu_type → comparable.
- #mcu;
- @ (aux_pseudo_type mcu)
- ##[ napply (match mcu return λmcu. aux_pseudo_type mcu with
- [ HC05 ⇒ zeroc Freescalepseudo_is_comparable
- | HC08 ⇒ zeroc Freescalepseudo_is_comparable
- | HCS08 ⇒ zeroc Freescalepseudo_is_comparable
- | RS08 ⇒ zeroc Freescalepseudo_is_comparable
- | IP2022 ⇒ zeroc IP2022pseudo_is_comparable
- ])
- | napply (match mcu return λmcu. (aux_pseudo_type mcu → bool) → bool with
- [ HC05 ⇒ forallc Freescalepseudo_is_comparable
- | HC08 ⇒ forallc Freescalepseudo_is_comparable
- | HCS08 ⇒ forallc Freescalepseudo_is_comparable
- | RS08 ⇒ forallc Freescalepseudo_is_comparable
- | IP2022 ⇒ forallc IP2022pseudo_is_comparable
- ])
- | napply (match mcu return λmcu. aux_pseudo_type mcu → aux_pseudo_type mcu → bool with
- [ HC05 ⇒ eqc Freescalepseudo_is_comparable
- | HC08 ⇒ eqc Freescalepseudo_is_comparable
- | HCS08 ⇒ eqc Freescalepseudo_is_comparable
- | RS08 ⇒ eqc Freescalepseudo_is_comparable
- | IP2022 ⇒ eqc IP2022pseudo_is_comparable
- ])
- |##*: ncases daemon ]
-nqed.
-
-
-(* come suggerire di unificare?
- carr (pseudo_is_comparable M) = aux_pseudo_type M *)
+(* su tutta la lista quante volte compare il byte *)
+nlet rec get_byte_count (m:mcu_type) (b:byte8) (c:word16) (l:list (aux_table_type m)) on l ≝
+ match l with
+ [ nil ⇒ c
+ | cons hd tl ⇒ match thd4T … hd with
+ [ Byte b' ⇒ match eqc ? b b' with
+ [ true ⇒ get_byte_count m b (succc ? c) tl
+ | false ⇒ get_byte_count m b c tl
+ ]
+ | Word _ ⇒ get_byte_count m b c tl
+ ]
+ ].
-unification hint 0 ≔ MCU:mcu_type ⊢
- carr (pseudo_is_comparable MCU) ≡ aux_pseudo_type MCU.
+(* su tutta la lista quante volte compare la word *)
+nlet rec get_word_count (m:mcu_type) (w:word16) (c:word16) (l:list (aux_table_type m)) on l ≝
+ match l with
+ [ nil ⇒ c
+ | cons hd tl ⇒ match thd4T … hd with
+ [ Byte _ ⇒ get_word_count m w c tl
+ | Word w' ⇒ match eqc ? w w' with
+ [ true ⇒ get_word_count m w (succc ? c) tl
+ | false ⇒ get_word_count m w c tl
+ ]
+ ]
+ ].
(* su tutta la lista quante volte compare lo pseudocodice *)
nlet rec get_pseudo_count (m:mcu_type) (o:aux_pseudo_type m) (c:word16) (l:list (aux_table_type m)) on l ≝
| false ⇒ get_pseudo_count m o c tl
]
].
+
+(* su tutta la lista quante volte compare la modalita' *)
+nlet rec get_mode_count (m:mcu_type) (i:aux_im_type m) (c:word16) (l:list (aux_table_type m)) on l ≝
+ match l with
+ [ nil ⇒ c
+ | cons hd tl ⇒ match eqc ? i (snd4T … hd) with
+ [ true ⇒ get_mode_count m i (succc ? c) tl
+ | false ⇒ get_mode_count m i c tl
+ ]
+ ].
+
+(* b e' non implementato? *)
+nlet rec test_not_impl_byte (b:byte8) (l:list byte8) on l ≝
+ match l with
+ [ nil ⇒ false
+ | cons hd tl ⇒ match eqc ? b hd with
+ [ true ⇒ true
+ | false ⇒ test_not_impl_byte b tl
+ ]
+ ].
+
+(* su tutta la lista quante volte compare la coppia pseudo,instr_mode *)
+nlet rec get_PsIm_count (m:mcu_type) (o:aux_pseudo_type m) (i:aux_im_type m) (c:word16) (l:list (aux_table_type m)) on l ≝
+ match l with
+ [ nil ⇒ c
+ | cons hd tl ⇒
+ match (eqc ? o (fst4T … hd)) ⊗
+ (eqc ? i (snd4T … hd)) with
+ [ true ⇒ get_PsIm_count m o i (succc ? c) tl
+ | false ⇒ get_PsIm_count m o i c tl
+ ]
+ ].
+
+(* o e' non implementato? *)
+nlet rec test_not_impl_pseudo (m:mcu_type) (o:aux_pseudo_type m) (l:list (aux_pseudo_type m)) on l ≝
+ match l with
+ [ nil ⇒ false
+ | cons hd tl ⇒ match eqc ? o hd with
+ [ true ⇒ true
+ | false ⇒ test_not_impl_pseudo m o tl
+ ]
+ ].
+
+(* i e' non implementato? *)
+nlet rec test_not_impl_mode (m:mcu_type) (i:aux_im_type m) (l:list (aux_im_type m)) on l ≝
+ match l with
+ [ nil ⇒ false
+ | cons hd tl ⇒ match eqc ? i hd with
+ [ true ⇒ true
+ | false ⇒ test_not_impl_mode m i tl
+ ]
+ ].
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/status/HC05_status_base.ma".
+
+(* *********************************** *)
+(* STATUS INTERNO DEL PROCESSORE (ALU) *)
+(* *********************************** *)
+
+nlemma aluHC05_destruct_1 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
+ x1 = y1.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
+ with [ mk_alu_HC05 a _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x1 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC05_destruct_2 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
+ x2 = y2.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
+ with [ mk_alu_HC05 _ a _ _ _ _ _ _ _ _ _ _ _ ⇒ x2 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC05_destruct_3 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
+ x3 = y3.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
+ with [ mk_alu_HC05 _ _ a _ _ _ _ _ _ _ _ _ _ ⇒ x3 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC05_destruct_4 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
+ x4 = y4.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
+ with [ mk_alu_HC05 _ _ _ a _ _ _ _ _ _ _ _ _ ⇒ x4 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC05_destruct_5 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
+ x5 = y5.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
+ with [ mk_alu_HC05 _ _ _ _ a _ _ _ _ _ _ _ _ ⇒ x5 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC05_destruct_6 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
+ x6 = y6.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
+ with [ mk_alu_HC05 _ _ _ _ _ a _ _ _ _ _ _ _ ⇒ x6 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC05_destruct_7 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
+ x7 = y7.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
+ with [ mk_alu_HC05 _ _ _ _ _ _ a _ _ _ _ _ _ ⇒ x7 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC05_destruct_8 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
+ x8 = y8.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
+ with [ mk_alu_HC05 _ _ _ _ _ _ _ a _ _ _ _ _ ⇒ x8 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC05_destruct_9 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
+ x9 = y9.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
+ with [ mk_alu_HC05 _ _ _ _ _ _ _ _ a _ _ _ _ ⇒ x9 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC05_destruct_10 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
+ x10 = y10.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
+ with [ mk_alu_HC05 _ _ _ _ _ _ _ _ _ a _ _ _ ⇒ x10 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC05_destruct_11 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
+ x11 = y11.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
+ with [ mk_alu_HC05 _ _ _ _ _ _ _ _ _ _ a _ _ ⇒ x11 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC05_destruct_12 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
+ x12 = y12.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
+ with [ mk_alu_HC05 _ _ _ _ _ _ _ _ _ _ _ a _ ⇒ x12 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC05_destruct_13 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
+ x13 = y13.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
+ with [ mk_alu_HC05 _ _ _ _ _ _ _ _ _ _ _ _ a ⇒ x13 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma eq_to_eqaluHC05 : ∀alu1,alu2.alu1 = alu2 → eq_HC05_alu alu1 alu2 = true.
+ #alu1; #alu2;
+ ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nrewrite > (aluHC05_destruct_1 … H);
+ nrewrite > (aluHC05_destruct_2 … H);
+ nrewrite > (aluHC05_destruct_3 … H);
+ nrewrite > (aluHC05_destruct_4 … H);
+ nrewrite > (aluHC05_destruct_5 … H);
+ nrewrite > (aluHC05_destruct_6 … H);
+ nrewrite > (aluHC05_destruct_7 … H);
+ nrewrite > (aluHC05_destruct_8 … H);
+ nrewrite > (aluHC05_destruct_9 … H);
+ nrewrite > (aluHC05_destruct_10 … H);
+ nrewrite > (aluHC05_destruct_11 … H);
+ nrewrite > (aluHC05_destruct_12 … H);
+ nrewrite > (aluHC05_destruct_13 … H);
+ nchange with (
+ ((eqc ? y1 y1) ⊗ (eqc ? y2 y2) ⊗
+ (eqc ? y3 y3) ⊗ (eqc ? y4 y4) ⊗
+ (eqc ? y5 y5) ⊗ (eqc ? y6 y6) ⊗
+ (eqc ? y7 y7) ⊗ (eqc ? y8 y8) ⊗
+ (eqc ? y9 y9) ⊗ (eqc ? y10 y10) ⊗
+ (eqc ? y11 y11) ⊗ (eqc ? y12 y12) ⊗
+ (eqc ? y13 y13)) = true);
+ nrewrite > (eq_to_eqc ? y1 y1 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y2 y2 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y3 y3 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y4 y4 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y5 y5 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y6 y6 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y7 y7 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y8 y8 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y9 y9 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y10 y10 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y11 y11 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y12 y12 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y13 y13 (refl_eq …));
+ napply refl_eq.
+nqed.
+
+nlemma neqaluHC05_to_neq : ∀alu1,alu2.eq_HC05_alu alu1 alu2 = false → alu1 ≠ alu2.
+ #s1; #s2; #H;
+ napply (not_to_not (s1 = s2) (eq_HC05_alu s1 s2 = true) …);
+ ##[ ##1: napply (eq_to_eqaluHC05 s1 s2)
+ ##| ##2: napply (eqfalse_to_neqtrue … H)
+ ##]
+nqed.
+
+nlemma eqaluHC05_to_eq : ∀alu1,alu2.eq_HC05_alu alu1 alu2 = true → alu1 = alu2.
+ #alu1; #alu2;
+ ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
+ nchange in H:(%) with (
+ ((eqc ? x1 y1) ⊗ (eqc ? x2 y2) ⊗
+ (eqc ? x3 y3) ⊗ (eqc ? x4 y4) ⊗
+ (eqc ? x5 y5) ⊗ (eqc ? x6 y6) ⊗
+ (eqc ? x7 y7) ⊗ (eqc ? x8 y8) ⊗
+ (eqc ? x9 y9) ⊗ (eqc ? x10 y10) ⊗
+ (eqc ? x11 y11) ⊗ (eqc ? x12 y12) ⊗
+ (eqc ? x13 y13)) = true);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H));
+ nletin H1 ≝ (andb_true_true_l … H);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … (andb_true_true_l … H)));
+ nletin H2 ≝ (andb_true_true_l … H1);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H2));
+ nletin H3 ≝ (andb_true_true_l … H2);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H3));
+ nletin H4 ≝ (andb_true_true_l … H3);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H4));
+ nletin H5 ≝ (andb_true_true_l … H4);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H5));
+ nletin H6 ≝ (andb_true_true_l … H5);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H6));
+ nletin H7 ≝ (andb_true_true_l … H6);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H7));
+ nletin H8 ≝ (andb_true_true_l … H7);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H8));
+ nletin H9 ≝ (andb_true_true_l … H8);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H9));
+ nletin H10 ≝ (andb_true_true_l … H9);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H10));
+ nletin H11 ≝ (andb_true_true_l … H10);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H11));
+ nrewrite > (eqc_to_eq … (andb_true_true_l … H11));
+ napply refl_eq.
+nqed.
+
+nlemma neq_to_neqaluHC05 : ∀alu1,alu2.alu1 ≠ alu2 → eq_HC05_alu alu1 alu2 = false.
+ #s1; #s2; #H;
+ napply (neqtrue_to_eqfalse (eq_HC05_alu s1 s2));
+ napply (not_to_not (eq_HC05_alu s1 s2 = true) (s1 = s2) ? H);
+ napply (eqaluHC05_to_eq s1 s2).
+nqed.
+
+nlemma decidable_aluHC05 : ∀x,y:alu_HC05.decidable (x = y).
+ #x; #y; nnormalize;
+ napply (or2_elim (eq_HC05_alu x y = true) (eq_HC05_alu x y = false) ? (decidable_bexpr ?));
+ ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqaluHC05_to_eq … H))
+ ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqaluHC05_to_neq … H))
+ ##]
+nqed.
+
+nlemma symmetric_eqaluHC05 : symmetricT alu_HC05 bool eq_HC05_alu.
+ #alu1; #alu2;
+ ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nchange with (
+ ((eqc ? x1 y1) ⊗ (eqc ? x2 y2) ⊗ (eqc ? x3 y3) ⊗ (eqc ? x4 y4) ⊗
+ (eqc ? x5 y5) ⊗ (eqc ? x6 y6) ⊗ (eqc ? x7 y7) ⊗ (eqc ? x8 y8) ⊗
+ (eqc ? x9 y9) ⊗ (eqc ? x10 y10) ⊗ (eqc ? x11 y11) ⊗ (eqc ? x12 y12) ⊗
+ (eqc ? x13 y13)) = ((eqc ? y1 x1) ⊗ (eqc ? y2 x2) ⊗ (eqc ? y3 x3) ⊗
+ (eqc ? y4 x4) ⊗ (eqc ? y5 x5) ⊗ (eqc ? y6 x6) ⊗ (eqc ? y7 x7) ⊗
+ (eqc ? y8 x8) ⊗ (eqc ? y9 x9) ⊗ (eqc ? y10 x10) ⊗ (eqc ? y11 x11) ⊗
+ (eqc ? y12 x12) ⊗ (eqc ? y13 x13)));
+ nrewrite > (symmetric_eqc ? x1 y1);
+ nrewrite > (symmetric_eqc ? x2 y2);
+ nrewrite > (symmetric_eqc ? x3 y3);
+ nrewrite > (symmetric_eqc ? x4 y4);
+ nrewrite > (symmetric_eqc ? x5 y5);
+ nrewrite > (symmetric_eqc ? x6 y6);
+ nrewrite > (symmetric_eqc ? x7 y7);
+ nrewrite > (symmetric_eqc ? x8 y8);
+ nrewrite > (symmetric_eqc ? x9 y9);
+ nrewrite > (symmetric_eqc ? x10 y10);
+ nrewrite > (symmetric_eqc ? x11 y11);
+ nrewrite > (symmetric_eqc ? x12 y12);
+ nrewrite > (symmetric_eqc ? x13 y13);
+ napply refl_eq.
+nqed.
+
+nlemma aluHC05_is_comparable : comparable.
+ @ alu_HC05
+ ##[ napply (mk_alu_HC05 (zeroc ?) (zeroc ?) (zeroc ?) (zeroc ?)
+ (zeroc ?) (zeroc ?) (zeroc ?) (zeroc ?)
+ (zeroc ?) (zeroc ?) (zeroc ?) (zeroc ?)
+ (zeroc ?))
+ ##| napply forall_HC05_alu
+ ##| napply eq_HC05_alu
+ ##| napply eqaluHC05_to_eq
+ ##| napply eq_to_eqaluHC05
+ ##| napply neqaluHC05_to_neq
+ ##| napply neq_to_neqaluHC05
+ ##| napply decidable_aluHC05
+ ##| napply symmetric_eqaluHC05
+ ##]
+nqed.
+
+unification hint 0 ≔ ⊢ carr aluHC05_is_comparable ≡ alu_HC05.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "num/word16.ma".
+
+(* *********************************** *)
+(* STATUS INTERNO DEL PROCESSORE (ALU) *)
+(* *********************************** *)
+
+(* ALU dell'HC05 *)
+nrecord alu_HC05: Type ≝
+ {
+ (* A: registo accumulatore *)
+ acc_low_reg_HC05 : byte8;
+ (* X: registro indice *)
+ indX_low_reg_HC05 : byte8;
+ (* SP: registo stack pointer *)
+ sp_reg_HC05 : word16;
+ (* modificatori di SP: per esempio e' definito come 0000000011xxxxxxb *)
+ (* la logica della sua costruzione e' quindi (SP∧mask)∨fix *)
+ (* totalmente racchiusa nella ALU, bastera' fare get(set(SP)) *)
+ sp_mask_HC05 : word16;
+ sp_fix_HC05 : word16;
+ (* PC: registro program counter *)
+ pc_reg_HC05 : word16;
+ (* modificatore di PC: per esempio e' definito come 00xxxxxxxxxxxxxxb *)
+ (* la logica della sua costruzione e' quindi (PC∧mask) *)
+ (* totalmente racchiusa nella ALU, bastera' fare get(set(PC)) *)
+ pc_mask_HC05 : word16;
+
+ (* H: flag semi-carry (somma nibble basso) *)
+ h_flag_HC05 : bool;
+ (* I: flag mascheramento degli interrupt mascherabili: 1=mascherati *)
+ i_flag_HC05 : bool;
+ (* N: flag segno/negativita' *)
+ n_flag_HC05 : bool;
+ (* Z: flag zero *)
+ z_flag_HC05 : bool;
+ (* C: flag carry *)
+ c_flag_HC05 : bool;
+
+ (* IRQ: flag che simula il pin esterno IRQ *)
+ irq_flag_HC05 : bool
+ }.
+
+notation "{hvbox('A_Reg' ≝ acclow ; break 'X_Reg' ≝ indxlow ; break 'Sp_Reg' ≝ sp ; break 'Sp_Mask' ≝ spm ; break 'Sp_Fix' ≝ spf ; break 'Pc_Reg' ≝ pc ; break 'Pc_Mask' ≝ pcm ; break 'H_Flag' ≝ hfl ; break 'I_Flag' ≝ ifl ; break 'N_Flag' ≝ nfl ; break 'Z_Flag' ≝ zfl ; break 'C_Flag' ≝ cfl ; break 'IRQ_Flag' ≝ irqfl)}"
+ non associative with precedence 80 for
+ @{ 'mk_alu_HC05 $acclow $indxlow $sp $spm $spf $pc $pcm $hfl $ifl $nfl $zfl $cfl $irqfl }.
+interpretation "mk_alu_HC05" 'mk_alu_HC05 acclow indxlow sp spm spf pc pcm hfl ifl nfl zfl cfl irqfl =
+ (mk_alu_HC05 acclow indxlow sp spm spf pc pcm hfl ifl nfl zfl cfl irqfl).
+
+(* ****** *)
+(* SETTER *)
+(* ****** *)
+
+(* setter specifico HC05 di A *)
+ndefinition set_acc_8_low_reg_HC05 ≝
+λalu.λacclow':byte8.
+ mk_alu_HC05
+ acclow'
+ (indX_low_reg_HC05 alu)
+ (sp_reg_HC05 alu)
+ (sp_mask_HC05 alu)
+ (sp_fix_HC05 alu)
+ (pc_reg_HC05 alu)
+ (pc_mask_HC05 alu)
+ (h_flag_HC05 alu)
+ (i_flag_HC05 alu)
+ (n_flag_HC05 alu)
+ (z_flag_HC05 alu)
+ (c_flag_HC05 alu)
+ (irq_flag_HC05 alu).
+
+(* setter specifico HC05 di X *)
+ndefinition set_indX_8_low_reg_HC05 ≝
+λalu.λindxlow':byte8.
+ mk_alu_HC05
+ (acc_low_reg_HC05 alu)
+ indxlow'
+ (sp_reg_HC05 alu)
+ (sp_mask_HC05 alu)
+ (sp_fix_HC05 alu)
+ (pc_reg_HC05 alu)
+ (pc_mask_HC05 alu)
+ (h_flag_HC05 alu)
+ (i_flag_HC05 alu)
+ (n_flag_HC05 alu)
+ (z_flag_HC05 alu)
+ (c_flag_HC05 alu)
+ (irq_flag_HC05 alu).
+
+(* setter specifico HC05 di SP, effettua (SP∧mask)∨fix *)
+ndefinition set_sp_reg_HC05 ≝
+λalu.λsp':word16.
+ mk_alu_HC05
+ (acc_low_reg_HC05 alu)
+ (indX_low_reg_HC05 alu)
+ (orc ? (andc ? sp' (sp_mask_HC05 alu)) (sp_fix_HC05 alu))
+ (sp_mask_HC05 alu)
+ (sp_fix_HC05 alu)
+ (pc_reg_HC05 alu)
+ (pc_mask_HC05 alu)
+ (h_flag_HC05 alu)
+ (i_flag_HC05 alu)
+ (n_flag_HC05 alu)
+ (z_flag_HC05 alu)
+ (c_flag_HC05 alu)
+ (irq_flag_HC05 alu).
+
+(* setter specifico HC05 di PC, effettua PC∧mask *)
+ndefinition set_pc_reg_HC05 ≝
+λalu.λpc':word16.
+ mk_alu_HC05
+ (acc_low_reg_HC05 alu)
+ (indX_low_reg_HC05 alu)
+ (sp_reg_HC05 alu)
+ (sp_mask_HC05 alu)
+ (sp_fix_HC05 alu)
+ (andc ? pc' (pc_mask_HC05 alu))
+ (pc_mask_HC05 alu)
+ (h_flag_HC05 alu)
+ (i_flag_HC05 alu)
+ (n_flag_HC05 alu)
+ (z_flag_HC05 alu)
+ (c_flag_HC05 alu)
+ (irq_flag_HC05 alu).
+
+(* setter specifico HC05 di H *)
+ndefinition set_h_flag_HC05 ≝
+λalu.λhfl':bool.
+ mk_alu_HC05
+ (acc_low_reg_HC05 alu)
+ (indX_low_reg_HC05 alu)
+ (sp_reg_HC05 alu)
+ (sp_mask_HC05 alu)
+ (sp_fix_HC05 alu)
+ (pc_reg_HC05 alu)
+ (pc_mask_HC05 alu)
+ hfl'
+ (i_flag_HC05 alu)
+ (n_flag_HC05 alu)
+ (z_flag_HC05 alu)
+ (c_flag_HC05 alu)
+ (irq_flag_HC05 alu).
+
+(* setter specifico HC05 di I *)
+ndefinition set_i_flag_HC05 ≝
+λalu.λifl':bool.
+ mk_alu_HC05
+ (acc_low_reg_HC05 alu)
+ (indX_low_reg_HC05 alu)
+ (sp_reg_HC05 alu)
+ (sp_mask_HC05 alu)
+ (sp_fix_HC05 alu)
+ (pc_reg_HC05 alu)
+ (pc_mask_HC05 alu)
+ (h_flag_HC05 alu)
+ ifl'
+ (n_flag_HC05 alu)
+ (z_flag_HC05 alu)
+ (c_flag_HC05 alu)
+ (irq_flag_HC05 alu).
+
+(* setter specifico HC05 di N *)
+ndefinition set_n_flag_HC05 ≝
+λalu.λnfl':bool.
+ mk_alu_HC05
+ (acc_low_reg_HC05 alu)
+ (indX_low_reg_HC05 alu)
+ (sp_reg_HC05 alu)
+ (sp_mask_HC05 alu)
+ (sp_fix_HC05 alu)
+ (pc_reg_HC05 alu)
+ (pc_mask_HC05 alu)
+ (h_flag_HC05 alu)
+ (i_flag_HC05 alu)
+ nfl'
+ (z_flag_HC05 alu)
+ (c_flag_HC05 alu)
+ (irq_flag_HC05 alu).
+
+(* setter specifico HC05 di Z *)
+ndefinition set_z_flag_HC05 ≝
+λalu.λzfl':bool.
+ mk_alu_HC05
+ (acc_low_reg_HC05 alu)
+ (indX_low_reg_HC05 alu)
+ (sp_reg_HC05 alu)
+ (sp_mask_HC05 alu)
+ (sp_fix_HC05 alu)
+ (pc_reg_HC05 alu)
+ (pc_mask_HC05 alu)
+ (h_flag_HC05 alu)
+ (i_flag_HC05 alu)
+ (n_flag_HC05 alu)
+ zfl'
+ (c_flag_HC05 alu)
+ (irq_flag_HC05 alu).
+
+(* setter specifico HC05 di C *)
+ndefinition set_c_flag_HC05 ≝
+λalu.λcfl':bool.
+ mk_alu_HC05
+ (acc_low_reg_HC05 alu)
+ (indX_low_reg_HC05 alu)
+ (sp_reg_HC05 alu)
+ (sp_mask_HC05 alu)
+ (sp_fix_HC05 alu)
+ (pc_reg_HC05 alu)
+ (pc_mask_HC05 alu)
+ (h_flag_HC05 alu)
+ (i_flag_HC05 alu)
+ (n_flag_HC05 alu)
+ (z_flag_HC05 alu)
+ cfl'
+ (irq_flag_HC05 alu).
+
+(* setter specifico HC05 di IRQ *)
+ndefinition set_irq_flag_HC05 ≝
+λalu.λirqfl':bool.
+ mk_alu_HC05
+ (acc_low_reg_HC05 alu)
+ (indX_low_reg_HC05 alu)
+ (sp_reg_HC05 alu)
+ (sp_mask_HC05 alu)
+ (sp_fix_HC05 alu)
+ (pc_reg_HC05 alu)
+ (pc_mask_HC05 alu)
+ (h_flag_HC05 alu)
+ (i_flag_HC05 alu)
+ (n_flag_HC05 alu)
+ (z_flag_HC05 alu)
+ (c_flag_HC05 alu)
+ irqfl'.
+
+(* ***************** *)
+(* CONFRONTO FRA ALU *)
+(* ***************** *)
+
+(* confronto registro per registro dell'HC05 *)
+ndefinition eq_HC05_alu ≝
+λalu1,alu2:alu_HC05.
+ (eqc ? (acc_low_reg_HC05 alu1) (acc_low_reg_HC05 alu2)) ⊗
+ (eqc ? (indX_low_reg_HC05 alu1) (indX_low_reg_HC05 alu2)) ⊗
+ (eqc ? (sp_reg_HC05 alu1) (sp_reg_HC05 alu2)) ⊗
+ (eqc ? (sp_mask_HC05 alu1) (sp_mask_HC05 alu2)) ⊗
+ (eqc ? (sp_fix_HC05 alu1) (sp_fix_HC05 alu2)) ⊗
+ (eqc ? (pc_reg_HC05 alu1) (pc_reg_HC05 alu2)) ⊗
+ (eqc ? (pc_mask_HC05 alu1) (pc_mask_HC05 alu2)) ⊗
+ (eqc ? (h_flag_HC05 alu1) (h_flag_HC05 alu2)) ⊗
+ (eqc ? (i_flag_HC05 alu1) (i_flag_HC05 alu2)) ⊗
+ (eqc ? (n_flag_HC05 alu1) (n_flag_HC05 alu2)) ⊗
+ (eqc ? (z_flag_HC05 alu1) (z_flag_HC05 alu2)) ⊗
+ (eqc ? (c_flag_HC05 alu1) (c_flag_HC05 alu2)) ⊗
+ (eqc ? (irq_flag_HC05 alu1) (irq_flag_HC05 alu2)).
+
+ndefinition forall_HC05_alu ≝ λP:alu_HC05 → bool.
+ forallc ? (λr1.forallc ? (λr2.
+ forallc ? (λr3.forallc ? (λr4.
+ forallc ? (λr5.forallc ? (λr6.
+ forallc ? (λr7.forallc ? (λr8.
+ forallc ? (λr9.forallc ? (λr10.
+ forallc ? (λr11.forallc ? (λr12.
+ forallc ? (λr13.P (mk_alu_HC05 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13)))))))))))))).
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/status/HC08_status_base.ma".
+
+(* *********************************** *)
+(* STATUS INTERNO DEL PROCESSORE (ALU) *)
+(* *********************************** *)
+
+nlemma aluHC08_destruct_1 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
+ x1 = y1.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
+ nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
+ with [ mk_alu_HC08 a _ _ _ _ _ _ _ _ _ _ _ ⇒ x1 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC08_destruct_2 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
+ x2 = y2.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
+ nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
+ with [ mk_alu_HC08 _ a _ _ _ _ _ _ _ _ _ _ ⇒ x2 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC08_destruct_3 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
+ x3 = y3.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
+ nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
+ with [ mk_alu_HC08 _ _ a _ _ _ _ _ _ _ _ _ ⇒ x3 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC08_destruct_4 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
+ x4 = y4.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
+ nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
+ with [ mk_alu_HC08 _ _ _ a _ _ _ _ _ _ _ _ ⇒ x4 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC08_destruct_5 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
+ x5 = y5.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
+ nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
+ with [ mk_alu_HC08 _ _ _ _ a _ _ _ _ _ _ _ ⇒ x5 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC08_destruct_6 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
+ x6 = y6.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
+ nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
+ with [ mk_alu_HC08 _ _ _ _ _ a _ _ _ _ _ _ ⇒ x6 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC08_destruct_7 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
+ x7 = y7.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
+ nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
+ with [ mk_alu_HC08 _ _ _ _ _ _ a _ _ _ _ _ ⇒ x7 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC08_destruct_8 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
+ x8 = y8.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
+ nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
+ with [ mk_alu_HC08 _ _ _ _ _ _ _ a _ _ _ _ ⇒ x8 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC08_destruct_9 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
+ x9 = y9.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
+ nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
+ with [ mk_alu_HC08 _ _ _ _ _ _ _ _ a _ _ _ ⇒ x9 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC08_destruct_10 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
+ x10 = y10.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
+ nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
+ with [ mk_alu_HC08 _ _ _ _ _ _ _ _ _ a _ _ ⇒ x10 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC08_destruct_11 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
+ x11 = y11.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
+ nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
+ with [ mk_alu_HC08 _ _ _ _ _ _ _ _ _ _ a _ ⇒ x11 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluHC08_destruct_12 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
+ x12 = y12.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
+ nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
+ with [ mk_alu_HC08 _ _ _ _ _ _ _ _ _ _ _ a ⇒ x12 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma eq_to_eqaluHC08 : ∀alu1,alu2.alu1 = alu2 → eq_HC08_alu alu1 alu2 = true.
+ #alu1; #alu2;
+ ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
+ nrewrite > (aluHC08_destruct_1 … H);
+ nrewrite > (aluHC08_destruct_2 … H);
+ nrewrite > (aluHC08_destruct_3 … H);
+ nrewrite > (aluHC08_destruct_4 … H);
+ nrewrite > (aluHC08_destruct_5 … H);
+ nrewrite > (aluHC08_destruct_6 … H);
+ nrewrite > (aluHC08_destruct_7 … H);
+ nrewrite > (aluHC08_destruct_8 … H);
+ nrewrite > (aluHC08_destruct_9 … H);
+ nrewrite > (aluHC08_destruct_10 … H);
+ nrewrite > (aluHC08_destruct_11 … H);
+ nrewrite > (aluHC08_destruct_12 … H);
+ nchange with (
+ ((eqc ? y1 y1) ⊗ (eqc ? y2 y2) ⊗ (eqc ? y3 y3) ⊗ (eqc ? y4 y4) ⊗
+ (eqc ? y5 y5) ⊗ (eqc ? y6 y6) ⊗ (eqc ? y7 y7) ⊗ (eqc ? y8 y8) ⊗
+ (eqc ? y9 y9) ⊗ (eqc ? y10 y10) ⊗ (eqc ? y11 y11) ⊗ (eqc ? y12 y12)) = true);
+ nrewrite > (eq_to_eqc ? y1 y1 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y2 y2 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y3 y3 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y4 y4 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y5 y5 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y6 y6 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y7 y7 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y8 y8 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y9 y9 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y10 y10 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y11 y11 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y12 y12 (refl_eq …));
+ napply refl_eq.
+nqed.
+
+nlemma neqaluHC08_to_neq : ∀alu1,alu2.eq_HC08_alu alu1 alu2 = false → alu1 ≠ alu2.
+ #s1; #s2; #H;
+ napply (not_to_not (s1 = s2) (eq_HC08_alu s1 s2 = true) …);
+ ##[ ##1: napply (eq_to_eqaluHC08 s1 s2)
+ ##| ##2: napply (eqfalse_to_neqtrue … H)
+ ##]
+nqed.
+
+nlemma eqaluHC08_to_eq : ∀alu1,alu2.eq_HC08_alu alu1 alu2 = true → alu1 = alu2.
+ #alu1; #alu2;
+ ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
+ nchange in H:(%) with (
+ ((eqc ? x1 y1) ⊗ (eqc ? x2 y2) ⊗ (eqc ? x3 y3) ⊗ (eqc ? x4 y4) ⊗
+ (eqc ? x5 y5) ⊗ (eqc ? x6 y6) ⊗ (eqc ? x7 y7) ⊗ (eqc ? x8 y8) ⊗
+ (eqc ? x9 y9) ⊗ (eqc ? x10 y10) ⊗ (eqc ? x11 y11) ⊗ (eqc ? x12 y12)) = true);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H));
+ nletin H1 ≝ (andb_true_true_l … H);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H1));
+ nletin H2 ≝ (andb_true_true_l … H1);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H2));
+ nletin H3 ≝ (andb_true_true_l … H2);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H3));
+ nletin H4 ≝ (andb_true_true_l … H3);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H4));
+ nletin H5 ≝ (andb_true_true_l … H4);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H5));
+ nletin H6 ≝ (andb_true_true_l … H5);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H6));
+ nletin H7 ≝ (andb_true_true_l … H6);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H7));
+ nletin H8 ≝ (andb_true_true_l … H7);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H8));
+ nletin H9 ≝ (andb_true_true_l … H8);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H9));
+ nletin H10 ≝ (andb_true_true_l … H9);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H10));
+ nrewrite > (eqc_to_eq … (andb_true_true_l … H10));
+ napply refl_eq.
+nqed.
+
+nlemma neq_to_neqaluHC08 : ∀alu1,alu2.alu1 ≠ alu2 → eq_HC08_alu alu1 alu2 = false.
+ #s1; #s2; #H;
+ napply (neqtrue_to_eqfalse (eq_HC08_alu s1 s2));
+ napply (not_to_not (eq_HC08_alu s1 s2 = true) (s1 = s2) ? H);
+ napply (eqaluHC08_to_eq s1 s2).
+nqed.
+
+nlemma decidable_aluHC08 : ∀x,y:alu_HC08.decidable (x = y).
+ #x; #y; nnormalize;
+ napply (or2_elim (eq_HC08_alu x y = true) (eq_HC08_alu x y = false) ? (decidable_bexpr ?));
+ ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqaluHC08_to_eq … H))
+ ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqaluHC08_to_neq … H))
+ ##]
+nqed.
+
+nlemma symmetric_eqaluHC08 : symmetricT alu_HC08 bool eq_HC08_alu.
+ #alu1; #alu2;
+ ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
+ nchange with (
+ ((eqc ? x1 y1) ⊗ (eqc ? x2 y2) ⊗ (eqc ? x3 y3) ⊗ (eqc ? x4 y4) ⊗
+ (eqc ? x5 y5) ⊗ (eqc ? x6 y6) ⊗ (eqc ? x7 y7) ⊗ (eqc ? x8 y8) ⊗
+ (eqc ? x9 y9) ⊗ (eqc ? x10 y10) ⊗ (eqc ? x11 y11) ⊗ (eqc ? x12 y12)) =
+ ((eqc ? y1 x1) ⊗ (eqc ? y2 x2) ⊗ (eqc ? y3 x3) ⊗ (eqc ? y4 x4) ⊗
+ (eqc ? y5 x5) ⊗ (eqc ? y6 x6) ⊗ (eqc ? y7 x7) ⊗ (eqc ? y8 x8) ⊗
+ (eqc ? y9 x9) ⊗ (eqc ? y10 x10) ⊗ (eqc ? y11 x11) ⊗ (eqc ? y12 x12)));
+ nrewrite > (symmetric_eqc ? x1 y1);
+ nrewrite > (symmetric_eqc ? x2 y2);
+ nrewrite > (symmetric_eqc ? x3 y3);
+ nrewrite > (symmetric_eqc ? x4 y4);
+ nrewrite > (symmetric_eqc ? x5 y5);
+ nrewrite > (symmetric_eqc ? x6 y6);
+ nrewrite > (symmetric_eqc ? x7 y7);
+ nrewrite > (symmetric_eqc ? x8 y8);
+ nrewrite > (symmetric_eqc ? x9 y9);
+ nrewrite > (symmetric_eqc ? x10 y10);
+ nrewrite > (symmetric_eqc ? x11 y11);
+ nrewrite > (symmetric_eqc ? x12 y12);
+ napply refl_eq.
+nqed.
+
+nlemma aluHC08_is_comparable : comparable.
+ @ alu_HC08
+ ##[ napply (mk_alu_HC08 (zeroc ?) (zeroc ?) (zeroc ?) (zeroc ?)
+ (zeroc ?) (zeroc ?) (zeroc ?) (zeroc ?)
+ (zeroc ?) (zeroc ?) (zeroc ?) (zeroc ?))
+ ##| napply forall_HC08_alu
+ ##| napply eq_HC08_alu
+ ##| napply eqaluHC08_to_eq
+ ##| napply eq_to_eqaluHC08
+ ##| napply neqaluHC08_to_neq
+ ##| napply neq_to_neqaluHC08
+ ##| napply decidable_aluHC08
+ ##| napply symmetric_eqaluHC08
+ ##]
+nqed.
+
+unification hint 0 ≔ ⊢ carr aluHC08_is_comparable ≡ alu_HC08.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "num/word16.ma".
+
+(* *********************************** *)
+(* STATUS INTERNO DEL PROCESSORE (ALU) *)
+(* *********************************** *)
+
+(* ALU dell'HC08/HCS08 *)
+nrecord alu_HC08: Type ≝
+ {
+ (* A: registo accumulatore *)
+ acc_low_reg_HC08 : byte8;
+ (* X: registro indice parte bassa *)
+ indX_low_reg_HC08 : byte8;
+ (* H: registro indice parte alta *)
+ indX_high_reg_HC08 : byte8;
+ (* SP: registo stack pointer *)
+ sp_reg_HC08 : word16;
+ (* PC: registro program counter *)
+ pc_reg_HC08 : word16;
+
+ (* V: flag overflow *)
+ v_flag_HC08 : bool;
+ (* H: flag semi-carry (somma nibble basso) *)
+ h_flag_HC08 : bool;
+ (* I: flag mascheramento degli interrupt mascherabili: 1=mascherati *)
+ i_flag_HC08 : bool;
+ (* N: flag segno/negativita' *)
+ n_flag_HC08 : bool;
+ (* Z: flag zero *)
+ z_flag_HC08 : bool;
+ (* C: flag carry *)
+ c_flag_HC08 : bool;
+
+ (* IRQ: flag che simula il pin esterno IRQ *)
+ irq_flag_HC08 : bool
+ }.
+
+notation "{hvbox('A_Reg' ≝ acclow ; break 'X_Reg' ≝ indxlow ; break 'H_Reg' ≝ indxhigh ; break 'Sp_Reg' ≝ sp ; break 'Pc_Reg' ≝ pc ; break 'V_Flag' ≝ vfl ; break 'H_Flag' ≝ hfl ; break 'I_Flag' ≝ ifl ; break 'N_Flag' ≝ nfl ; break 'Z_Flag' ≝ zfl ; break 'C_Flag' ≝ cfl ; break 'IRQ_Flag' ≝ irqfl)}"
+ non associative with precedence 80 for
+ @{ 'mk_alu_HC08 $acclow $indxlow $indxhigh $sp $pc $vfl $hfl $ifl $nfl $zfl $cfl $irqfl }.
+interpretation "mk_alu_HC08" 'mk_alu_HC08 acclow indxlow indxhigh sp pc vfl hfl ifl nfl zfl cfl irqfl =
+ (mk_alu_HC08 acclow indxlow indxhigh sp pc vfl hfl ifl nfl zfl cfl irqfl).
+
+(* ****** *)
+(* SETTER *)
+(* ****** *)
+
+(* setter specifico HC08/HCS08 di A *)
+ndefinition set_acc_8_low_reg_HC08 ≝
+λalu.λacclow':byte8.
+ mk_alu_HC08
+ acclow'
+ (indX_low_reg_HC08 alu)
+ (indX_high_reg_HC08 alu)
+ (sp_reg_HC08 alu)
+ (pc_reg_HC08 alu)
+ (v_flag_HC08 alu)
+ (h_flag_HC08 alu)
+ (i_flag_HC08 alu)
+ (n_flag_HC08 alu)
+ (z_flag_HC08 alu)
+ (c_flag_HC08 alu)
+ (irq_flag_HC08 alu).
+
+(* setter specifico HC08/HCS08 di X *)
+ndefinition set_indX_8_low_reg_HC08 ≝
+λalu.λindxlow':byte8.
+ mk_alu_HC08
+ (acc_low_reg_HC08 alu)
+ indxlow'
+ (indX_high_reg_HC08 alu)
+ (sp_reg_HC08 alu)
+ (pc_reg_HC08 alu)
+ (v_flag_HC08 alu)
+ (h_flag_HC08 alu)
+ (i_flag_HC08 alu)
+ (n_flag_HC08 alu)
+ (z_flag_HC08 alu)
+ (c_flag_HC08 alu)
+ (irq_flag_HC08 alu).
+
+(* setter specifico HC08/HCS08 di H *)
+ndefinition set_indX_8_high_reg_HC08 ≝
+λalu.λindxhigh':byte8.
+ mk_alu_HC08
+ (acc_low_reg_HC08 alu)
+ (indX_low_reg_HC08 alu)
+ indxhigh'
+ (sp_reg_HC08 alu)
+ (pc_reg_HC08 alu)
+ (v_flag_HC08 alu)
+ (h_flag_HC08 alu)
+ (i_flag_HC08 alu)
+ (n_flag_HC08 alu)
+ (z_flag_HC08 alu)
+ (c_flag_HC08 alu)
+ (irq_flag_HC08 alu).
+
+(* setter specifico HC08/HCS08 di H:X *)
+ndefinition set_indX_16_reg_HC08 ≝
+λalu.λindx16:word16.
+ mk_alu_HC08
+ (acc_low_reg_HC08 alu)
+ (cnL ? indx16)
+ (cnH ? indx16)
+ (sp_reg_HC08 alu)
+ (pc_reg_HC08 alu)
+ (v_flag_HC08 alu)
+ (h_flag_HC08 alu)
+ (i_flag_HC08 alu)
+ (n_flag_HC08 alu)
+ (z_flag_HC08 alu)
+ (c_flag_HC08 alu)
+ (irq_flag_HC08 alu).
+
+(* setter specifico HC08/HCS08 di SP *)
+ndefinition set_sp_reg_HC08 ≝
+λalu.λsp':word16.
+ mk_alu_HC08
+ (acc_low_reg_HC08 alu)
+ (indX_low_reg_HC08 alu)
+ (indX_high_reg_HC08 alu)
+ sp'
+ (pc_reg_HC08 alu)
+ (v_flag_HC08 alu)
+ (h_flag_HC08 alu)
+ (i_flag_HC08 alu)
+ (n_flag_HC08 alu)
+ (z_flag_HC08 alu)
+ (c_flag_HC08 alu)
+ (irq_flag_HC08 alu).
+
+(* setter specifico HC08/HCS08 di PC *)
+ndefinition set_pc_reg_HC08 ≝
+λalu.λpc':word16.
+ mk_alu_HC08
+ (acc_low_reg_HC08 alu)
+ (indX_low_reg_HC08 alu)
+ (indX_high_reg_HC08 alu)
+ (sp_reg_HC08 alu)
+ pc'
+ (v_flag_HC08 alu)
+ (h_flag_HC08 alu)
+ (i_flag_HC08 alu)
+ (n_flag_HC08 alu)
+ (z_flag_HC08 alu)
+ (c_flag_HC08 alu)
+ (irq_flag_HC08 alu).
+
+(* setter specifico HC08/HCS08 di V *)
+ndefinition set_v_flag_HC08 ≝
+λalu.λvfl':bool.
+ mk_alu_HC08
+ (acc_low_reg_HC08 alu)
+ (indX_low_reg_HC08 alu)
+ (indX_high_reg_HC08 alu)
+ (sp_reg_HC08 alu)
+ (pc_reg_HC08 alu)
+ vfl'
+ (h_flag_HC08 alu)
+ (i_flag_HC08 alu)
+ (n_flag_HC08 alu)
+ (z_flag_HC08 alu)
+ (c_flag_HC08 alu)
+ (irq_flag_HC08 alu).
+
+(* setter specifico HC08/HCS08 di H *)
+ndefinition set_h_flag_HC08 ≝
+λalu.λhfl':bool.
+ mk_alu_HC08
+ (acc_low_reg_HC08 alu)
+ (indX_low_reg_HC08 alu)
+ (indX_high_reg_HC08 alu)
+ (sp_reg_HC08 alu)
+ (pc_reg_HC08 alu)
+ (v_flag_HC08 alu)
+ hfl'
+ (i_flag_HC08 alu)
+ (n_flag_HC08 alu)
+ (z_flag_HC08 alu)
+ (c_flag_HC08 alu)
+ (irq_flag_HC08 alu).
+
+(* setter specifico HC08/HCS08 di I *)
+ndefinition set_i_flag_HC08 ≝
+λalu.λifl':bool.
+ mk_alu_HC08
+ (acc_low_reg_HC08 alu)
+ (indX_low_reg_HC08 alu)
+ (indX_high_reg_HC08 alu)
+ (sp_reg_HC08 alu)
+ (pc_reg_HC08 alu)
+ (v_flag_HC08 alu)
+ (h_flag_HC08 alu)
+ ifl'
+ (n_flag_HC08 alu)
+ (z_flag_HC08 alu)
+ (c_flag_HC08 alu)
+ (irq_flag_HC08 alu).
+
+(* setter specifico HC08/HCS08 di N *)
+ndefinition set_n_flag_HC08 ≝
+λalu.λnfl':bool.
+ mk_alu_HC08
+ (acc_low_reg_HC08 alu)
+ (indX_low_reg_HC08 alu)
+ (indX_high_reg_HC08 alu)
+ (sp_reg_HC08 alu)
+ (pc_reg_HC08 alu)
+ (v_flag_HC08 alu)
+ (h_flag_HC08 alu)
+ (i_flag_HC08 alu)
+ nfl'
+ (z_flag_HC08 alu)
+ (c_flag_HC08 alu)
+ (irq_flag_HC08 alu).
+
+(* setter specifico HC08/HCS08 di Z *)
+ndefinition set_z_flag_HC08 ≝
+λalu.λzfl':bool.
+ mk_alu_HC08
+ (acc_low_reg_HC08 alu)
+ (indX_low_reg_HC08 alu)
+ (indX_high_reg_HC08 alu)
+ (sp_reg_HC08 alu)
+ (pc_reg_HC08 alu)
+ (v_flag_HC08 alu)
+ (h_flag_HC08 alu)
+ (i_flag_HC08 alu)
+ (n_flag_HC08 alu)
+ zfl'
+ (c_flag_HC08 alu)
+ (irq_flag_HC08 alu).
+
+(* setter specifico HC08/HCS08 di C *)
+ndefinition set_c_flag_HC08 ≝
+λalu.λcfl':bool.
+ mk_alu_HC08
+ (acc_low_reg_HC08 alu)
+ (indX_low_reg_HC08 alu)
+ (indX_high_reg_HC08 alu)
+ (sp_reg_HC08 alu)
+ (pc_reg_HC08 alu)
+ (v_flag_HC08 alu)
+ (h_flag_HC08 alu)
+ (i_flag_HC08 alu)
+ (n_flag_HC08 alu)
+ (z_flag_HC08 alu)
+ cfl'
+ (irq_flag_HC08 alu).
+
+(* setter specifico HC08/HCS08 di IRQ *)
+ndefinition set_irq_flag_HC08 ≝
+λalu.λirqfl':bool.
+ mk_alu_HC08
+ (acc_low_reg_HC08 alu)
+ (indX_low_reg_HC08 alu)
+ (indX_high_reg_HC08 alu)
+ (sp_reg_HC08 alu)
+ (pc_reg_HC08 alu)
+ (v_flag_HC08 alu)
+ (h_flag_HC08 alu)
+ (i_flag_HC08 alu)
+ (n_flag_HC08 alu)
+ (z_flag_HC08 alu)
+ (c_flag_HC08 alu)
+ irqfl'.
+
+(* ***************** *)
+(* CONFRONTO FRA ALU *)
+(* ***************** *)
+
+(* confronto registro per registro dell'HC08 *)
+ndefinition eq_HC08_alu ≝
+λalu1,alu2:alu_HC08.
+ (eqc ? (acc_low_reg_HC08 alu1) (acc_low_reg_HC08 alu2)) ⊗
+ (eqc ? (indX_low_reg_HC08 alu1) (indX_low_reg_HC08 alu2)) ⊗
+ (eqc ? (indX_high_reg_HC08 alu1) (indX_high_reg_HC08 alu2)) ⊗
+ (eqc ? (sp_reg_HC08 alu1) (sp_reg_HC08 alu2)) ⊗
+ (eqc ? (pc_reg_HC08 alu1) (pc_reg_HC08 alu2)) ⊗
+ (eqc ? (v_flag_HC08 alu1) (v_flag_HC08 alu2)) ⊗
+ (eqc ? (h_flag_HC08 alu1) (h_flag_HC08 alu2)) ⊗
+ (eqc ? (i_flag_HC08 alu1) (i_flag_HC08 alu2)) ⊗
+ (eqc ? (n_flag_HC08 alu1) (n_flag_HC08 alu2)) ⊗
+ (eqc ? (z_flag_HC08 alu1) (z_flag_HC08 alu2)) ⊗
+ (eqc ? (c_flag_HC08 alu1) (c_flag_HC08 alu2)) ⊗
+ (eqc ? (irq_flag_HC08 alu1) (irq_flag_HC08 alu2)).
+
+ndefinition forall_HC08_alu ≝ λP:alu_HC08 → bool.
+ forallc ? (λr1.forallc ? (λr2.
+ forallc ? (λr3.forallc ? (λr4.
+ forallc ? (λr5.forallc ? (λr6.
+ forallc ? (λr7.forallc ? (λr8.
+ forallc ? (λr9.forallc ? (λr10.
+ forallc ? (λr11.forallc ? (λr12.
+ P (mk_alu_HC08 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12))))))))))))).
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/status/IP2022_status_base.ma".
+
+(* *********************************** *)
+(* STATUS INTERNO DEL PROCESSORE (ALU) *)
+(* *********************************** *)
+
+nlemma aluIP2022_destruct_1 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x1 = y1.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 a _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x1 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_2 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x2 = y2.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ a _ _ _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x2 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_3 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x3 = y3.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ a _ _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x3 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_4 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x4 = y4.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ a _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x4 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_5 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x5 = y5.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ a _ _ _ _ _ _ _ _ _ _ _ ⇒ x5 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_6 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x6 = y6.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ a _ _ _ _ _ _ _ _ _ _ ⇒ x6 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_7 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x7 = y7.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ a _ _ _ _ _ _ _ _ _ ⇒ x7 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_8 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x8 = y8.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ a _ _ _ _ _ _ _ _ ⇒ x8 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_9 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x9 = y9.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ a _ _ _ _ _ _ _ ⇒ x9 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_10 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x10 = y10.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ _ a _ _ _ _ _ _ ⇒ x10 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_11 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x11 = y11.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ _ _ a _ _ _ _ _ ⇒ x11 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_12 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x12 = y12.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ _ _ _ a _ _ _ _ ⇒ x12 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_13 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x13 = y13.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ _ _ _ _ a _ _ _ ⇒ x13 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_14 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x14 = y14.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ _ _ _ _ _ a _ _ ⇒ x14 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_15 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x15 = y15.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ _ _ _ _ _ _ a _ ⇒ x15 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_16 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x16 = y16.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ a ⇒ x16 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+(* !!! ci mette troppo tempo a compilare *)
+naxiom eq_to_eqaluIP2022 : ∀alu1,alu2.alu1 = alu2 → eq_IP2022_alu alu1 alu2 = true.
+(* #alu1; ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #alu2; ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nrewrite > (aluIP2022_destruct_1 … H);
+ nrewrite > (aluIP2022_destruct_2 … H);
+ nrewrite > (aluIP2022_destruct_3 … H);
+ nrewrite > (aluIP2022_destruct_4 … H);
+ nrewrite > (aluIP2022_destruct_5 … H);
+ nrewrite > (aluIP2022_destruct_6 … H);
+ nrewrite > (aluIP2022_destruct_7 … H);
+ nrewrite > (aluIP2022_destruct_8 … H);
+ nrewrite > (aluIP2022_destruct_9 … H);
+ nrewrite > (aluIP2022_destruct_10 … H);
+ nrewrite > (aluIP2022_destruct_11 … H);
+ nrewrite > (aluIP2022_destruct_12 … H);
+ nrewrite > (aluIP2022_destruct_13 … H);
+ nrewrite > (aluIP2022_destruct_14 … H);
+ nrewrite > (aluIP2022_destruct_15 … H);
+ nrewrite > (aluIP2022_destruct_16 … H);
+ nchange with (
+ ((eqc ? y1 y1) ⊗ (eqc ? y2 y2) ⊗ (eqc ? y3 y3) ⊗ (eqc ? y4 y4) ⊗
+ (eqc ? y5 y5) ⊗ (eqc ? y6 y6) ⊗ (eqc ? y7 y7) ⊗ (eqc ? y8 y8) ⊗
+ (eqc ? y9 y9) ⊗ (eqc ? y10 y10) ⊗ (eqc ? y11 y11) ⊗ (eqc ? y12 y12) ⊗
+ (eqc ? y13 y13) ⊗ (eqc ? y14 y14) ⊗ (eqc ? y15 y15) ⊗ (eqc ? y16 y16)) = true);
+ nrewrite > (eq_to_eqc ? y1 y1 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y2 y2 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y3 y3 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y4 y4 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y5 y5 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y6 y6 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y7 y7 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y8 y8 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y9 y9 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y10 y10 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y11 y11 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y12 y12 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y13 y13 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y14 y14 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y15 y15 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y16 y16 (refl_eq …));
+ napply refl_eq.
+nqed.*)
+
+nlemma neqaluIP2022_to_neq : ∀alu1,alu2.eq_IP2022_alu alu1 alu2 = false → alu1 ≠ alu2.
+ #s1; #s2; #H;
+ napply (not_to_not (s1 = s2) (eq_IP2022_alu s1 s2 = true) …);
+ ##[ ##1: napply (eq_to_eqaluIP2022 s1 s2)
+ ##| ##2: napply (eqfalse_to_neqtrue … H)
+ ##]
+nqed.
+
+nlemma eqaluIP2022_to_eq : ∀alu1,alu2.eq_IP2022_alu alu1 alu2 = true → alu1 = alu2.
+ #alu1; ncases alu1;
+ #z1; #z2; #z3; #z4; #z5; #z6; #z7; #z8; #z9; #z10; #z11; #z12; #z13; #z14; #z15; #z16;
+ #alu2; ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange in H:(%) with (
+ ((eqc ? z1 y1) ⊗ (eqc ? z2 y2) ⊗ (eqc ? z3 y3) ⊗ (eqc ? z4 y4) ⊗
+ (eqc ? z5 y5) ⊗ (eqc ? z6 y6) ⊗ (eqc ? z7 y7) ⊗ (eqc ? z8 y8) ⊗
+ (eqc ? z9 y9) ⊗ (eqc ? z10 y10) ⊗ (eqc ? z11 y11) ⊗ (eqc ? z12 y12) ⊗
+ (eqc ? z13 y13) ⊗ (eqc ? z14 y14) ⊗ (eqc ? z15 y15) ⊗ (eqc ? z16 y16)) = true);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H));
+ nletin H1 ≝ (andb_true_true_l … H);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … (andb_true_true_l … H)));
+ nletin H2 ≝ (andb_true_true_l … H1);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H2));
+ nletin H3 ≝ (andb_true_true_l … H2);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H3));
+ nletin H4 ≝ (andb_true_true_l … H3);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H4));
+ nletin H5 ≝ (andb_true_true_l … H4);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H5));
+ nletin H6 ≝ (andb_true_true_l … H5);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H6));
+ nletin H7 ≝ (andb_true_true_l … H6);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H7));
+ nletin H8 ≝ (andb_true_true_l … H7);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H8));
+ nletin H9 ≝ (andb_true_true_l … H8);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H9));
+ nletin H10 ≝ (andb_true_true_l … H9);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H10));
+ nletin H11 ≝ (andb_true_true_l … H10);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H11));
+ nletin H12 ≝ (andb_true_true_l … H11);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H12));
+ nletin H13 ≝ (andb_true_true_l … H12);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H13));
+ nletin H14 ≝ (andb_true_true_l … H13);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H14));
+ nrewrite > (eqc_to_eq … (andb_true_true_l … H14));
+ napply refl_eq.
+nqed.
+
+nlemma neq_to_neqaluIP2022 : ∀alu1,alu2.alu1 ≠ alu2 → eq_IP2022_alu alu1 alu2 = false.
+ #s1; #s2; #H;
+ napply (neqtrue_to_eqfalse (eq_IP2022_alu s1 s2));
+ napply (not_to_not (eq_IP2022_alu s1 s2 = true) (s1 = s2) ? H);
+ napply (eqaluIP2022_to_eq s1 s2).
+nqed.
+
+nlemma decidable_aluIP2022 : ∀x,y:alu_IP2022.decidable (x = y).
+ #x; #y; nnormalize;
+ napply (or2_elim (eq_IP2022_alu x y = true) (eq_IP2022_alu x y = false) ? (decidable_bexpr ?));
+ ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqaluIP2022_to_eq … H))
+ ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqaluIP2022_to_neq … H))
+ ##]
+nqed.
+
+(* !!! ci mette troppo tempo a compilare *)
+naxiom symmetric_eqaluIP2022 : symmetricT alu_IP2022 bool eq_IP2022_alu.
+(* #alu1; ncases alu1;
+ #z1; #z2; #z3; #z4; #z5; #z6; #z7; #z8; #z9; #z10; #z11; #z12; #z13; #z14; #z15; #z16;
+ #alu2; ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nchange with (
+ ((eqc ? z1 y1) ⊗ (eqc ? z2 y2) ⊗ (eqc ? z3 y3) ⊗ (eqc ? z4 y4) ⊗
+ (eqc ? z5 y5) ⊗ (eqc ? z6 y6) ⊗ (eqc ? z7 y7) ⊗ (eqc ? z8 y8) ⊗
+ (eqc ? z9 y9) ⊗ (eqc ? z10 y10) ⊗ (eqc ? z11 y11) ⊗ (eqc ? z12 y12) ⊗
+ (eqc ? z13 y13) ⊗ (eqc ? z14 y14) ⊗ (eqc ? z15 y15) ⊗ (eqc ? z16 y16)) =
+ ((eqc ? y1 z1) ⊗ (eqc ? y2 z2) ⊗ (eqc ? y3 z3) ⊗ (eqc ? y4 z4) ⊗
+ (eqc ? y5 z5) ⊗ (eqc ? y6 z6) ⊗ (eqc ? y7 z7) ⊗ (eqc ? y8 z8) ⊗
+ (eqc ? y9 z9) ⊗ (eqc ? y10 z10) ⊗ (eqc ? y11 z11) ⊗ (eqc ? y12 z12) ⊗
+ (eqc ? y13 z13) ⊗ (eqc ? y14 z14) ⊗ (eqc ? y15 z15) ⊗ (eqc ? y16 z16)));
+ nrewrite > (symmetric_eqc ? z1 y1);
+ nrewrite > (symmetric_eqc ? z2 y2);
+ nrewrite > (symmetric_eqc ? z3 y3);
+ nrewrite > (symmetric_eqc ? z4 y4);
+ nrewrite > (symmetric_eqc ? z5 y5);
+ nrewrite > (symmetric_eqc ? z6 y6);
+ nrewrite > (symmetric_eqc ? z7 y7);
+ nrewrite > (symmetric_eqc ? z8 y8);
+ nrewrite > (symmetric_eqc ? z9 y9);
+ nrewrite > (symmetric_eqc ? z10 y10);
+ nrewrite > (symmetric_eqc ? z11 y11);
+ nrewrite > (symmetric_eqc ? z12 y12);
+ nrewrite > (symmetric_eqc ? z13 y13);
+ nrewrite > (symmetric_eqc ? z14 y14);
+ nrewrite > (symmetric_eqc ? z15 y15);
+ nrewrite > (symmetric_eqc ? z16 y16);
+ napply refl_eq.
+nqed.*)
+
+nlemma aluIP2022_is_comparable : comparable.
+ @ alu_IP2022
+ ##[ napply (mk_alu_IP2022 (zeroc ?) (zeroc ?) (zeroc ?) (zeroc ?)
+ (zeroc ?) (zeroc ?) (zeroc ?) (zeroc ?)
+ (zeroc ?) (zeroc ?) (zeroc ?) (zeroc ?)
+ (zeroc ?) (zeroc ?) (zeroc ?) (zeroc ?))
+ ##| napply forall_IP2022_alu
+ ##| napply eq_IP2022_alu
+ ##| napply eqaluIP2022_to_eq
+ ##| napply eq_to_eqaluIP2022
+ ##| napply neqaluIP2022_to_neq
+ ##| napply neq_to_neqaluIP2022
+ ##| napply decidable_aluIP2022
+ ##| napply symmetric_eqaluIP2022
+ ##]
+nqed.
+
+unification hint 0 ≔ ⊢ carr aluIP2022_is_comparable ≡ alu_IP2022.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/memory/memory_struct.ma".
+include "num/word16.ma".
+include "num/word24.ma".
+
+(* ******************************** *)
+(* IP2022 REGISTER SPECIAL HARDWARE *)
+(* ******************************** *)
+
+(* (Top Of Stack) : CALLH/CALL ↑ CALLH/CALL ↓ *)
+(* Pos2-15 : ... ↑ ... ↓ *)
+(* Pos16 : 0xFFFF ↑ ... ↓ *)
+ndefinition aux_callstack_type ≝ Array16T word16.
+
+(* Top Of Stack : 0xFFFF on reset *)
+ndefinition new_callstack ≝
+ mk_Array16T ? (〈〈xF,xF〉:〈xF,xF〉〉) (〈〈xF,xF〉:〈xF,xF〉〉) (〈〈xF,xF〉:〈xF,xF〉〉) (〈〈xF,xF〉:〈xF,xF〉〉)
+ (〈〈xF,xF〉:〈xF,xF〉〉) (〈〈xF,xF〉:〈xF,xF〉〉) (〈〈xF,xF〉:〈xF,xF〉〉) (〈〈xF,xF〉:〈xF,xF〉〉)
+ (〈〈xF,xF〉:〈xF,xF〉〉) (〈〈xF,xF〉:〈xF,xF〉〉) (〈〈xF,xF〉:〈xF,xF〉〉) (〈〈xF,xF〉:〈xF,xF〉〉)
+ (〈〈xF,xF〉:〈xF,xF〉〉) (〈〈xF,xF〉:〈xF,xF〉〉) (〈〈xF,xF〉:〈xF,xF〉〉) (〈〈xF,xF〉:〈xF,xF〉〉).
+
+ndefinition pop_callstack ≝
+λcs:aux_callstack_type.
+ pair … (a16_1 ? cs)
+ (mk_Array16T ? (a16_2 ? cs) (a16_3 ? cs) (a16_4 ? cs) (a16_5 ? cs)
+ (a16_6 ? cs) (a16_7 ? cs) (a16_8 ? cs) (a16_9 ? cs)
+ (a16_10 ? cs) (a16_11 ? cs) (a16_12 ? cs) (a16_13 ? cs)
+ (a16_14 ? cs) (a16_15 ? cs) (a16_16 ? cs) 〈〈xF,xF〉:〈xF,xF〉〉).
+
+ndefinition push_callstack ≝
+λcs:aux_callstack_type.λtop.
+ mk_Array16T ? top (a16_1 ? cs) (a16_2 ? cs) (a16_3 ? cs)
+ (a16_4 ? cs) (a16_5 ? cs) (a16_6 ? cs) (a16_7 ? cs)
+ (a16_8 ? cs) (a16_9 ? cs) (a16_10 ? cs) (a16_11 ? cs)
+ (a16_12 ? cs) (a16_13 ? cs) (a16_14 ? cs) (a16_15 ? cs).
+
+nlemma callstack_is_comparable : comparable.
+ @ (aux_callstack_type)
+ ##[ napply (zeroc (ar16_is_comparable word16_is_comparable))
+ ##| napply (forallc (ar16_is_comparable word16_is_comparable))
+ ##| napply (eqc (ar16_is_comparable word16_is_comparable))
+ ##| napply (eqc_to_eq (ar16_is_comparable word16_is_comparable))
+ ##| napply (eq_to_eqc (ar16_is_comparable word16_is_comparable))
+ ##| napply (neqc_to_neq (ar16_is_comparable word16_is_comparable))
+ ##| napply (neq_to_neqc (ar16_is_comparable word16_is_comparable))
+ ##| napply (decidable_c (ar16_is_comparable word16_is_comparable))
+ ##| napply (symmetric_eqc (ar16_is_comparable word16_is_comparable))
+ ##]
+nqed.
+
+unification hint 0 ≔ ⊢ carr callstack_is_comparable ≡ aux_callstack_type.
+
+(* array ad accesso diretto di 8 registri ADDR a 24bit *)
+(* selezione con registro ADDRSEL, solo i primi 3bit validi *)
+ndefinition aux_addrarray_type ≝ Array8T word24.
+
+(* tutti a 0x000000 on reset *)
+ndefinition new_addrarray ≝
+ mk_Array8T ? (〈〈x0,x0〉;〈x0,x0〉;〈x0,x0〉〉) (〈〈x0,x0〉;〈x0,x0〉;〈x0,x0〉〉)
+ (〈〈x0,x0〉;〈x0,x0〉;〈x0,x0〉〉) (〈〈x0,x0〉;〈x0,x0〉;〈x0,x0〉〉)
+ (〈〈x0,x0〉;〈x0,x0〉;〈x0,x0〉〉) (〈〈x0,x0〉;〈x0,x0〉;〈x0,x0〉〉)
+ (〈〈x0,x0〉;〈x0,x0〉;〈x0,x0〉〉) (〈〈x0,x0〉;〈x0,x0〉;〈x0,x0〉〉).
+
+ndefinition get_addrarray ≝
+λaddrsel:byte8.λaa:aux_addrarray_type.
+ getn_array8T (oct_of_exL (cnL ? addrsel)) ? aa.
+
+ndefinition set_addrarray ≝
+λaddrsel:byte8.λaa:aux_addrarray_type.λv.
+ setn_array8T (oct_of_exL (cnL ? addrsel)) ? aa v.
+
+nlemma addrarray_is_comparable : comparable.
+ @ (aux_addrarray_type)
+ ##[ napply (zeroc (ar8_is_comparable word24_is_comparable))
+ ##| napply (forallc (ar8_is_comparable word24_is_comparable))
+ ##| napply (eqc (ar8_is_comparable word24_is_comparable))
+ ##| napply (eqc_to_eq (ar8_is_comparable word24_is_comparable))
+ ##| napply (eq_to_eqc (ar8_is_comparable word24_is_comparable))
+ ##| napply (neqc_to_neq (ar8_is_comparable word24_is_comparable))
+ ##| napply (neq_to_neqc (ar8_is_comparable word24_is_comparable))
+ ##| napply (decidable_c (ar8_is_comparable word24_is_comparable))
+ ##| napply (symmetric_eqc (ar8_is_comparable word24_is_comparable))
+ ##]
+nqed.
+
+unification hint 0 ≔ ⊢ carr addrarray_is_comparable ≡ aux_addrarray_type.
+
+(* *********************************** *)
+(* STATUS INTERNO DEL PROCESSORE (ALU) *)
+(* *********************************** *)
+
+(* ALU dell'IP2022 *)
+nrecord alu_IP2022: Type ≝
+ {
+ (* W: accumulatore *)
+ acc_low_reg_IP2022 : byte8;
+ (* MULH: parte alta moltiplicazione *)
+ mulh_reg_IP2022 : byte8;
+
+ (* ADDRSEL: selettore di indirizzo *)
+ addrsel_reg_IP2022 : byte8;
+ (* ADDR [ADDRX|ADDRH|ADDRL] : array indirizzi indicizzati da ADDRSEL *)
+ addr_array_IP2022 : aux_addrarray_type;
+
+ (* CALL [CALLH|CALLL] : stack indirizzi di ritorno *)
+ call_stack_IP2022 : aux_callstack_type;
+
+ (* IP [IPH|IPL] : indirect pointer *)
+ ip_reg_IP2022 : word16;
+ (* DP [DPH|DPL] : data pointer *)
+ dp_reg_IP2022 : word16;
+ (* DATA [DATAH|DATAL] : data value *)
+ data_reg_IP2022 : word16;
+ (* SP [SPH|SPL] : stack pointer *)
+ sp_reg_IP2022 : word16;
+ (* PC [PCH|PCL] : program counter *)
+ pc_reg_IP2022 : word16;
+
+ (* SPEED[xxxxSSSS] : divisore del clock *)
+ speed_reg_IP2022 : exadecim;
+ (* PAGE [PPPxxxxx] : selettore pagina *)
+ page_reg_IP2022 : oct;
+
+ (* H: flag semi-carry (somma nibble basso) *)
+ h_flag_IP2022 : bool;
+ (* Z: flag zero *)
+ z_flag_IP2022 : bool;
+ (* C: flag carry *)
+ c_flag_IP2022 : bool;
+
+ (* skip mode : effettua fetch-decode, no execute *)
+ skip_mode_IP2022 : bool
+ }.
+
+notation "{hvbox('W_Reg' ≝ w ; break 'MulH_Reg' ≝ mulh ; break 'Addrsel_Reg' ≝ addrsel ; break 'Addr_Array' ≝ addr ; break 'Call_Stack' ≝ call ; break 'Ip_Reg' ≝ ip ; break 'Dp_Reg' ≝ dp ; break 'Data_Reg' ≝ data ; break 'Sp_Reg' ≝ sp ; break 'Pc_Reg' ≝ pc ; break 'Speed_Reg' ≝ speed ; break 'Page_Reg' ≝ page ; break 'H_Flag' ≝ hfl ; break 'Z_Flag' ≝ zfl ; break 'C_Flag' ≝ cfl ; break 'Skip_Mode' ≝ skipmode)}"
+ non associative with precedence 80 for
+ @{ 'mk_alu_IP2022 $w $mulh $addrsel $addr $call $ip $dp $data $sp $pc $speed $page $hfl $zfl $cfl $skipmode }.
+interpretation "mk_alu_IP2022" 'mk_alu_IP2022 w mulh addrsel addr call ip dp data sp pc speed page hfl zfl cfl skipmode =
+ (mk_alu_IP2022 w mulh addrsel addr call ip dp data sp pc speed page hfl zfl cfl skipmode).
+
+(* ****** *)
+(* SETTER *)
+(* ****** *)
+
+(* setter specifico IP2022 di A *)
+ndefinition set_acc_8_low_reg_IP2022 ≝
+λalu.λacclow':byte8.
+ mk_alu_IP2022
+ acclow'
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (call_stack_IP2022 alu)
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+(* setter specifico IP2022 di MULH *)
+ndefinition set_mulh_reg_IP2022 ≝
+λalu.λmulh':byte8.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ mulh'
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (call_stack_IP2022 alu)
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+(* setter specifico IP2022 di ADDRSEL *)
+ndefinition set_addrsel_reg_IP2022 ≝
+λalu.λaddrsel':byte8.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ addrsel'
+ (addr_array_IP2022 alu)
+ (call_stack_IP2022 alu)
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+(* setter specifico IP2022 di ADDR *)
+ndefinition set_addr_reg_IP2022 ≝
+λalu.λaddr':word24.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (set_addrarray (addrsel_reg_IP2022 alu) (addr_array_IP2022 alu) addr')
+ (call_stack_IP2022 alu)
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+ndefinition get_addr_reg_IP2022 ≝
+λalu.get_addrarray (addrsel_reg_IP2022 alu) (addr_array_IP2022 alu).
+
+(* setter specifico IP2022 di CALL *)
+ndefinition set_call_reg_IP2022 ≝
+λalu.λcall':word16.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (setn_array16T x0 ? (call_stack_IP2022 alu) call')
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+ndefinition get_call_reg_IP2022 ≝
+λalu.getn_array16T x0 ? (call_stack_IP2022 alu).
+
+ndefinition set_call_stack_IP2022 ≝
+λalu.λcall':aux_callstack_type.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ call'
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+ndefinition push_call_reg_IP2022 ≝
+λalu.λcall':word16.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (push_callstack (call_stack_IP2022 alu) call')
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+ndefinition pop_call_reg_IP2022 ≝
+λalu.match pop_callstack (call_stack_IP2022 alu) with
+ [ pair val call' ⇒ pair … val (set_call_stack_IP2022 alu call') ].
+
+(* setter specifico IP2022 di IP *)
+ndefinition set_ip_reg_IP2022 ≝
+λalu.λip':word16.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (call_stack_IP2022 alu)
+ ip'
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+(* setter specifico IP2022 di DP *)
+ndefinition set_dp_reg_IP2022 ≝
+λalu.λdp':word16.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (call_stack_IP2022 alu)
+ (ip_reg_IP2022 alu)
+ dp'
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+(* setter specifico IP2022 di DATA *)
+ndefinition set_data_reg_IP2022 ≝
+λalu.λdata':word16.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (call_stack_IP2022 alu)
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ data'
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+(* setter specifico IP2022 di SP *)
+ndefinition set_sp_reg_IP2022 ≝
+λalu.λsp':word16.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (call_stack_IP2022 alu)
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ sp'
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+(* setter specifico IP2022 di PC *)
+ndefinition set_pc_reg_IP2022 ≝
+λalu.λpc':word16.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (call_stack_IP2022 alu)
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ pc'
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+(* setter specifico IP2022 di SPEED *)
+ndefinition set_speed_reg_IP2022 ≝
+λalu.λspeed':exadecim.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (call_stack_IP2022 alu)
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ speed'
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+(* setter specifico IP2022 di PAGE *)
+ndefinition set_page_reg_IP2022 ≝
+λalu.λpage':oct.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (call_stack_IP2022 alu)
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ page'
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+(* setter specifico IP2022 di H *)
+ndefinition set_h_flag_IP2022 ≝
+λalu.λhfl':bool.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (call_stack_IP2022 alu)
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ hfl'
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+(* setter specifico IP2022 di Z *)
+ndefinition set_z_flag_IP2022 ≝
+λalu.λzfl':bool.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (call_stack_IP2022 alu)
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ zfl'
+ (c_flag_IP2022 alu)
+ (skip_mode_IP2022 alu).
+
+(* setter specifico IP2022 di C *)
+ndefinition set_c_flag_IP2022 ≝
+λalu.λcfl':bool.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (call_stack_IP2022 alu)
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ cfl'
+ (skip_mode_IP2022 alu).
+
+(* setter specifico IP2022 di SKIP *)
+ndefinition set_skip_mode_IP2022 ≝
+λalu.λskipmode':bool.
+ mk_alu_IP2022
+ (acc_low_reg_IP2022 alu)
+ (mulh_reg_IP2022 alu)
+ (addrsel_reg_IP2022 alu)
+ (addr_array_IP2022 alu)
+ (call_stack_IP2022 alu)
+ (ip_reg_IP2022 alu)
+ (dp_reg_IP2022 alu)
+ (data_reg_IP2022 alu)
+ (sp_reg_IP2022 alu)
+ (pc_reg_IP2022 alu)
+ (speed_reg_IP2022 alu)
+ (page_reg_IP2022 alu)
+ (h_flag_IP2022 alu)
+ (z_flag_IP2022 alu)
+ (c_flag_IP2022 alu)
+ skipmode'.
+
+(* ***************** *)
+(* CONFRONTO FRA ALU *)
+(* ***************** *)
+
+(* confronto registro per registro dell'IP2022 *)
+ndefinition eq_IP2022_alu ≝
+λalu1,alu2:alu_IP2022.
+ (eqc ? (acc_low_reg_IP2022 alu1) (acc_low_reg_IP2022 alu2)) ⊗
+ (eqc ? (mulh_reg_IP2022 alu1) (mulh_reg_IP2022 alu2)) ⊗
+ (eqc ? (addrsel_reg_IP2022 alu1) (addrsel_reg_IP2022 alu2)) ⊗
+ (eqc ? (addr_array_IP2022 alu1) (addr_array_IP2022 alu2)) ⊗
+ (eqc ? (call_stack_IP2022 alu1) (call_stack_IP2022 alu2)) ⊗
+ (eqc ? (ip_reg_IP2022 alu1) (ip_reg_IP2022 alu2)) ⊗
+ (eqc ? (dp_reg_IP2022 alu1) (dp_reg_IP2022 alu2)) ⊗
+ (eqc ? (data_reg_IP2022 alu1) (data_reg_IP2022 alu2)) ⊗
+ (eqc ? (sp_reg_IP2022 alu1) (sp_reg_IP2022 alu2)) ⊗
+ (eqc ? (pc_reg_IP2022 alu1) (pc_reg_IP2022 alu2)) ⊗
+ (eqc ? (speed_reg_IP2022 alu1) (speed_reg_IP2022 alu2)) ⊗
+ (eqc ? (page_reg_IP2022 alu1) (page_reg_IP2022 alu2)) ⊗
+ (eqc ? (h_flag_IP2022 alu1) (h_flag_IP2022 alu2)) ⊗
+ (eqc ? (z_flag_IP2022 alu1) (z_flag_IP2022 alu2)) ⊗
+ (eqc ? (c_flag_IP2022 alu1) (c_flag_IP2022 alu2)) ⊗
+ (eqc ? (skip_mode_IP2022 alu1) (skip_mode_IP2022 alu2)).
+
+ndefinition forall_IP2022_alu ≝ λP:alu_IP2022 → bool.
+ forallc ? (λr1.forallc ? (λr2.
+ forallc ? (λr3.forallc ? (λr4.
+ forallc ? (λr5.forallc ? (λr6.
+ forallc ? (λr7.forallc ? (λr8.
+ forallc ? (λr9.forallc ? (λr10.
+ forallc ? (λr11.forallc ? (λr12.
+ forallc ? (λr13.forallc ? (λr14.
+ forallc ? (λr15.forallc ? (λr16.
+ P (mk_alu_IP2022 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15 r16))))))))))))))))).
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/status/RS08_status_base.ma".
+
+(* *********************************** *)
+(* STATUS INTERNO DEL PROCESSORE (ALU) *)
+(* *********************************** *)
+
+nlemma aluRS08_destruct_1 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
+ x1 = y1.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_alu_RS08 a _ _ _ _ _ _ _ ⇒ x1 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluRS08_destruct_2 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
+ x2 = y2.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_alu_RS08 _ a _ _ _ _ _ _ ⇒ x2 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluRS08_destruct_3 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
+ x3 = y3.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_alu_RS08 _ _ a _ _ _ _ _ ⇒ x3 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluRS08_destruct_4 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
+ x4 = y4.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_alu_RS08 _ _ _ a _ _ _ _ ⇒ x4 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluRS08_destruct_5 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
+ x5 = y5.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_alu_RS08 _ _ _ _ a _ _ _ ⇒ x5 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluRS08_destruct_6 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
+ x6 = y6.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_alu_RS08 _ _ _ _ _ a _ _ ⇒ x6 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluRS08_destruct_7 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
+ x7 = y7.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_alu_RS08 _ _ _ _ _ _ a _ ⇒ x7 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluRS08_destruct_8 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
+ x8 = y8.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
+ with [ mk_alu_RS08 _ _ _ _ _ _ _ a ⇒ x8 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma eq_to_eqaluRS08 : ∀alu1,alu2.alu1 = alu2 → eq_RS08_alu alu1 alu2 = true.
+ #alu1; #alu2;
+ ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nrewrite > (aluRS08_destruct_1 … H);
+ nrewrite > (aluRS08_destruct_2 … H);
+ nrewrite > (aluRS08_destruct_3 … H);
+ nrewrite > (aluRS08_destruct_4 … H);
+ nrewrite > (aluRS08_destruct_5 … H);
+ nrewrite > (aluRS08_destruct_6 … H);
+ nrewrite > (aluRS08_destruct_7 … H);
+ nrewrite > (aluRS08_destruct_8 … H);
+ nchange with (
+ ((eqc ? y1 y1) ⊗ (eqc ? y2 y2) ⊗
+ (eqc ? y3 y3) ⊗ (eqc ? y4 y4) ⊗
+ (eqc ? y5 y5) ⊗ (eqc ? y6 y6) ⊗
+ (eqc ? y7 y7) ⊗ (eqc ? y8 y8)) = true);
+ nrewrite > (eq_to_eqc ? y1 y1 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y2 y2 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y3 y3 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y4 y4 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y5 y5 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y6 y6 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y7 y7 (refl_eq …));
+ nrewrite > (eq_to_eqc ? y8 y8 (refl_eq …));
+ napply refl_eq.
+nqed.
+
+nlemma neqaluRS08_to_neq : ∀alu1,alu2.eq_RS08_alu alu1 alu2 = false → alu1 ≠ alu2.
+ #s1; #s2; #H;
+ napply (not_to_not (s1 = s2) (eq_RS08_alu s1 s2 = true) …);
+ ##[ ##1: napply (eq_to_eqaluRS08 s1 s2)
+ ##| ##2: napply (eqfalse_to_neqtrue … H)
+ ##]
+nqed.
+
+nlemma eqaluRS08_to_eq : ∀alu1,alu2.eq_RS08_alu alu1 alu2 = true → alu1 = alu2.
+ #alu1; #alu2;
+ ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
+ nchange in H:(%) with (
+ ((eqc ? x1 y1) ⊗ (eqc ? x2 y2) ⊗
+ (eqc ? x3 y3) ⊗ (eqc ? x4 y4) ⊗
+ (eqc ? x5 y5) ⊗ (eqc ? x6 y6) ⊗
+ (eqc ? x7 y7) ⊗ (eqc ? x8 y8)) = true);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H));
+ nletin H1 ≝ (andb_true_true_l … H);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H1));
+ nletin H2 ≝ (andb_true_true_l … H1);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H2));
+ nletin H3 ≝ (andb_true_true_l … H2);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H3));
+ nletin H4 ≝ (andb_true_true_l … H3);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H4));
+ nletin H5 ≝ (andb_true_true_l … H4);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H5));
+ nletin H6 ≝ (andb_true_true_l … H5);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H6));
+ nrewrite > (eqc_to_eq … (andb_true_true_l … H6));
+ napply refl_eq.
+nqed.
+
+nlemma neq_to_neqaluRS08 : ∀alu1,alu2.alu1 ≠ alu2 → eq_RS08_alu alu1 alu2 = false.
+ #s1; #s2; #H;
+ napply (neqtrue_to_eqfalse (eq_RS08_alu s1 s2));
+ napply (not_to_not (eq_RS08_alu s1 s2 = true) (s1 = s2) ? H);
+ napply (eqaluRS08_to_eq s1 s2).
+nqed.
+
+nlemma decidable_aluRS08 : ∀x,y:alu_RS08.decidable (x = y).
+ #x; #y; nnormalize;
+ napply (or2_elim (eq_RS08_alu x y = true) (eq_RS08_alu x y = false) ? (decidable_bexpr ?));
+ ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqaluRS08_to_eq … H))
+ ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqaluRS08_to_neq … H))
+ ##]
+nqed.
+
+
+nlemma symmetric_eqaluRS08 : symmetricT alu_RS08 bool eq_RS08_alu.
+ #alu1; #alu2;
+ ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nchange with (
+ ((eqc ? x1 y1) ⊗ (eqc ? x2 y2) ⊗
+ (eqc ? x3 y3) ⊗ (eqc ? x4 y4) ⊗
+ (eqc ? x5 y5) ⊗ (eqc ? x6 y6) ⊗
+ (eqc ? x7 y7) ⊗ (eqc ? x8 y8)) =
+ ((eqc ? y1 x1) ⊗ (eqc ? y2 x2) ⊗
+ (eqc ? y3 x3) ⊗ (eqc ? y4 x4) ⊗
+ (eqc ? y5 x5) ⊗ (eqc ? y6 x6) ⊗
+ (eqc ? y7 x7) ⊗ (eqc ? y8 x8)));
+ nrewrite > (symmetric_eqc ? x1 y1);
+ nrewrite > (symmetric_eqc ? x2 y2);
+ nrewrite > (symmetric_eqc ? x3 y3);
+ nrewrite > (symmetric_eqc ? x4 y4);
+ nrewrite > (symmetric_eqc ? x5 y5);
+ nrewrite > (symmetric_eqc ? x6 y6);
+ nrewrite > (symmetric_eqc ? x7 y7);
+ nrewrite > (symmetric_eqc ? x8 y8);
+ napply refl_eq.
+nqed.
+
+nlemma aluRS08_is_comparable : comparable.
+ @ alu_RS08
+ ##[ napply (mk_alu_RS08 (zeroc ?) (zeroc ?) (zeroc ?) (zeroc ?)
+ (zeroc ?) (zeroc ?) (zeroc ?) (zeroc ?))
+ ##| napply forall_RS08_alu
+ ##| napply eq_RS08_alu
+ ##| napply eqaluRS08_to_eq
+ ##| napply eq_to_eqaluRS08
+ ##| napply neqaluRS08_to_neq
+ ##| napply neq_to_neqaluRS08
+ ##| napply decidable_aluRS08
+ ##| napply symmetric_eqaluRS08
+ ##]
+nqed.
+
+unification hint 0 ≔ ⊢ carr aluRS08_is_comparable ≡ alu_RS08.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "num/word16.ma".
+
+(* *********************************** *)
+(* STATUS INTERNO DEL PROCESSORE (ALU) *)
+(* *********************************** *)
+
+(* ALU dell'RS08 *)
+nrecord alu_RS08: Type ≝
+ {
+ (* A: registo accumulatore *)
+ acc_low_reg_RS08 : byte8;
+ (* PC: registro program counter *)
+ pc_reg_RS08 : word16;
+ (* modificatore di PC: per esempio e' definito come 00xxxxxxxxxxxxxxb *)
+ (* la logica della sua costruzione e' quindi (PC∧mask) *)
+ (* totalmente racchiusa nella ALU, bastera' fare get(set(PC)) *)
+ pc_mask_RS08 : word16;
+ (* SPC: registro shadow program counter *)
+ (* NB: il suo modificatore e' lo stesso di PC *)
+ spc_reg_RS08 : word16;
+
+ (* X: registro indice parte bassa *)
+ (* NB: in realta' e' mappato in memoria e non risiede nella ALU *)
+ (* la lettura/scrittura avviene tramite la locazione [0x000F] *)
+ x_map_RS08 : byte8;
+ (* PS: registro selezione di pagina *)
+ (* serve a indirizzare la finestra RAM di 64b [0x00C0-0x00FF] *)
+ (* su tutta la memoria installata [0x0000-0x3FFF]: [00pp pppp ppxx xxxx] *)
+ (* NB: in realta' e' mappato in memoria e non risiede nella ALU *)
+ (* la lettura/scrittura avviene tramite la locazione [0x001F] *)
+ ps_map_RS08 : byte8;
+
+ (* Z: flag zero *)
+ z_flag_RS08 : bool;
+ (* C: flag carry *)
+ c_flag_RS08 : bool
+ }.
+
+notation "{hvbox('A_Reg' ≝ acclow ; break 'Pc_Reg' ≝ pc ; break 'Pc_Mask' ≝ pcm ; break 'Spc_Reg' ≝ spc ; break 'X_Map' ≝ xm ; break 'Ps_Map' ≝ psm ; break 'Z_Flag' ≝ zfl ; break 'C_Flag' ≝ cfl)}"
+ non associative with precedence 80 for
+ @{ 'mk_alu_RS08 $acclow $pc $pcm $spc $xm $psm $zfl $cfl }.
+interpretation "mk_alu_RS08" 'mk_alu_RS08 acclow pc pcm spc xm psm zfl cfl =
+ (mk_alu_RS08 acclow pc pcm spc xm psm zfl cfl).
+
+(* ****** *)
+(* SETTER *)
+(* ****** *)
+
+(* setter specifico RS08 di A *)
+ndefinition set_acc_8_low_reg_RS08 ≝
+λalu.λacclow':byte8.
+ mk_alu_RS08
+ acclow'
+ (pc_reg_RS08 alu)
+ (pc_mask_RS08 alu)
+ (spc_reg_RS08 alu)
+ (x_map_RS08 alu)
+ (ps_map_RS08 alu)
+ (z_flag_RS08 alu)
+ (c_flag_RS08 alu).
+
+(* setter specifico RS08 di PC, effettua PC∧mask *)
+ndefinition set_pc_reg_RS08 ≝
+λalu.λpc':word16.
+ mk_alu_RS08
+ (acc_low_reg_RS08 alu)
+ (andc ? pc' (pc_mask_RS08 alu))
+ (pc_mask_RS08 alu)
+ (spc_reg_RS08 alu)
+ (x_map_RS08 alu)
+ (ps_map_RS08 alu)
+ (z_flag_RS08 alu)
+ (c_flag_RS08 alu).
+
+(* setter specifico RS08 di SPC, effettua SPC∧mask *)
+ndefinition set_spc_reg_RS08 ≝
+λalu.λspc':word16.
+ mk_alu_RS08
+ (acc_low_reg_RS08 alu)
+ (pc_reg_RS08 alu)
+ (pc_mask_RS08 alu)
+ (andc ? spc' (pc_mask_RS08 alu))
+ (x_map_RS08 alu)
+ (ps_map_RS08 alu)
+ (z_flag_RS08 alu)
+ (c_flag_RS08 alu).
+
+(* setter specifico RS08 di memory mapped X *)
+ndefinition set_x_map_RS08 ≝
+λalu.λxm':byte8.
+ mk_alu_RS08
+ (acc_low_reg_RS08 alu)
+ (pc_reg_RS08 alu)
+ (pc_mask_RS08 alu)
+ (spc_reg_RS08 alu)
+ xm'
+ (ps_map_RS08 alu)
+ (z_flag_RS08 alu)
+ (c_flag_RS08 alu).
+
+(* setter specifico RS08 di memory mapped PS *)
+ndefinition set_ps_map_RS08 ≝
+λalu.λpsm':byte8.
+ mk_alu_RS08
+ (acc_low_reg_RS08 alu)
+ (pc_reg_RS08 alu)
+ (pc_mask_RS08 alu)
+ (spc_reg_RS08 alu)
+ (x_map_RS08 alu)
+ psm'
+ (z_flag_RS08 alu)
+ (c_flag_RS08 alu).
+
+(* setter sprcifico RS08 di Z *)
+ndefinition set_z_flag_RS08 ≝
+λalu.λzfl':bool.
+ mk_alu_RS08
+ (acc_low_reg_RS08 alu)
+ (pc_reg_RS08 alu)
+ (pc_mask_RS08 alu)
+ (spc_reg_RS08 alu)
+ (x_map_RS08 alu)
+ (ps_map_RS08 alu)
+ zfl'
+ (c_flag_RS08 alu).
+
+(* setter specifico RS08 di C *)
+ndefinition set_c_flag_RS08 ≝
+λalu.λcfl':bool.
+ mk_alu_RS08
+ (acc_low_reg_RS08 alu)
+ (pc_reg_RS08 alu)
+ (pc_mask_RS08 alu)
+ (spc_reg_RS08 alu)
+ (x_map_RS08 alu)
+ (ps_map_RS08 alu)
+ (z_flag_RS08 alu)
+ cfl'.
+
+(* ***************** *)
+(* CONFRONTO FRA ALU *)
+(* ***************** *)
+
+(* confronto registro per registro dell'RS08 *)
+ndefinition eq_RS08_alu ≝
+λalu1,alu2:alu_RS08.
+ (eqc ? (acc_low_reg_RS08 alu1) (acc_low_reg_RS08 alu2)) ⊗
+ (eqc ? (pc_reg_RS08 alu1) (pc_reg_RS08 alu2)) ⊗
+ (eqc ? (pc_mask_RS08 alu1) (pc_mask_RS08 alu2)) ⊗
+ (eqc ? (spc_reg_RS08 alu1) (spc_reg_RS08 alu2)) ⊗
+ (eqc ? (x_map_RS08 alu1) (x_map_RS08 alu2)) ⊗
+ (eqc ? (ps_map_RS08 alu1) (ps_map_RS08 alu2)) ⊗
+ (eqc ? (z_flag_RS08 alu1) (z_flag_RS08 alu2)) ⊗
+ (eqc ? (c_flag_RS08 alu1) (c_flag_RS08 alu2)).
+
+ndefinition forall_RS08_alu ≝ λP:alu_RS08 → bool.
+ forallc ? (λr1.forallc ? (λr2.
+ forallc ? (λr3.forallc ? (λr4.
+ forallc ? (λr5.forallc ? (λr6.
+ forallc ? (λr7.forallc ? (λr8.
+ P (mk_alu_RS08 r1 r2 r3 r4 r5 r6 r7 r8))))))))).
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/status/status_base.ma".
+
+(* *********************************** *)
+(* STATUS INTERNO DEL PROCESSORE (ALU) *)
+(* *********************************** *)
+
+nlemma symmetric_forallmemoryranged :
+∀t.∀chk1,chk2:aux_chk_type t.∀mem1,mem2:aux_mem_type t.∀sel.∀addrl.
+ forall_memory_ranged t chk1 chk2 mem1 mem2 sel addrl =
+ forall_memory_ranged t chk2 chk1 mem2 mem1 sel addrl.
+ #t; #chk1; #chk2; #mem1; #mem2; #sel; #addrl;
+ nelim addrl;
+ ##[ ##1: nnormalize; napply refl_eq
+ ##| ##2: #a; #l; #H;
+ nchange with (
+ ((eqc ? (mem_read t mem1 chk1 sel a)
+ (mem_read t mem2 chk2 sel a)) ⊗
+ (forall_memory_ranged t chk1 chk2 mem1 mem2 sel l)) =
+ ((eqc ? (mem_read t mem2 chk2 sel a)
+ (mem_read t mem1 chk1 sel a)) ⊗
+ (forall_memory_ranged t chk2 chk1 mem2 mem1 sel l)));
+ nrewrite > H;
+ nrewrite > (symmetric_eqc ? … (mem_read t mem1 chk1 sel a) (mem_read t mem2 chk2 sel a));
+ napply refl_eq
+ ##]
+nqed.
+
+nlemma anystatus_destruct_1 :
+∀m,t.∀x1,x2,x3,x4,y1,y2,y3,y4.
+ mk_any_status m t x1 x2 x3 x4 = mk_any_status m t y1 y2 y3 y4 →
+ x1 = y1.
+ #m; #t;
+ #x1; #x2; #x3; #x4;
+ #y1; #y2; #y3; #y4; #H;
+ nchange with (match mk_any_status m t y1 y2 y3 y4
+ with [ mk_any_status a _ _ _ ⇒ x1 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma anystatus_destruct_2 :
+∀m,t.∀x1,x2,x3,x4,y1,y2,y3,y4.
+ mk_any_status m t x1 x2 x3 x4 = mk_any_status m t y1 y2 y3 y4 →
+ x2 = y2.
+ #m; #t;
+ #x1; #x2; #x3; #x4;
+ #y1; #y2; #y3; #y4; #H;
+ nchange with (match mk_any_status m t y1 y2 y3 y4
+ with [ mk_any_status _ a _ _ ⇒ x2 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma anystatus_destruct_3 :
+∀m,t.∀x1,x2,x3,x4,y1,y2,y3,y4.
+ mk_any_status m t x1 x2 x3 x4 = mk_any_status m t y1 y2 y3 y4 →
+ x3 = y3.
+ #m; #t;
+ #x1; #x2; #x3; #x4;
+ #y1; #y2; #y3; #y4; #H;
+ nchange with (match mk_any_status m t y1 y2 y3 y4
+ with [ mk_any_status _ _ a _ ⇒ x3 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma anystatus_destruct_4 :
+∀m,t.∀x1,x2,x3,x4,y1,y2,y3,y4.
+ mk_any_status m t x1 x2 x3 x4 = mk_any_status m t y1 y2 y3 y4 →
+ x4 = y4.
+ #m; #t;
+ #x1; #x2; #x3; #x4;
+ #y1; #y2; #y3; #y4; #H;
+ nchange with (match mk_any_status m t y1 y2 y3 y4
+ with [ mk_any_status _ _ _ a ⇒ x4 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma eq_to_eqanystatus : ∀m,t.∀s1,s2:any_status m t.s1 = s2 → eq_anystatus m t s1 s2 = true.
+ #m; #t;
+ #s1; ncases s1; #alu1; #mem1; #chk1; #clk1;
+ #s2; ncases s2; #alu2; #mem2; #chk2; #clk2;
+ #H;
+ nrewrite > (anystatus_destruct_1 … H);
+ nrewrite > (anystatus_destruct_2 … H);
+ nrewrite > (anystatus_destruct_3 … H);
+ nrewrite > (anystatus_destruct_4 … H);
+ nchange with (
+ ((eqc ? alu2 alu2) ⊗ (eqc ? mem2 mem2) ⊗ (eqc ? chk2 chk2) ⊗ (eqc ? clk2 clk2)) = true);
+ nrewrite > (eq_to_eqc ? alu2 alu2 (refl_eq …));
+ nrewrite > (eq_to_eqc ? mem2 mem2 (refl_eq …));
+ nrewrite > (eq_to_eqc ? chk2 chk2 (refl_eq …));
+ nrewrite > (eq_to_eqc ? clk2 clk2 (refl_eq …));
+ napply refl_eq.
+nqed.
+
+nlemma neqanystatus_to_neq : ∀m,t.∀s1,s2:any_status m t.eq_anystatus m t s1 s2 = false → s1 ≠ s2.
+ #m; #t; #s1; #s2; #H;
+ napply (not_to_not (s1 = s2) (eq_anystatus m t s1 s2 = true) …);
+ ##[ ##1: napply (eq_to_eqanystatus m t s1 s2)
+ ##| ##2: napply (eqfalse_to_neqtrue … H)
+ ##]
+nqed.
+
+nlemma eqanystatus_to_eq : ∀m,t.∀s1,s2:any_status m t.eq_anystatus m t s1 s2 = true → s1 = s2.
+ #m; #t;
+ #s1; ncases s1; #alu1; #mem1; #chk1; #clk1;
+ #s2; ncases s2; #alu2; #mem2; #chk2; #clk2;
+ nchange with (
+ ((eqc ? alu1 alu2) ⊗ (eqc ? mem1 mem2) ⊗ (eqc ? chk1 chk2) ⊗ (eqc ? clk1 clk2)) = true → ?);
+ #H;
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H));
+ nletin H1 ≝ (andb_true_true_l … H);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H1));
+ nletin H2 ≝ (andb_true_true_l … H1);
+ nrewrite > (eqc_to_eq … (andb_true_true_r … H2));
+ nrewrite > (eqc_to_eq … (andb_true_true_l … H2));
+ napply refl_eq.
+nqed.
+
+nlemma neq_to_neqanystatus : ∀m,t.∀s1,s2:any_status m t.s1 ≠ s2 → eq_anystatus m t s1 s2 = false.
+ #m; #t; #s1; #s2; #H;
+ napply (neqtrue_to_eqfalse (eq_anystatus m t s1 s2));
+ napply (not_to_not (eq_anystatus m t s1 s2 = true) (s1 = s2) ? H);
+ napply (eqanystatus_to_eq m t s1 s2).
+nqed.
+
+nlemma decidable_anystatus : ∀m,t.∀x,y:any_status m t.decidable (x = y).
+ #m; #t; #x; #y; nnormalize;
+ napply (or2_elim (eq_anystatus m t x y = true) (eq_anystatus m t x y = false) ? (decidable_bexpr ?));
+ ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqanystatus_to_eq … H))
+ ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqanystatus_to_neq … H))
+ ##]
+nqed.
+
+nlemma symmetric_eqanystatus : ∀m,t.symmetricT (any_status m t) bool (eq_anystatus m t).
+ #m; #t;
+ #s1; ncases s1; #alu1; #mem1; #chk1; #clk1;
+ #s2; ncases s2; #alu2; #mem2; #chk2; #clk2;
+ nchange with (
+ ((eqc ? alu1 alu2) ⊗ (eqc ? mem1 mem2) ⊗ (eqc ? chk1 chk2) ⊗ (eqc ? clk1 clk2)) =
+ ((eqc ? alu2 alu1) ⊗ (eqc ? mem2 mem1) ⊗ (eqc ? chk2 chk1) ⊗ (eqc ? clk2 clk1)));
+ nrewrite > (symmetric_eqc … alu1 alu2);
+ nrewrite > (symmetric_eqc … mem1 mem2);
+ nrewrite > (symmetric_eqc … chk1 chk2);
+ nrewrite > (symmetric_eqc … clk1 clk2);
+ napply refl_eq.
+nqed.
+
+nlemma anystatus_is_comparable : mcu_type → memory_impl → comparable.
+ #m; #t; @ (any_status m t)
+ ##[ napply (mk_any_status m t (zeroc ?) (zeroc ?) (zeroc ?) (zeroc ?))
+ ##| napply forall_anystatus
+ ##| napply eq_anystatus
+ ##| napply eqanystatus_to_eq
+ ##| napply eq_to_eqanystatus
+ ##| napply neqanystatus_to_neq
+ ##| napply neq_to_neqanystatus
+ ##| napply decidable_anystatus
+ ##| napply symmetric_eqanystatus
+ ##]
+nqed.
+
+unification hint 0 ≔ M:mcu_type, T:memory_impl ⊢
+ carr (anystatus_is_comparable M T) ≡ any_status M T.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/memory/memory_abs.ma".
+include "emulator/status/HC05_status.ma".
+include "emulator/status/HC08_status.ma".
+include "emulator/status/RS08_status.ma".
+include "emulator/status/IP2022_status.ma".
+include "emulator/opcodes/pseudo.ma".
+
+(* *********************************** *)
+(* STATUS INTERNO DEL PROCESSORE (ALU) *)
+(* *********************************** *)
+
+(* descrittore del click = stato di avanzamento dell'esecuzione *)
+(* 1) None = istruzione eseguita, attesa del fetch *)
+(* 2) Some cur_clk,pseudo,mode,clks,cur_pc = fetch eseguito *)
+ndefinition aux_clk_type ≝ λm:mcu_type.Prod5T byte8 (aux_pseudo_type m) (aux_im_type m) byte8 word16.
+
+nlemma clk_is_comparable : mcu_type → comparable.
+ #m; @ (aux_clk_type m)
+ ##[ napply (zeroc (quintuple_is_comparable byte8_is_comparable (pseudo_is_comparable m) (im_is_comparable m) byte8_is_comparable word16_is_comparable))
+ ##| napply (forallc (quintuple_is_comparable byte8_is_comparable (pseudo_is_comparable m) (im_is_comparable m) byte8_is_comparable word16_is_comparable))
+ ##| napply (eqc (quintuple_is_comparable byte8_is_comparable (pseudo_is_comparable m) (im_is_comparable m) byte8_is_comparable word16_is_comparable))
+ ##| napply (eqc_to_eq (quintuple_is_comparable byte8_is_comparable (pseudo_is_comparable m) (im_is_comparable m) byte8_is_comparable word16_is_comparable))
+ ##| napply (eq_to_eqc (quintuple_is_comparable byte8_is_comparable (pseudo_is_comparable m) (im_is_comparable m) byte8_is_comparable word16_is_comparable))
+ ##| napply (neqc_to_neq (quintuple_is_comparable byte8_is_comparable (pseudo_is_comparable m) (im_is_comparable m) byte8_is_comparable word16_is_comparable))
+ ##| napply (neq_to_neqc (quintuple_is_comparable byte8_is_comparable (pseudo_is_comparable m) (im_is_comparable m) byte8_is_comparable word16_is_comparable))
+ ##| napply (decidable_c (quintuple_is_comparable byte8_is_comparable (pseudo_is_comparable m) (im_is_comparable m) byte8_is_comparable word16_is_comparable))
+ ##| napply (symmetric_eqc (quintuple_is_comparable byte8_is_comparable (pseudo_is_comparable m) (im_is_comparable m) byte8_is_comparable word16_is_comparable))
+ ##]
+nqed.
+
+unification hint 0 ≔ M:mcu_type ⊢ carr (clk_is_comparable M) ≡ aux_clk_type M.
+
+(* descritture della alu *)
+ndefinition aux_alu_type ≝
+λm.match m with
+ [ HC05 ⇒ alu_HC05
+ | HC08 ⇒ alu_HC08
+ | HCS08 ⇒ alu_HC08
+ | RS08 ⇒ alu_RS08
+ | IP2022 ⇒ alu_IP2022
+ ].
+
+nlemma alu_is_comparable : mcu_type → comparable.
+ #m; @ (aux_alu_type m)
+ ##[ nelim m;
+ ##[ napply (zeroc aluHC05_is_comparable)
+ ##| napply (zeroc aluHC08_is_comparable)
+ ##| napply (zeroc aluHC08_is_comparable)
+ ##| napply (zeroc aluRS08_is_comparable)
+ ##| napply (zeroc aluIP2022_is_comparable) ##]
+ ##| nelim m;
+ ##[ napply (forallc aluHC05_is_comparable)
+ ##| napply (forallc aluHC08_is_comparable)
+ ##| napply (forallc aluHC08_is_comparable)
+ ##| napply (forallc aluRS08_is_comparable)
+ ##| napply (forallc aluIP2022_is_comparable) ##]
+ ##| nelim m;
+ ##[ napply (eqc aluHC05_is_comparable)
+ ##| napply (eqc aluHC08_is_comparable)
+ ##| napply (eqc aluHC08_is_comparable)
+ ##| napply (eqc aluRS08_is_comparable)
+ ##| napply (eqc aluIP2022_is_comparable) ##]
+ ##| nelim m;
+ ##[ napply (eqc_to_eq aluHC05_is_comparable)
+ ##| napply (eqc_to_eq aluHC08_is_comparable)
+ ##| napply (eqc_to_eq aluHC08_is_comparable)
+ ##| napply (eqc_to_eq aluRS08_is_comparable)
+ ##| napply (eqc_to_eq aluIP2022_is_comparable) ##]
+ ##| nelim m;
+ ##[ napply (eq_to_eqc aluHC05_is_comparable)
+ ##| napply (eq_to_eqc aluHC08_is_comparable)
+ ##| napply (eq_to_eqc aluHC08_is_comparable)
+ ##| napply (eq_to_eqc aluRS08_is_comparable)
+ ##| napply (eq_to_eqc aluIP2022_is_comparable) ##]
+ ##| nelim m;
+ ##[ napply (neqc_to_neq aluHC05_is_comparable)
+ ##| napply (neqc_to_neq aluHC08_is_comparable)
+ ##| napply (neqc_to_neq aluHC08_is_comparable)
+ ##| napply (neqc_to_neq aluRS08_is_comparable)
+ ##| napply (neqc_to_neq aluIP2022_is_comparable) ##]
+ ##| nelim m;
+ ##[ napply (neq_to_neqc aluHC05_is_comparable)
+ ##| napply (neq_to_neqc aluHC08_is_comparable)
+ ##| napply (neq_to_neqc aluHC08_is_comparable)
+ ##| napply (neq_to_neqc aluRS08_is_comparable)
+ ##| napply (neq_to_neqc aluIP2022_is_comparable) ##]
+ ##| nelim m;
+ ##[ napply (decidable_c aluHC05_is_comparable)
+ ##| napply (decidable_c aluHC08_is_comparable)
+ ##| napply (decidable_c aluHC08_is_comparable)
+ ##| napply (decidable_c aluRS08_is_comparable)
+ ##| napply (decidable_c aluIP2022_is_comparable) ##]
+ ##| nelim m;
+ ##[ napply (symmetric_eqc aluHC05_is_comparable)
+ ##| napply (symmetric_eqc aluHC08_is_comparable)
+ ##| napply (symmetric_eqc aluHC08_is_comparable)
+ ##| napply (symmetric_eqc aluRS08_is_comparable)
+ ##| napply (symmetric_eqc aluIP2022_is_comparable) ##]
+ ##]
+nqed.
+
+unification hint 0 ≔ M:mcu_type ⊢ carr (alu_is_comparable M) ≡ aux_alu_type M.
+
+(* tipo processore dipendente dalla mcu, varia solo la ALU *)
+nrecord any_status (mcu:mcu_type) (t:memory_impl): Type ≝
+ {
+ (* descrittore della alu *)
+ alu : aux_alu_type mcu;
+ (* descritore della memoria *)
+ mem_desc : aux_mem_type t;
+ (* descrittore del tipo di memoria installata *)
+ chk_desc : aux_chk_type t;
+ (* descrittore del clik *)
+ clk_desc : option (aux_clk_type mcu)
+ }.
+
+(* evitare di mostrare la memoria/descrittore che impalla il visualizzatore *)
+notation > "{hvbox('Alu' ≝ alu ; break 'Clk' ≝ clk)}" non associative with precedence 80
+ for @{ 'mk_any_status $alu $mem $chk $clk }.
+interpretation "mk_any_status" 'mk_any_status alu mem chk clk =
+ (mk_any_status alu mem chk clk).
+
+(* ******************** *)
+(* CONFRONTO FRA STATUS *)
+(* ******************** *)
+
+ndefinition eq_anystatus ≝
+λm,t.λs1,s2:any_status m t.
+ (eqc ? (alu … s1) (alu … s2)) ⊗
+ (eqc ? (mem_desc … s1) (mem_desc … s2)) ⊗
+ (eqc ? (chk_desc … s1) (chk_desc … s2)) ⊗
+ (eqc ? (clk_desc … s1) (clk_desc … s2)).
+
+ndefinition forall_anystatus ≝ λm,t.λP:any_status m t → bool.
+ forallc ? (λr1.forallc ? (λr2.
+ forallc ? (λr3.forallc ? (λr4.
+ P (mk_any_status m t r1 r2 r3 r4))))).
+
+(* confronto di una regione di memoria [addr1 ; ... ; addrn] *)
+nlet rec forall_memory_ranged
+ (t:memory_impl)
+ (chk1:aux_chk_type t) (chk2:aux_chk_type t)
+ (mem1:aux_mem_type t) (mem2:aux_mem_type t)
+ (sel:oct) (addrl:list word16) on addrl ≝
+ match addrl return λ_.bool with
+ [ nil ⇒ true
+ | cons hd tl ⇒ (eqc ? (mem_read t mem1 chk1 sel hd) (mem_read t mem2 chk2 sel hd)) ⊗
+ (forall_memory_ranged t chk1 chk2 mem1 mem2 sel tl)
+ ].
P t10 ⊗ P t11 ⊗ P t12 ⊗ P t13 ⊗ P t14 ⊗ P t15 ⊗ P t16 ⊗ P t17 ⊗
P t18 ⊗ P t19 ⊗ P t1A ⊗ P t1B ⊗ P t1C ⊗ P t1D ⊗ P t1E ⊗ P t1F.
+(* operatore and *)
+ndefinition and_bit ≝
+λe1,e2.match e1 with
+ [ t00 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t00 | t03 ⇒ t00 | t04 ⇒ t00 | t05 ⇒ t00 | t06 ⇒ t00 | t07 ⇒ t00
+ | t08 ⇒ t00 | t09 ⇒ t00 | t0A ⇒ t00 | t0B ⇒ t00 | t0C ⇒ t00 | t0D ⇒ t00 | t0E ⇒ t00 | t0F ⇒ t00
+ | t10 ⇒ t00 | t11 ⇒ t00 | t12 ⇒ t00 | t13 ⇒ t00 | t14 ⇒ t00 | t15 ⇒ t00 | t16 ⇒ t00 | t17 ⇒ t00
+ | t18 ⇒ t00 | t19 ⇒ t00 | t1A ⇒ t00 | t1B ⇒ t00 | t1C ⇒ t00 | t1D ⇒ t00 | t1E ⇒ t00 | t1F ⇒ t00 ]
+ | t01 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t00 | t03 ⇒ t01 | t04 ⇒ t00 | t05 ⇒ t01 | t06 ⇒ t00 | t07 ⇒ t01
+ | t08 ⇒ t00 | t09 ⇒ t01 | t0A ⇒ t00 | t0B ⇒ t01 | t0C ⇒ t00 | t0D ⇒ t01 | t0E ⇒ t00 | t0F ⇒ t01
+ | t10 ⇒ t00 | t11 ⇒ t01 | t12 ⇒ t00 | t13 ⇒ t01 | t14 ⇒ t00 | t15 ⇒ t01 | t16 ⇒ t00 | t17 ⇒ t01
+ | t18 ⇒ t00 | t19 ⇒ t01 | t1A ⇒ t00 | t1B ⇒ t01 | t1C ⇒ t00 | t1D ⇒ t01 | t1E ⇒ t00 | t1F ⇒ t01 ]
+ | t02 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t02 | t03 ⇒ t02 | t04 ⇒ t00 | t05 ⇒ t00 | t06 ⇒ t02 | t07 ⇒ t02
+ | t08 ⇒ t00 | t09 ⇒ t00 | t0A ⇒ t02 | t0B ⇒ t02 | t0C ⇒ t00 | t0D ⇒ t00 | t0E ⇒ t02 | t0F ⇒ t02
+ | t10 ⇒ t00 | t11 ⇒ t00 | t12 ⇒ t02 | t13 ⇒ t02 | t14 ⇒ t00 | t15 ⇒ t00 | t16 ⇒ t02 | t17 ⇒ t02
+ | t18 ⇒ t00 | t19 ⇒ t00 | t1A ⇒ t02 | t1B ⇒ t02 | t1C ⇒ t00 | t1D ⇒ t00 | t1E ⇒ t02 | t1F ⇒ t02 ]
+ | t03 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t02 | t03 ⇒ t03 | t04 ⇒ t00 | t05 ⇒ t01 | t06 ⇒ t02 | t07 ⇒ t03
+ | t08 ⇒ t00 | t09 ⇒ t01 | t0A ⇒ t02 | t0B ⇒ t03 | t0C ⇒ t00 | t0D ⇒ t01 | t0E ⇒ t02 | t0F ⇒ t03
+ | t10 ⇒ t00 | t11 ⇒ t01 | t12 ⇒ t02 | t13 ⇒ t03 | t14 ⇒ t00 | t15 ⇒ t01 | t16 ⇒ t02 | t17 ⇒ t03
+ | t18 ⇒ t00 | t19 ⇒ t01 | t1A ⇒ t02 | t1B ⇒ t03 | t1C ⇒ t00 | t1D ⇒ t01 | t1E ⇒ t02 | t1F ⇒ t03 ]
+ | t04 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t00 | t03 ⇒ t00 | t04 ⇒ t04 | t05 ⇒ t04 | t06 ⇒ t04 | t07 ⇒ t04
+ | t08 ⇒ t00 | t09 ⇒ t00 | t0A ⇒ t00 | t0B ⇒ t00 | t0C ⇒ t04 | t0D ⇒ t04 | t0E ⇒ t04 | t0F ⇒ t04
+ | t10 ⇒ t00 | t11 ⇒ t00 | t12 ⇒ t00 | t13 ⇒ t00 | t14 ⇒ t04 | t15 ⇒ t04 | t16 ⇒ t04 | t17 ⇒ t04
+ | t18 ⇒ t00 | t19 ⇒ t00 | t1A ⇒ t00 | t1B ⇒ t00 | t1C ⇒ t04 | t1D ⇒ t04 | t1E ⇒ t04 | t1F ⇒ t04 ]
+ | t05 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t00 | t03 ⇒ t01 | t04 ⇒ t04 | t05 ⇒ t05 | t06 ⇒ t04 | t07 ⇒ t05
+ | t08 ⇒ t00 | t09 ⇒ t01 | t0A ⇒ t00 | t0B ⇒ t01 | t0C ⇒ t04 | t0D ⇒ t05 | t0E ⇒ t04 | t0F ⇒ t05
+ | t10 ⇒ t00 | t11 ⇒ t01 | t12 ⇒ t00 | t13 ⇒ t01 | t14 ⇒ t04 | t15 ⇒ t05 | t16 ⇒ t04 | t17 ⇒ t05
+ | t18 ⇒ t00 | t19 ⇒ t01 | t1A ⇒ t00 | t1B ⇒ t01 | t1C ⇒ t04 | t1D ⇒ t05 | t1E ⇒ t04 | t1F ⇒ t05 ]
+ | t06 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t02 | t03 ⇒ t02 | t04 ⇒ t04 | t05 ⇒ t04 | t06 ⇒ t06 | t07 ⇒ t06
+ | t08 ⇒ t00 | t09 ⇒ t00 | t0A ⇒ t02 | t0B ⇒ t02 | t0C ⇒ t04 | t0D ⇒ t04 | t0E ⇒ t06 | t0F ⇒ t06
+ | t10 ⇒ t00 | t11 ⇒ t00 | t12 ⇒ t02 | t13 ⇒ t02 | t14 ⇒ t04 | t15 ⇒ t04 | t16 ⇒ t06 | t17 ⇒ t06
+ | t18 ⇒ t00 | t19 ⇒ t00 | t1A ⇒ t02 | t1B ⇒ t02 | t1C ⇒ t04 | t1D ⇒ t04 | t1E ⇒ t06 | t1F ⇒ t06 ]
+ | t07 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t02 | t03 ⇒ t03 | t04 ⇒ t04 | t05 ⇒ t05 | t06 ⇒ t06 | t07 ⇒ t07
+ | t08 ⇒ t00 | t09 ⇒ t01 | t0A ⇒ t02 | t0B ⇒ t03 | t0C ⇒ t04 | t0D ⇒ t05 | t0E ⇒ t06 | t0F ⇒ t07
+ | t10 ⇒ t00 | t11 ⇒ t01 | t12 ⇒ t02 | t13 ⇒ t03 | t14 ⇒ t04 | t15 ⇒ t05 | t16 ⇒ t06 | t17 ⇒ t07
+ | t18 ⇒ t00 | t19 ⇒ t01 | t1A ⇒ t02 | t1B ⇒ t03 | t1C ⇒ t04 | t1D ⇒ t05 | t1E ⇒ t06 | t1F ⇒ t07 ]
+ | t08 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t00 | t03 ⇒ t00 | t04 ⇒ t00 | t05 ⇒ t00 | t06 ⇒ t00 | t07 ⇒ t00
+ | t08 ⇒ t08 | t09 ⇒ t08 | t0A ⇒ t08 | t0B ⇒ t08 | t0C ⇒ t08 | t0D ⇒ t08 | t0E ⇒ t08 | t0F ⇒ t08
+ | t10 ⇒ t00 | t11 ⇒ t00 | t12 ⇒ t00 | t13 ⇒ t00 | t14 ⇒ t00 | t15 ⇒ t00 | t16 ⇒ t00 | t17 ⇒ t00
+ | t18 ⇒ t08 | t19 ⇒ t08 | t1A ⇒ t08 | t1B ⇒ t08 | t1C ⇒ t08 | t1D ⇒ t08 | t1E ⇒ t08 | t1F ⇒ t08 ]
+ | t09 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t00 | t03 ⇒ t01 | t04 ⇒ t00 | t05 ⇒ t01 | t06 ⇒ t00 | t07 ⇒ t01
+ | t08 ⇒ t08 | t09 ⇒ t09 | t0A ⇒ t08 | t0B ⇒ t09 | t0C ⇒ t08 | t0D ⇒ t09 | t0E ⇒ t08 | t0F ⇒ t09
+ | t10 ⇒ t00 | t11 ⇒ t01 | t12 ⇒ t00 | t13 ⇒ t01 | t14 ⇒ t00 | t15 ⇒ t01 | t16 ⇒ t00 | t17 ⇒ t01
+ | t18 ⇒ t08 | t19 ⇒ t09 | t1A ⇒ t08 | t1B ⇒ t09 | t1C ⇒ t08 | t1D ⇒ t09 | t1E ⇒ t08 | t1F ⇒ t09 ]
+ | t0A ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t02 | t03 ⇒ t02 | t04 ⇒ t00 | t05 ⇒ t00 | t06 ⇒ t02 | t07 ⇒ t02
+ | t08 ⇒ t08 | t09 ⇒ t08 | t0A ⇒ t0A | t0B ⇒ t0A | t0C ⇒ t08 | t0D ⇒ t08 | t0E ⇒ t0A | t0F ⇒ t0A
+ | t10 ⇒ t00 | t11 ⇒ t00 | t12 ⇒ t02 | t13 ⇒ t02 | t14 ⇒ t00 | t15 ⇒ t00 | t16 ⇒ t02 | t17 ⇒ t02
+ | t18 ⇒ t08 | t19 ⇒ t08 | t1A ⇒ t0A | t1B ⇒ t0A | t1C ⇒ t08 | t1D ⇒ t08 | t1E ⇒ t0A | t1F ⇒ t0A ]
+ | t0B ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t02 | t03 ⇒ t03 | t04 ⇒ t00 | t05 ⇒ t01 | t06 ⇒ t02 | t07 ⇒ t03
+ | t08 ⇒ t08 | t09 ⇒ t09 | t0A ⇒ t0A | t0B ⇒ t0B | t0C ⇒ t08 | t0D ⇒ t09 | t0E ⇒ t0A | t0F ⇒ t0B
+ | t10 ⇒ t00 | t11 ⇒ t01 | t12 ⇒ t02 | t13 ⇒ t03 | t14 ⇒ t00 | t15 ⇒ t01 | t16 ⇒ t02 | t17 ⇒ t03
+ | t18 ⇒ t08 | t19 ⇒ t09 | t1A ⇒ t0A | t1B ⇒ t0B | t1C ⇒ t08 | t1D ⇒ t09 | t1E ⇒ t0A | t1F ⇒ t0B ]
+ | t0C ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t00 | t03 ⇒ t00 | t04 ⇒ t04 | t05 ⇒ t04 | t06 ⇒ t04 | t07 ⇒ t04
+ | t08 ⇒ t08 | t09 ⇒ t08 | t0A ⇒ t08 | t0B ⇒ t08 | t0C ⇒ t0C | t0D ⇒ t0C | t0E ⇒ t0C | t0F ⇒ t0C
+ | t10 ⇒ t00 | t11 ⇒ t00 | t12 ⇒ t00 | t13 ⇒ t00 | t14 ⇒ t04 | t15 ⇒ t04 | t16 ⇒ t04 | t17 ⇒ t04
+ | t18 ⇒ t08 | t19 ⇒ t08 | t1A ⇒ t08 | t1B ⇒ t08 | t1C ⇒ t0C | t1D ⇒ t0C | t1E ⇒ t0C | t1F ⇒ t0C ]
+ | t0D ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t00 | t03 ⇒ t01 | t04 ⇒ t04 | t05 ⇒ t05 | t06 ⇒ t04 | t07 ⇒ t05
+ | t08 ⇒ t08 | t09 ⇒ t09 | t0A ⇒ t08 | t0B ⇒ t09 | t0C ⇒ t0C | t0D ⇒ t0D | t0E ⇒ t0C | t0F ⇒ t0D
+ | t10 ⇒ t00 | t11 ⇒ t01 | t12 ⇒ t00 | t13 ⇒ t01 | t14 ⇒ t04 | t15 ⇒ t05 | t16 ⇒ t04 | t17 ⇒ t05
+ | t18 ⇒ t08 | t19 ⇒ t09 | t1A ⇒ t08 | t1B ⇒ t09 | t1C ⇒ t0C | t1D ⇒ t0D | t1E ⇒ t0C | t1F ⇒ t0D ]
+ | t0E ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t02 | t03 ⇒ t02 | t04 ⇒ t04 | t05 ⇒ t04 | t06 ⇒ t06 | t07 ⇒ t06
+ | t08 ⇒ t08 | t09 ⇒ t08 | t0A ⇒ t0A | t0B ⇒ t0A | t0C ⇒ t0C | t0D ⇒ t0C | t0E ⇒ t0E | t0F ⇒ t0E
+ | t10 ⇒ t00 | t11 ⇒ t00 | t12 ⇒ t02 | t13 ⇒ t02 | t14 ⇒ t04 | t15 ⇒ t04 | t16 ⇒ t06 | t17 ⇒ t06
+ | t18 ⇒ t08 | t19 ⇒ t08 | t1A ⇒ t0A | t1B ⇒ t0A | t1C ⇒ t0C | t1D ⇒ t0C | t1E ⇒ t0E | t1F ⇒ t0E ]
+ | t0F ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t02 | t03 ⇒ t03 | t04 ⇒ t04 | t05 ⇒ t05 | t06 ⇒ t06 | t07 ⇒ t07
+ | t08 ⇒ t08 | t09 ⇒ t09 | t0A ⇒ t0A | t0B ⇒ t0B | t0C ⇒ t0C | t0D ⇒ t0D | t0E ⇒ t0E | t0F ⇒ t0F
+ | t10 ⇒ t00 | t11 ⇒ t01 | t12 ⇒ t02 | t13 ⇒ t03 | t14 ⇒ t04 | t15 ⇒ t05 | t16 ⇒ t06 | t17 ⇒ t07
+ | t18 ⇒ t08 | t19 ⇒ t09 | t1A ⇒ t0A | t1B ⇒ t0B | t1C ⇒ t0C | t1D ⇒ t0D | t1E ⇒ t0E | t1F ⇒ t0F ]
+ | t10 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t00 | t03 ⇒ t00 | t04 ⇒ t00 | t05 ⇒ t00 | t06 ⇒ t00 | t07 ⇒ t00
+ | t08 ⇒ t00 | t09 ⇒ t00 | t0A ⇒ t00 | t0B ⇒ t00 | t0C ⇒ t00 | t0D ⇒ t00 | t0E ⇒ t00 | t0F ⇒ t00
+ | t10 ⇒ t10 | t11 ⇒ t10 | t12 ⇒ t10 | t13 ⇒ t10 | t14 ⇒ t10 | t15 ⇒ t10 | t16 ⇒ t10 | t17 ⇒ t10
+ | t18 ⇒ t10 | t19 ⇒ t10 | t1A ⇒ t10 | t1B ⇒ t10 | t1C ⇒ t10 | t1D ⇒ t10 | t1E ⇒ t10 | t1F ⇒ t10 ]
+ | t11 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t00 | t03 ⇒ t01 | t04 ⇒ t00 | t05 ⇒ t01 | t06 ⇒ t00 | t07 ⇒ t01
+ | t08 ⇒ t00 | t09 ⇒ t01 | t0A ⇒ t00 | t0B ⇒ t01 | t0C ⇒ t00 | t0D ⇒ t01 | t0E ⇒ t00 | t0F ⇒ t01
+ | t10 ⇒ t10 | t11 ⇒ t11 | t12 ⇒ t10 | t13 ⇒ t11 | t14 ⇒ t10 | t15 ⇒ t11 | t16 ⇒ t10 | t17 ⇒ t11
+ | t18 ⇒ t10 | t19 ⇒ t11 | t1A ⇒ t10 | t1B ⇒ t11 | t1C ⇒ t10 | t1D ⇒ t11 | t1E ⇒ t10 | t1F ⇒ t11 ]
+ | t12 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t02 | t03 ⇒ t02 | t04 ⇒ t00 | t05 ⇒ t00 | t06 ⇒ t02 | t07 ⇒ t02
+ | t08 ⇒ t00 | t09 ⇒ t00 | t0A ⇒ t02 | t0B ⇒ t02 | t0C ⇒ t00 | t0D ⇒ t00 | t0E ⇒ t02 | t0F ⇒ t02
+ | t10 ⇒ t10 | t11 ⇒ t10 | t12 ⇒ t12 | t13 ⇒ t12 | t14 ⇒ t10 | t15 ⇒ t10 | t16 ⇒ t12 | t17 ⇒ t12
+ | t18 ⇒ t10 | t19 ⇒ t10 | t1A ⇒ t12 | t1B ⇒ t12 | t1C ⇒ t10 | t1D ⇒ t10 | t1E ⇒ t12 | t1F ⇒ t12 ]
+ | t13 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t02 | t03 ⇒ t03 | t04 ⇒ t00 | t05 ⇒ t01 | t06 ⇒ t02 | t07 ⇒ t03
+ | t08 ⇒ t00 | t09 ⇒ t01 | t0A ⇒ t02 | t0B ⇒ t03 | t0C ⇒ t00 | t0D ⇒ t01 | t0E ⇒ t02 | t0F ⇒ t03
+ | t10 ⇒ t10 | t11 ⇒ t11 | t12 ⇒ t12 | t13 ⇒ t13 | t14 ⇒ t10 | t15 ⇒ t11 | t16 ⇒ t12 | t17 ⇒ t13
+ | t18 ⇒ t10 | t19 ⇒ t11 | t1A ⇒ t12 | t1B ⇒ t13 | t1C ⇒ t10 | t1D ⇒ t11 | t1E ⇒ t12 | t1F ⇒ t13 ]
+ | t14 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t00 | t03 ⇒ t00 | t04 ⇒ t04 | t05 ⇒ t04 | t06 ⇒ t04 | t07 ⇒ t04
+ | t08 ⇒ t00 | t09 ⇒ t00 | t0A ⇒ t00 | t0B ⇒ t00 | t0C ⇒ t04 | t0D ⇒ t04 | t0E ⇒ t04 | t0F ⇒ t04
+ | t10 ⇒ t10 | t11 ⇒ t10 | t12 ⇒ t10 | t13 ⇒ t10 | t14 ⇒ t14 | t15 ⇒ t14 | t16 ⇒ t14 | t17 ⇒ t14
+ | t18 ⇒ t10 | t19 ⇒ t10 | t1A ⇒ t10 | t1B ⇒ t10 | t1C ⇒ t14 | t1D ⇒ t14 | t1E ⇒ t14 | t1F ⇒ t14 ]
+ | t15 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t00 | t03 ⇒ t01 | t04 ⇒ t04 | t05 ⇒ t05 | t06 ⇒ t04 | t07 ⇒ t05
+ | t08 ⇒ t00 | t09 ⇒ t01 | t0A ⇒ t00 | t0B ⇒ t01 | t0C ⇒ t04 | t0D ⇒ t05 | t0E ⇒ t04 | t0F ⇒ t05
+ | t10 ⇒ t10 | t11 ⇒ t11 | t12 ⇒ t10 | t13 ⇒ t11 | t14 ⇒ t14 | t15 ⇒ t15 | t16 ⇒ t14 | t17 ⇒ t15
+ | t18 ⇒ t10 | t19 ⇒ t11 | t1A ⇒ t10 | t1B ⇒ t11 | t1C ⇒ t14 | t1D ⇒ t15 | t1E ⇒ t14 | t1F ⇒ t15 ]
+ | t16 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t02 | t03 ⇒ t02 | t04 ⇒ t04 | t05 ⇒ t04 | t06 ⇒ t06 | t07 ⇒ t06
+ | t08 ⇒ t00 | t09 ⇒ t00 | t0A ⇒ t02 | t0B ⇒ t02 | t0C ⇒ t04 | t0D ⇒ t04 | t0E ⇒ t06 | t0F ⇒ t06
+ | t10 ⇒ t10 | t11 ⇒ t10 | t12 ⇒ t12 | t13 ⇒ t12 | t14 ⇒ t14 | t15 ⇒ t14 | t16 ⇒ t16 | t17 ⇒ t16
+ | t18 ⇒ t10 | t19 ⇒ t10 | t1A ⇒ t12 | t1B ⇒ t12 | t1C ⇒ t14 | t1D ⇒ t14 | t1E ⇒ t16 | t1F ⇒ t16 ]
+ | t17 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t02 | t03 ⇒ t03 | t04 ⇒ t04 | t05 ⇒ t05 | t06 ⇒ t06 | t07 ⇒ t07
+ | t08 ⇒ t00 | t09 ⇒ t01 | t0A ⇒ t02 | t0B ⇒ t03 | t0C ⇒ t04 | t0D ⇒ t05 | t0E ⇒ t06 | t0F ⇒ t07
+ | t10 ⇒ t10 | t11 ⇒ t11 | t12 ⇒ t12 | t13 ⇒ t13 | t14 ⇒ t14 | t15 ⇒ t15 | t16 ⇒ t16 | t17 ⇒ t17
+ | t18 ⇒ t10 | t19 ⇒ t11 | t1A ⇒ t12 | t1B ⇒ t13 | t1C ⇒ t14 | t1D ⇒ t15 | t1E ⇒ t16 | t1F ⇒ t17 ]
+ | t18 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t00 | t03 ⇒ t00 | t04 ⇒ t00 | t05 ⇒ t00 | t06 ⇒ t00 | t07 ⇒ t00
+ | t08 ⇒ t08 | t09 ⇒ t08 | t0A ⇒ t08 | t0B ⇒ t08 | t0C ⇒ t08 | t0D ⇒ t08 | t0E ⇒ t08 | t0F ⇒ t08
+ | t10 ⇒ t10 | t11 ⇒ t10 | t12 ⇒ t10 | t13 ⇒ t10 | t14 ⇒ t10 | t15 ⇒ t10 | t16 ⇒ t10 | t17 ⇒ t10
+ | t18 ⇒ t18 | t19 ⇒ t18 | t1A ⇒ t18 | t1B ⇒ t18 | t1C ⇒ t18 | t1D ⇒ t18 | t1E ⇒ t18 | t1F ⇒ t18 ]
+ | t19 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t00 | t03 ⇒ t01 | t04 ⇒ t00 | t05 ⇒ t01 | t06 ⇒ t00 | t07 ⇒ t01
+ | t08 ⇒ t08 | t09 ⇒ t09 | t0A ⇒ t08 | t0B ⇒ t09 | t0C ⇒ t08 | t0D ⇒ t09 | t0E ⇒ t08 | t0F ⇒ t09
+ | t10 ⇒ t10 | t11 ⇒ t11 | t12 ⇒ t10 | t13 ⇒ t11 | t14 ⇒ t10 | t15 ⇒ t11 | t16 ⇒ t10 | t17 ⇒ t11
+ | t18 ⇒ t18 | t19 ⇒ t19 | t1A ⇒ t18 | t1B ⇒ t19 | t1C ⇒ t18 | t1D ⇒ t19 | t1E ⇒ t18 | t1F ⇒ t19 ]
+ | t1A ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t02 | t03 ⇒ t02 | t04 ⇒ t00 | t05 ⇒ t00 | t06 ⇒ t02 | t07 ⇒ t02
+ | t08 ⇒ t08 | t09 ⇒ t08 | t0A ⇒ t0A | t0B ⇒ t0A | t0C ⇒ t08 | t0D ⇒ t08 | t0E ⇒ t0A | t0F ⇒ t0A
+ | t10 ⇒ t10 | t11 ⇒ t10 | t12 ⇒ t12 | t13 ⇒ t12 | t14 ⇒ t10 | t15 ⇒ t10 | t16 ⇒ t12 | t17 ⇒ t12
+ | t18 ⇒ t18 | t19 ⇒ t18 | t1A ⇒ t1A | t1B ⇒ t1A | t1C ⇒ t18 | t1D ⇒ t18 | t1E ⇒ t1A | t1F ⇒ t1A ]
+ | t1B ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t02 | t03 ⇒ t03 | t04 ⇒ t00 | t05 ⇒ t01 | t06 ⇒ t02 | t07 ⇒ t03
+ | t08 ⇒ t08 | t09 ⇒ t09 | t0A ⇒ t0A | t0B ⇒ t0B | t0C ⇒ t08 | t0D ⇒ t09 | t0E ⇒ t0A | t0F ⇒ t0B
+ | t10 ⇒ t10 | t11 ⇒ t11 | t12 ⇒ t12 | t13 ⇒ t13 | t14 ⇒ t10 | t15 ⇒ t11 | t16 ⇒ t12 | t17 ⇒ t13
+ | t18 ⇒ t18 | t19 ⇒ t19 | t1A ⇒ t1A | t1B ⇒ t1B | t1C ⇒ t18 | t1D ⇒ t19 | t1E ⇒ t1A | t1F ⇒ t1B ]
+ | t1C ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t00 | t03 ⇒ t00 | t04 ⇒ t04 | t05 ⇒ t04 | t06 ⇒ t04 | t07 ⇒ t04
+ | t08 ⇒ t08 | t09 ⇒ t08 | t0A ⇒ t08 | t0B ⇒ t08 | t0C ⇒ t0C | t0D ⇒ t0C | t0E ⇒ t0C | t0F ⇒ t0C
+ | t10 ⇒ t10 | t11 ⇒ t10 | t12 ⇒ t10 | t13 ⇒ t10 | t14 ⇒ t14 | t15 ⇒ t14 | t16 ⇒ t14 | t17 ⇒ t14
+ | t18 ⇒ t18 | t19 ⇒ t18 | t1A ⇒ t18 | t1B ⇒ t18 | t1C ⇒ t1C | t1D ⇒ t1C | t1E ⇒ t1C | t1F ⇒ t1C ]
+ | t1D ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t00 | t03 ⇒ t01 | t04 ⇒ t04 | t05 ⇒ t05 | t06 ⇒ t04 | t07 ⇒ t05
+ | t08 ⇒ t08 | t09 ⇒ t09 | t0A ⇒ t08 | t0B ⇒ t09 | t0C ⇒ t0C | t0D ⇒ t0D | t0E ⇒ t0C | t0F ⇒ t0D
+ | t10 ⇒ t10 | t11 ⇒ t11 | t12 ⇒ t10 | t13 ⇒ t11 | t14 ⇒ t14 | t15 ⇒ t15 | t16 ⇒ t14 | t17 ⇒ t15
+ | t18 ⇒ t18 | t19 ⇒ t19 | t1A ⇒ t18 | t1B ⇒ t19 | t1C ⇒ t1C | t1D ⇒ t1D | t1E ⇒ t1C | t1F ⇒ t1D ]
+ | t1E ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t00 | t02 ⇒ t02 | t03 ⇒ t02 | t04 ⇒ t04 | t05 ⇒ t04 | t06 ⇒ t06 | t07 ⇒ t06
+ | t08 ⇒ t08 | t09 ⇒ t08 | t0A ⇒ t0A | t0B ⇒ t0A | t0C ⇒ t0C | t0D ⇒ t0C | t0E ⇒ t0E | t0F ⇒ t0E
+ | t10 ⇒ t10 | t11 ⇒ t10 | t12 ⇒ t12 | t13 ⇒ t12 | t14 ⇒ t14 | t15 ⇒ t14 | t16 ⇒ t16 | t17 ⇒ t16
+ | t18 ⇒ t18 | t19 ⇒ t18 | t1A ⇒ t1A | t1B ⇒ t1A | t1C ⇒ t1C | t1D ⇒ t1C | t1E ⇒ t1E | t1F ⇒ t1E ]
+ | t1F ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t02 | t03 ⇒ t03 | t04 ⇒ t04 | t05 ⇒ t05 | t06 ⇒ t06 | t07 ⇒ t07
+ | t08 ⇒ t08 | t09 ⇒ t09 | t0A ⇒ t0A | t0B ⇒ t0B | t0C ⇒ t0C | t0D ⇒ t0D | t0E ⇒ t0E | t0F ⇒ t0F
+ | t10 ⇒ t10 | t11 ⇒ t11 | t12 ⇒ t12 | t13 ⇒ t13 | t14 ⇒ t14 | t15 ⇒ t15 | t16 ⇒ t16 | t17 ⇒ t17
+ | t18 ⇒ t18 | t19 ⇒ t19 | t1A ⇒ t1A | t1B ⇒ t1B | t1C ⇒ t1C | t1D ⇒ t1D | t1E ⇒ t1E | t1F ⇒ t1F ]
+ ].
+
+(* operatore or *)
+ndefinition or_bit ≝
+λe1,e2.match e1 with
+ [ t00 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t02 | t03 ⇒ t03 | t04 ⇒ t04 | t05 ⇒ t05 | t06 ⇒ t06 | t07 ⇒ t07
+ | t08 ⇒ t08 | t09 ⇒ t09 | t0A ⇒ t0A | t0B ⇒ t0B | t0C ⇒ t0C | t0D ⇒ t0D | t0E ⇒ t0E | t0F ⇒ t0F
+ | t10 ⇒ t10 | t11 ⇒ t11 | t12 ⇒ t12 | t13 ⇒ t13 | t14 ⇒ t14 | t15 ⇒ t15 | t16 ⇒ t16 | t17 ⇒ t17
+ | t18 ⇒ t18 | t19 ⇒ t19 | t1A ⇒ t1A | t1B ⇒ t1B | t1C ⇒ t1C | t1D ⇒ t1D | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t01 ⇒ match e2 with
+ [ t00 ⇒ t01 | t01 ⇒ t01 | t02 ⇒ t03 | t03 ⇒ t03 | t04 ⇒ t05 | t05 ⇒ t05 | t06 ⇒ t07 | t07 ⇒ t07
+ | t08 ⇒ t09 | t09 ⇒ t09 | t0A ⇒ t0B | t0B ⇒ t0B | t0C ⇒ t0D | t0D ⇒ t0D | t0E ⇒ t0F | t0F ⇒ t0F
+ | t10 ⇒ t11 | t11 ⇒ t11 | t12 ⇒ t13 | t13 ⇒ t13 | t14 ⇒ t15 | t15 ⇒ t15 | t16 ⇒ t17 | t17 ⇒ t17
+ | t18 ⇒ t19 | t19 ⇒ t19 | t1A ⇒ t1B | t1B ⇒ t1B | t1C ⇒ t1D | t1D ⇒ t1D | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t02 ⇒ match e2 with
+ [ t00 ⇒ t02 | t01 ⇒ t03 | t02 ⇒ t02 | t03 ⇒ t03 | t04 ⇒ t06 | t05 ⇒ t07 | t06 ⇒ t06 | t07 ⇒ t07
+ | t08 ⇒ t0A | t09 ⇒ t0B | t0A ⇒ t0A | t0B ⇒ t0B | t0C ⇒ t0E | t0D ⇒ t0F | t0E ⇒ t0E | t0F ⇒ t0F
+ | t10 ⇒ t12 | t11 ⇒ t13 | t12 ⇒ t12 | t13 ⇒ t13 | t14 ⇒ t16 | t15 ⇒ t17 | t16 ⇒ t16 | t17 ⇒ t17
+ | t18 ⇒ t1A | t19 ⇒ t1B | t1A ⇒ t1A | t1B ⇒ t1B | t1C ⇒ t1E | t1D ⇒ t1F | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t03 ⇒ match e2 with
+ [ t00 ⇒ t03 | t01 ⇒ t03 | t02 ⇒ t03 | t03 ⇒ t03 | t04 ⇒ t07 | t05 ⇒ t07 | t06 ⇒ t07 | t07 ⇒ t07
+ | t08 ⇒ t0B | t09 ⇒ t0B | t0A ⇒ t0B | t0B ⇒ t0B | t0C ⇒ t0F | t0D ⇒ t0F | t0E ⇒ t0F | t0F ⇒ t0F
+ | t10 ⇒ t13 | t11 ⇒ t13 | t12 ⇒ t13 | t13 ⇒ t13 | t14 ⇒ t17 | t15 ⇒ t17 | t16 ⇒ t17 | t17 ⇒ t17
+ | t18 ⇒ t1B | t19 ⇒ t1B | t1A ⇒ t1B | t1B ⇒ t1B | t1C ⇒ t1F | t1D ⇒ t1F | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t04 ⇒ match e2 with
+ [ t00 ⇒ t04 | t01 ⇒ t05 | t02 ⇒ t06 | t03 ⇒ t07 | t04 ⇒ t04 | t05 ⇒ t05 | t06 ⇒ t06 | t07 ⇒ t07
+ | t08 ⇒ t0C | t09 ⇒ t0D | t0A ⇒ t0E | t0B ⇒ t0F | t0C ⇒ t0C | t0D ⇒ t0D | t0E ⇒ t0E | t0F ⇒ t0F
+ | t10 ⇒ t14 | t11 ⇒ t15 | t12 ⇒ t16 | t13 ⇒ t17 | t14 ⇒ t14 | t15 ⇒ t15 | t16 ⇒ t16 | t17 ⇒ t17
+ | t18 ⇒ t1C | t19 ⇒ t1D | t1A ⇒ t1E | t1B ⇒ t1F | t1C ⇒ t1C | t1D ⇒ t1D | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t05 ⇒ match e2 with
+ [ t00 ⇒ t05 | t01 ⇒ t05 | t02 ⇒ t07 | t03 ⇒ t07 | t04 ⇒ t05 | t05 ⇒ t05 | t06 ⇒ t07 | t07 ⇒ t07
+ | t08 ⇒ t0D | t09 ⇒ t0D | t0A ⇒ t0F | t0B ⇒ t0F | t0C ⇒ t0D | t0D ⇒ t0D | t0E ⇒ t0F | t0F ⇒ t0F
+ | t10 ⇒ t15 | t11 ⇒ t15 | t12 ⇒ t17 | t13 ⇒ t17 | t14 ⇒ t15 | t15 ⇒ t15 | t16 ⇒ t17 | t17 ⇒ t17
+ | t18 ⇒ t1D | t19 ⇒ t1D | t1A ⇒ t1F | t1B ⇒ t1F | t1C ⇒ t1D | t1D ⇒ t1D | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t06 ⇒ match e2 with
+ [ t00 ⇒ t06 | t01 ⇒ t07 | t02 ⇒ t06 | t03 ⇒ t07 | t04 ⇒ t06 | t05 ⇒ t07 | t06 ⇒ t06 | t07 ⇒ t07
+ | t08 ⇒ t0E | t09 ⇒ t0F | t0A ⇒ t0E | t0B ⇒ t0F | t0C ⇒ t0E | t0D ⇒ t0F | t0E ⇒ t0E | t0F ⇒ t0F
+ | t10 ⇒ t16 | t11 ⇒ t17 | t12 ⇒ t16 | t13 ⇒ t17 | t14 ⇒ t16 | t15 ⇒ t17 | t16 ⇒ t16 | t17 ⇒ t17
+ | t18 ⇒ t1E | t19 ⇒ t1F | t1A ⇒ t1E | t1B ⇒ t1F | t1C ⇒ t1E | t1D ⇒ t1F | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t07 ⇒ match e2 with
+ [ t00 ⇒ t07 | t01 ⇒ t07 | t02 ⇒ t07 | t03 ⇒ t07 | t04 ⇒ t07 | t05 ⇒ t07 | t06 ⇒ t07 | t07 ⇒ t07
+ | t08 ⇒ t0F | t09 ⇒ t0F | t0A ⇒ t0F | t0B ⇒ t0F | t0C ⇒ t0F | t0D ⇒ t0F | t0E ⇒ t0F | t0F ⇒ t0F
+ | t10 ⇒ t17 | t11 ⇒ t17 | t12 ⇒ t17 | t13 ⇒ t17 | t14 ⇒ t17 | t15 ⇒ t17 | t16 ⇒ t17 | t17 ⇒ t17
+ | t18 ⇒ t1F | t19 ⇒ t1F | t1A ⇒ t1F | t1B ⇒ t1F | t1C ⇒ t1F | t1D ⇒ t1F | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t08 ⇒ match e2 with
+ [ t00 ⇒ t08 | t01 ⇒ t09 | t02 ⇒ t0A | t03 ⇒ t0B | t04 ⇒ t0C | t05 ⇒ t0D | t06 ⇒ t0E | t07 ⇒ t0F
+ | t08 ⇒ t08 | t09 ⇒ t09 | t0A ⇒ t0A | t0B ⇒ t0B | t0C ⇒ t0C | t0D ⇒ t0D | t0E ⇒ t0E | t0F ⇒ t0F
+ | t10 ⇒ t18 | t11 ⇒ t19 | t12 ⇒ t1A | t13 ⇒ t1B | t14 ⇒ t1C | t15 ⇒ t1D | t16 ⇒ t1E | t17 ⇒ t1F
+ | t18 ⇒ t18 | t19 ⇒ t19 | t1A ⇒ t1A | t1B ⇒ t1B | t1C ⇒ t1C | t1D ⇒ t1D | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t09 ⇒ match e2 with
+ [ t00 ⇒ t09 | t01 ⇒ t09 | t02 ⇒ t0B | t03 ⇒ t0B | t04 ⇒ t0D | t05 ⇒ t0D | t06 ⇒ t0F | t07 ⇒ t0F
+ | t08 ⇒ t09 | t09 ⇒ t09 | t0A ⇒ t0B | t0B ⇒ t0B | t0C ⇒ t0D | t0D ⇒ t0D | t0E ⇒ t0F | t0F ⇒ t0F
+ | t10 ⇒ t19 | t11 ⇒ t19 | t12 ⇒ t1B | t13 ⇒ t1B | t14 ⇒ t1D | t15 ⇒ t1D | t16 ⇒ t1F | t17 ⇒ t1F
+ | t18 ⇒ t19 | t19 ⇒ t19 | t1A ⇒ t1B | t1B ⇒ t1B | t1C ⇒ t1D | t1D ⇒ t1D | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t0A ⇒ match e2 with
+ [ t00 ⇒ t0A | t01 ⇒ t0B | t02 ⇒ t0A | t03 ⇒ t0B | t04 ⇒ t0E | t05 ⇒ t0F | t06 ⇒ t0E | t07 ⇒ t0F
+ | t08 ⇒ t0A | t09 ⇒ t0B | t0A ⇒ t0A | t0B ⇒ t0B | t0C ⇒ t0E | t0D ⇒ t0F | t0E ⇒ t0E | t0F ⇒ t0F
+ | t10 ⇒ t1A | t11 ⇒ t1B | t12 ⇒ t1A | t13 ⇒ t1B | t14 ⇒ t1E | t15 ⇒ t1F | t16 ⇒ t1E | t17 ⇒ t1F
+ | t18 ⇒ t1A | t19 ⇒ t1B | t1A ⇒ t1A | t1B ⇒ t1B | t1C ⇒ t1E | t1D ⇒ t1F | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t0B ⇒ match e2 with
+ [ t00 ⇒ t0B | t01 ⇒ t0B | t02 ⇒ t0B | t03 ⇒ t0B | t04 ⇒ t0F | t05 ⇒ t0F | t06 ⇒ t0F | t07 ⇒ t0F
+ | t08 ⇒ t0B | t09 ⇒ t0B | t0A ⇒ t0B | t0B ⇒ t0B | t0C ⇒ t0F | t0D ⇒ t0F | t0E ⇒ t0F | t0F ⇒ t0F
+ | t10 ⇒ t1B | t11 ⇒ t1B | t12 ⇒ t1B | t13 ⇒ t1B | t14 ⇒ t1F | t15 ⇒ t1F | t16 ⇒ t1F | t17 ⇒ t1F
+ | t18 ⇒ t1B | t19 ⇒ t1B | t1A ⇒ t1B | t1B ⇒ t1B | t1C ⇒ t1F | t1D ⇒ t1F | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t0C ⇒ match e2 with
+ [ t00 ⇒ t0C | t01 ⇒ t0D | t02 ⇒ t0E | t03 ⇒ t0F | t04 ⇒ t0C | t05 ⇒ t0D | t06 ⇒ t0E | t07 ⇒ t0F
+ | t08 ⇒ t0C | t09 ⇒ t0D | t0A ⇒ t0E | t0B ⇒ t0F | t0C ⇒ t0C | t0D ⇒ t0D | t0E ⇒ t0E | t0F ⇒ t0F
+ | t10 ⇒ t1C | t11 ⇒ t1D | t12 ⇒ t1E | t13 ⇒ t1F | t14 ⇒ t1C | t15 ⇒ t1D | t16 ⇒ t1E | t17 ⇒ t1F
+ | t18 ⇒ t1C | t19 ⇒ t1D | t1A ⇒ t1E | t1B ⇒ t1F | t1C ⇒ t1C | t1D ⇒ t1D | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t0D ⇒ match e2 with
+ [ t00 ⇒ t0D | t01 ⇒ t0D | t02 ⇒ t0F | t03 ⇒ t0F | t04 ⇒ t0D | t05 ⇒ t0D | t06 ⇒ t0F | t07 ⇒ t0F
+ | t08 ⇒ t0D | t09 ⇒ t0D | t0A ⇒ t0F | t0B ⇒ t0F | t0C ⇒ t0D | t0D ⇒ t0D | t0E ⇒ t0F | t0F ⇒ t0F
+ | t10 ⇒ t1D | t11 ⇒ t1D | t12 ⇒ t1F | t13 ⇒ t1F | t14 ⇒ t1D | t15 ⇒ t1D | t16 ⇒ t1F | t17 ⇒ t1F
+ | t18 ⇒ t1D | t19 ⇒ t1D | t1A ⇒ t1F | t1B ⇒ t1F | t1C ⇒ t1D | t1D ⇒ t1D | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t0E ⇒ match e2 with
+ [ t00 ⇒ t0E | t01 ⇒ t0F | t02 ⇒ t0E | t03 ⇒ t0F | t04 ⇒ t0E | t05 ⇒ t0F | t06 ⇒ t0E | t07 ⇒ t0F
+ | t08 ⇒ t0E | t09 ⇒ t0F | t0A ⇒ t0E | t0B ⇒ t0F | t0C ⇒ t0E | t0D ⇒ t0F | t0E ⇒ t0E | t0F ⇒ t0F
+ | t10 ⇒ t1E | t11 ⇒ t1F | t12 ⇒ t1E | t13 ⇒ t1F | t14 ⇒ t1E | t15 ⇒ t1F | t16 ⇒ t1E | t17 ⇒ t1F
+ | t18 ⇒ t1E | t19 ⇒ t1F | t1A ⇒ t1E | t1B ⇒ t1F | t1C ⇒ t1E | t1D ⇒ t1F | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t0F ⇒ match e2 with
+ [ t00 ⇒ t0F | t01 ⇒ t0F | t02 ⇒ t0F | t03 ⇒ t0F | t04 ⇒ t0F | t05 ⇒ t0F | t06 ⇒ t0F | t07 ⇒ t0F
+ | t08 ⇒ t0F | t09 ⇒ t0F | t0A ⇒ t0F | t0B ⇒ t0F | t0C ⇒ t0F | t0D ⇒ t0F | t0E ⇒ t0F | t0F ⇒ t0F
+ | t10 ⇒ t1F | t11 ⇒ t1F | t12 ⇒ t1F | t13 ⇒ t1F | t14 ⇒ t1F | t15 ⇒ t1F | t16 ⇒ t1F | t17 ⇒ t1F
+ | t18 ⇒ t1F | t19 ⇒ t1F | t1A ⇒ t1F | t1B ⇒ t1F | t1C ⇒ t1F | t1D ⇒ t1F | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t10 ⇒ match e2 with
+ [ t00 ⇒ t10 | t01 ⇒ t11 | t02 ⇒ t12 | t03 ⇒ t13 | t04 ⇒ t14 | t05 ⇒ t15 | t06 ⇒ t16 | t07 ⇒ t17
+ | t08 ⇒ t18 | t09 ⇒ t19 | t0A ⇒ t1A | t0B ⇒ t1B | t0C ⇒ t1C | t0D ⇒ t1D | t0E ⇒ t1E | t0F ⇒ t1F
+ | t10 ⇒ t10 | t11 ⇒ t11 | t12 ⇒ t12 | t13 ⇒ t13 | t14 ⇒ t14 | t15 ⇒ t15 | t16 ⇒ t16 | t17 ⇒ t17
+ | t18 ⇒ t18 | t19 ⇒ t19 | t1A ⇒ t1A | t1B ⇒ t1B | t1C ⇒ t1C | t1D ⇒ t1D | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t11 ⇒ match e2 with
+ [ t00 ⇒ t11 | t01 ⇒ t11 | t02 ⇒ t13 | t03 ⇒ t13 | t04 ⇒ t15 | t05 ⇒ t15 | t06 ⇒ t17 | t07 ⇒ t17
+ | t08 ⇒ t19 | t09 ⇒ t19 | t0A ⇒ t1B | t0B ⇒ t1B | t0C ⇒ t1D | t0D ⇒ t1D | t0E ⇒ t1F | t0F ⇒ t1F
+ | t10 ⇒ t11 | t11 ⇒ t11 | t12 ⇒ t13 | t13 ⇒ t13 | t14 ⇒ t15 | t15 ⇒ t15 | t16 ⇒ t17 | t17 ⇒ t17
+ | t18 ⇒ t19 | t19 ⇒ t19 | t1A ⇒ t1B | t1B ⇒ t1B | t1C ⇒ t1D | t1D ⇒ t1D | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t12 ⇒ match e2 with
+ [ t00 ⇒ t12 | t01 ⇒ t13 | t02 ⇒ t12 | t03 ⇒ t13 | t04 ⇒ t16 | t05 ⇒ t17 | t06 ⇒ t16 | t07 ⇒ t17
+ | t08 ⇒ t1A | t09 ⇒ t1B | t0A ⇒ t1A | t0B ⇒ t1B | t0C ⇒ t1E | t0D ⇒ t1F | t0E ⇒ t1E | t0F ⇒ t1F
+ | t10 ⇒ t12 | t11 ⇒ t13 | t12 ⇒ t12 | t13 ⇒ t13 | t14 ⇒ t16 | t15 ⇒ t17 | t16 ⇒ t16 | t17 ⇒ t17
+ | t18 ⇒ t1A | t19 ⇒ t1B | t1A ⇒ t1A | t1B ⇒ t1B | t1C ⇒ t1E | t1D ⇒ t1F | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t13 ⇒ match e2 with
+ [ t00 ⇒ t13 | t01 ⇒ t13 | t02 ⇒ t13 | t03 ⇒ t13 | t04 ⇒ t17 | t05 ⇒ t17 | t06 ⇒ t17 | t07 ⇒ t17
+ | t08 ⇒ t1B | t09 ⇒ t1B | t0A ⇒ t1B | t0B ⇒ t1B | t0C ⇒ t1F | t0D ⇒ t1F | t0E ⇒ t1F | t0F ⇒ t1F
+ | t10 ⇒ t13 | t11 ⇒ t13 | t12 ⇒ t13 | t13 ⇒ t13 | t14 ⇒ t17 | t15 ⇒ t17 | t16 ⇒ t17 | t17 ⇒ t17
+ | t18 ⇒ t1B | t19 ⇒ t1B | t1A ⇒ t1B | t1B ⇒ t1B | t1C ⇒ t1F | t1D ⇒ t1F | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t14 ⇒ match e2 with
+ [ t00 ⇒ t14 | t01 ⇒ t15 | t02 ⇒ t16 | t03 ⇒ t17 | t04 ⇒ t14 | t05 ⇒ t15 | t06 ⇒ t16 | t07 ⇒ t17
+ | t08 ⇒ t1C | t09 ⇒ t1D | t0A ⇒ t1E | t0B ⇒ t1F | t0C ⇒ t1C | t0D ⇒ t1D | t0E ⇒ t1E | t0F ⇒ t1F
+ | t10 ⇒ t14 | t11 ⇒ t15 | t12 ⇒ t16 | t13 ⇒ t17 | t14 ⇒ t14 | t15 ⇒ t15 | t16 ⇒ t16 | t17 ⇒ t17
+ | t18 ⇒ t1C | t19 ⇒ t1D | t1A ⇒ t1E | t1B ⇒ t1F | t1C ⇒ t1C | t1D ⇒ t1D | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t15 ⇒ match e2 with
+ [ t00 ⇒ t15 | t01 ⇒ t15 | t02 ⇒ t17 | t03 ⇒ t17 | t04 ⇒ t15 | t05 ⇒ t15 | t06 ⇒ t17 | t07 ⇒ t17
+ | t08 ⇒ t1D | t09 ⇒ t1D | t0A ⇒ t1F | t0B ⇒ t1F | t0C ⇒ t1D | t0D ⇒ t1D | t0E ⇒ t1F | t0F ⇒ t1F
+ | t10 ⇒ t15 | t11 ⇒ t15 | t12 ⇒ t17 | t13 ⇒ t17 | t14 ⇒ t15 | t15 ⇒ t15 | t16 ⇒ t17 | t17 ⇒ t17
+ | t18 ⇒ t1D | t19 ⇒ t1D | t1A ⇒ t1F | t1B ⇒ t1F | t1C ⇒ t1D | t1D ⇒ t1D | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t16 ⇒ match e2 with
+ [ t00 ⇒ t16 | t01 ⇒ t17 | t02 ⇒ t16 | t03 ⇒ t17 | t04 ⇒ t16 | t05 ⇒ t17 | t06 ⇒ t16 | t07 ⇒ t17
+ | t08 ⇒ t1E | t09 ⇒ t1F | t0A ⇒ t1E | t0B ⇒ t1F | t0C ⇒ t1E | t0D ⇒ t1F | t0E ⇒ t1E | t0F ⇒ t1F
+ | t10 ⇒ t16 | t11 ⇒ t17 | t12 ⇒ t16 | t13 ⇒ t17 | t14 ⇒ t16 | t15 ⇒ t17 | t16 ⇒ t16 | t17 ⇒ t17
+ | t18 ⇒ t1E | t19 ⇒ t1F | t1A ⇒ t1E | t1B ⇒ t1F | t1C ⇒ t1E | t1D ⇒ t1F | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t17 ⇒ match e2 with
+ [ t00 ⇒ t17 | t01 ⇒ t17 | t02 ⇒ t17 | t03 ⇒ t17 | t04 ⇒ t17 | t05 ⇒ t17 | t06 ⇒ t17 | t07 ⇒ t17
+ | t08 ⇒ t1F | t09 ⇒ t1F | t0A ⇒ t1F | t0B ⇒ t1F | t0C ⇒ t1F | t0D ⇒ t1F | t0E ⇒ t1F | t0F ⇒ t1F
+ | t10 ⇒ t17 | t11 ⇒ t17 | t12 ⇒ t17 | t13 ⇒ t17 | t14 ⇒ t17 | t15 ⇒ t17 | t16 ⇒ t17 | t17 ⇒ t17
+ | t18 ⇒ t1F | t19 ⇒ t1F | t1A ⇒ t1F | t1B ⇒ t1F | t1C ⇒ t1F | t1D ⇒ t1F | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t18 ⇒ match e2 with
+ [ t00 ⇒ t18 | t01 ⇒ t19 | t02 ⇒ t1A | t03 ⇒ t1B | t04 ⇒ t1C | t05 ⇒ t1D | t06 ⇒ t1E | t07 ⇒ t1F
+ | t08 ⇒ t18 | t09 ⇒ t19 | t0A ⇒ t1A | t0B ⇒ t1B | t0C ⇒ t1C | t0D ⇒ t1D | t0E ⇒ t1E | t0F ⇒ t1F
+ | t10 ⇒ t18 | t11 ⇒ t19 | t12 ⇒ t1A | t13 ⇒ t1B | t14 ⇒ t1C | t15 ⇒ t1D | t16 ⇒ t1E | t17 ⇒ t1F
+ | t18 ⇒ t18 | t19 ⇒ t19 | t1A ⇒ t1A | t1B ⇒ t1B | t1C ⇒ t1C | t1D ⇒ t1D | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t19 ⇒ match e2 with
+ [ t00 ⇒ t19 | t01 ⇒ t19 | t02 ⇒ t1B | t03 ⇒ t1B | t04 ⇒ t1D | t05 ⇒ t1D | t06 ⇒ t1F | t07 ⇒ t1F
+ | t08 ⇒ t19 | t09 ⇒ t19 | t0A ⇒ t1B | t0B ⇒ t1B | t0C ⇒ t1D | t0D ⇒ t1D | t0E ⇒ t1F | t0F ⇒ t1F
+ | t10 ⇒ t19 | t11 ⇒ t19 | t12 ⇒ t1B | t13 ⇒ t1B | t14 ⇒ t1D | t15 ⇒ t1D | t16 ⇒ t1F | t17 ⇒ t1F
+ | t18 ⇒ t19 | t19 ⇒ t19 | t1A ⇒ t1B | t1B ⇒ t1B | t1C ⇒ t1D | t1D ⇒ t1D | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t1A ⇒ match e2 with
+ [ t00 ⇒ t1A | t01 ⇒ t1B | t02 ⇒ t1A | t03 ⇒ t1B | t04 ⇒ t1E | t05 ⇒ t1F | t06 ⇒ t1E | t07 ⇒ t1F
+ | t08 ⇒ t1A | t09 ⇒ t1B | t0A ⇒ t1A | t0B ⇒ t1B | t0C ⇒ t1E | t0D ⇒ t1F | t0E ⇒ t1E | t0F ⇒ t1F
+ | t10 ⇒ t1A | t11 ⇒ t1B | t12 ⇒ t1A | t13 ⇒ t1B | t14 ⇒ t1E | t15 ⇒ t1F | t16 ⇒ t1E | t17 ⇒ t1F
+ | t18 ⇒ t1A | t19 ⇒ t1B | t1A ⇒ t1A | t1B ⇒ t1B | t1C ⇒ t1E | t1D ⇒ t1F | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t1B ⇒ match e2 with
+ [ t00 ⇒ t1B | t01 ⇒ t1B | t02 ⇒ t1B | t03 ⇒ t1B | t04 ⇒ t1F | t05 ⇒ t1F | t06 ⇒ t1F | t07 ⇒ t1F
+ | t08 ⇒ t1B | t09 ⇒ t1B | t0A ⇒ t1B | t0B ⇒ t1B | t0C ⇒ t1F | t0D ⇒ t1F | t0E ⇒ t1F | t0F ⇒ t1F
+ | t10 ⇒ t1B | t11 ⇒ t1B | t12 ⇒ t1B | t13 ⇒ t1B | t14 ⇒ t1F | t15 ⇒ t1F | t16 ⇒ t1F | t17 ⇒ t1F
+ | t18 ⇒ t1B | t19 ⇒ t1B | t1A ⇒ t1B | t1B ⇒ t1B | t1C ⇒ t1F | t1D ⇒ t1F | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t1C ⇒ match e2 with
+ [ t00 ⇒ t1C | t01 ⇒ t1D | t02 ⇒ t1E | t03 ⇒ t1F | t04 ⇒ t1C | t05 ⇒ t1D | t06 ⇒ t1E | t07 ⇒ t1F
+ | t08 ⇒ t1C | t09 ⇒ t1D | t0A ⇒ t1E | t0B ⇒ t1F | t0C ⇒ t1C | t0D ⇒ t1D | t0E ⇒ t1E | t0F ⇒ t1F
+ | t10 ⇒ t1C | t11 ⇒ t1D | t12 ⇒ t1E | t13 ⇒ t1F | t14 ⇒ t1C | t15 ⇒ t1D | t16 ⇒ t1E | t17 ⇒ t1F
+ | t18 ⇒ t1C | t19 ⇒ t1D | t1A ⇒ t1E | t1B ⇒ t1F | t1C ⇒ t1C | t1D ⇒ t1D | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t1D ⇒ match e2 with
+ [ t00 ⇒ t1D | t01 ⇒ t1D | t02 ⇒ t1F | t03 ⇒ t1F | t04 ⇒ t1D | t05 ⇒ t1D | t06 ⇒ t1F | t07 ⇒ t1F
+ | t08 ⇒ t1D | t09 ⇒ t1D | t0A ⇒ t1F | t0B ⇒ t1F | t0C ⇒ t1D | t0D ⇒ t1D | t0E ⇒ t1F | t0F ⇒ t1F
+ | t10 ⇒ t1D | t11 ⇒ t1D | t12 ⇒ t1F | t13 ⇒ t1F | t14 ⇒ t1D | t15 ⇒ t1D | t16 ⇒ t1F | t17 ⇒ t1F
+ | t18 ⇒ t1D | t19 ⇒ t1D | t1A ⇒ t1F | t1B ⇒ t1F | t1C ⇒ t1D | t1D ⇒ t1D | t1E ⇒ t1F | t1F ⇒ t1F ]
+ | t1E ⇒ match e2 with
+ [ t00 ⇒ t1E | t01 ⇒ t1F | t02 ⇒ t1E | t03 ⇒ t1F | t04 ⇒ t1E | t05 ⇒ t1F | t06 ⇒ t1E | t07 ⇒ t1F
+ | t08 ⇒ t1E | t09 ⇒ t1F | t0A ⇒ t1E | t0B ⇒ t1F | t0C ⇒ t1E | t0D ⇒ t1F | t0E ⇒ t1E | t0F ⇒ t1F
+ | t10 ⇒ t1E | t11 ⇒ t1F | t12 ⇒ t1E | t13 ⇒ t1F | t14 ⇒ t1E | t15 ⇒ t1F | t16 ⇒ t1E | t17 ⇒ t1F
+ | t18 ⇒ t1E | t19 ⇒ t1F | t1A ⇒ t1E | t1B ⇒ t1F | t1C ⇒ t1E | t1D ⇒ t1F | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t1F ⇒ match e2 with
+ [ t00 ⇒ t1F | t01 ⇒ t1F | t02 ⇒ t1F | t03 ⇒ t1F | t04 ⇒ t1F | t05 ⇒ t1F | t06 ⇒ t1F | t07 ⇒ t1F
+ | t08 ⇒ t1F | t09 ⇒ t1F | t0A ⇒ t1F | t0B ⇒ t1F | t0C ⇒ t1F | t0D ⇒ t1F | t0E ⇒ t1F | t0F ⇒ t1F
+ | t10 ⇒ t1F | t11 ⇒ t1F | t12 ⇒ t1F | t13 ⇒ t1F | t14 ⇒ t1F | t15 ⇒ t1F | t16 ⇒ t1F | t17 ⇒ t1F
+ | t18 ⇒ t1F | t19 ⇒ t1F | t1A ⇒ t1F | t1B ⇒ t1F | t1C ⇒ t1F | t1D ⇒ t1F | t1E ⇒ t1F | t1F ⇒ t1F ]
+ ].
+
+(* operatore xor *)
+ndefinition xor_bit ≝
+λe1,e2.match e1 with
+ [ t00 ⇒ match e2 with
+ [ t00 ⇒ t00 | t01 ⇒ t01 | t02 ⇒ t02 | t03 ⇒ t03 | t04 ⇒ t04 | t05 ⇒ t05 | t06 ⇒ t06 | t07 ⇒ t07
+ | t08 ⇒ t08 | t09 ⇒ t09 | t0A ⇒ t0A | t0B ⇒ t0B | t0C ⇒ t0C | t0D ⇒ t0D | t0E ⇒ t0E | t0F ⇒ t0F
+ | t10 ⇒ t10 | t11 ⇒ t11 | t12 ⇒ t12 | t13 ⇒ t13 | t14 ⇒ t14 | t15 ⇒ t15 | t16 ⇒ t16 | t17 ⇒ t17
+ | t18 ⇒ t18 | t19 ⇒ t19 | t1A ⇒ t1A | t1B ⇒ t1B | t1C ⇒ t1C | t1D ⇒ t1D | t1E ⇒ t1E | t1F ⇒ t1F ]
+ | t01 ⇒ match e2 with
+ [ t00 ⇒ t01 | t01 ⇒ t00 | t02 ⇒ t03 | t03 ⇒ t02 | t04 ⇒ t05 | t05 ⇒ t04 | t06 ⇒ t07 | t07 ⇒ t06
+ | t08 ⇒ t09 | t09 ⇒ t08 | t0A ⇒ t0B | t0B ⇒ t0A | t0C ⇒ t0D | t0D ⇒ t0C | t0E ⇒ t0F | t0F ⇒ t0E
+ | t10 ⇒ t11 | t11 ⇒ t10 | t12 ⇒ t13 | t13 ⇒ t12 | t14 ⇒ t15 | t15 ⇒ t14 | t16 ⇒ t17 | t17 ⇒ t16
+ | t18 ⇒ t19 | t19 ⇒ t18 | t1A ⇒ t1B | t1B ⇒ t1A | t1C ⇒ t1D | t1D ⇒ t1C | t1E ⇒ t1F | t1F ⇒ t1E ]
+ | t02 ⇒ match e2 with
+ [ t00 ⇒ t02 | t01 ⇒ t03 | t02 ⇒ t00 | t03 ⇒ t01 | t04 ⇒ t06 | t05 ⇒ t07 | t06 ⇒ t04 | t07 ⇒ t05
+ | t08 ⇒ t0A | t09 ⇒ t0B | t0A ⇒ t08 | t0B ⇒ t09 | t0C ⇒ t0E | t0D ⇒ t0F | t0E ⇒ t0C | t0F ⇒ t0D
+ | t10 ⇒ t12 | t11 ⇒ t13 | t12 ⇒ t10 | t13 ⇒ t11 | t14 ⇒ t16 | t15 ⇒ t17 | t16 ⇒ t14 | t17 ⇒ t15
+ | t18 ⇒ t1A | t19 ⇒ t1B | t1A ⇒ t18 | t1B ⇒ t19 | t1C ⇒ t1E | t1D ⇒ t1F | t1E ⇒ t1C | t1F ⇒ t1D ]
+ | t03 ⇒ match e2 with
+ [ t00 ⇒ t03 | t01 ⇒ t02 | t02 ⇒ t01 | t03 ⇒ t00 | t04 ⇒ t07 | t05 ⇒ t06 | t06 ⇒ t05 | t07 ⇒ t04
+ | t08 ⇒ t0B | t09 ⇒ t0A | t0A ⇒ t09 | t0B ⇒ t08 | t0C ⇒ t0F | t0D ⇒ t0E | t0E ⇒ t0D | t0F ⇒ t0C
+ | t10 ⇒ t13 | t11 ⇒ t12 | t12 ⇒ t11 | t13 ⇒ t10 | t14 ⇒ t17 | t15 ⇒ t16 | t16 ⇒ t15 | t17 ⇒ t14
+ | t18 ⇒ t1B | t19 ⇒ t1A | t1A ⇒ t19 | t1B ⇒ t18 | t1C ⇒ t1F | t1D ⇒ t1E | t1E ⇒ t1D | t1F ⇒ t1C ]
+ | t04 ⇒ match e2 with
+ [ t00 ⇒ t04 | t01 ⇒ t05 | t02 ⇒ t06 | t03 ⇒ t07 | t04 ⇒ t00 | t05 ⇒ t01 | t06 ⇒ t02 | t07 ⇒ t03
+ | t08 ⇒ t0C | t09 ⇒ t0D | t0A ⇒ t0E | t0B ⇒ t0F | t0C ⇒ t08 | t0D ⇒ t09 | t0E ⇒ t0A | t0F ⇒ t0B
+ | t10 ⇒ t14 | t11 ⇒ t15 | t12 ⇒ t16 | t13 ⇒ t17 | t14 ⇒ t10 | t15 ⇒ t11 | t16 ⇒ t12 | t17 ⇒ t13
+ | t18 ⇒ t1C | t19 ⇒ t1D | t1A ⇒ t1E | t1B ⇒ t1F | t1C ⇒ t18 | t1D ⇒ t19 | t1E ⇒ t1A | t1F ⇒ t1B ]
+ | t05 ⇒ match e2 with
+ [ t00 ⇒ t05 | t01 ⇒ t04 | t02 ⇒ t07 | t03 ⇒ t06 | t04 ⇒ t01 | t05 ⇒ t00 | t06 ⇒ t03 | t07 ⇒ t02
+ | t08 ⇒ t0D | t09 ⇒ t0C | t0A ⇒ t0F | t0B ⇒ t0E | t0C ⇒ t09 | t0D ⇒ t08 | t0E ⇒ t0B | t0F ⇒ t0A
+ | t10 ⇒ t15 | t11 ⇒ t14 | t12 ⇒ t17 | t13 ⇒ t16 | t14 ⇒ t11 | t15 ⇒ t10 | t16 ⇒ t13 | t17 ⇒ t12
+ | t18 ⇒ t1D | t19 ⇒ t1C | t1A ⇒ t1F | t1B ⇒ t1E | t1C ⇒ t19 | t1D ⇒ t18 | t1E ⇒ t1B | t1F ⇒ t1A ]
+ | t06 ⇒ match e2 with
+ [ t00 ⇒ t06 | t01 ⇒ t07 | t02 ⇒ t04 | t03 ⇒ t05 | t04 ⇒ t02 | t05 ⇒ t03 | t06 ⇒ t00 | t07 ⇒ t01
+ | t08 ⇒ t0E | t09 ⇒ t0F | t0A ⇒ t0C | t0B ⇒ t0D | t0C ⇒ t0A | t0D ⇒ t0B | t0E ⇒ t08 | t0F ⇒ t09
+ | t10 ⇒ t16 | t11 ⇒ t17 | t12 ⇒ t14 | t13 ⇒ t15 | t14 ⇒ t12 | t15 ⇒ t13 | t16 ⇒ t10 | t17 ⇒ t11
+ | t18 ⇒ t1E | t19 ⇒ t1F | t1A ⇒ t1C | t1B ⇒ t1D | t1C ⇒ t1A | t1D ⇒ t1B | t1E ⇒ t18 | t1F ⇒ t19 ]
+ | t07 ⇒ match e2 with
+ [ t00 ⇒ t07 | t01 ⇒ t06 | t02 ⇒ t05 | t03 ⇒ t04 | t04 ⇒ t03 | t05 ⇒ t02 | t06 ⇒ t01 | t07 ⇒ t00
+ | t08 ⇒ t0F | t09 ⇒ t0E | t0A ⇒ t0D | t0B ⇒ t0C | t0C ⇒ t0B | t0D ⇒ t0A | t0E ⇒ t09 | t0F ⇒ t08
+ | t10 ⇒ t17 | t11 ⇒ t16 | t12 ⇒ t15 | t13 ⇒ t14 | t14 ⇒ t13 | t15 ⇒ t12 | t16 ⇒ t11 | t17 ⇒ t10
+ | t18 ⇒ t1F | t19 ⇒ t1E | t1A ⇒ t1D | t1B ⇒ t1C | t1C ⇒ t1B | t1D ⇒ t1A | t1E ⇒ t19 | t1F ⇒ t18 ]
+ | t08 ⇒ match e2 with
+ [ t00 ⇒ t08 | t01 ⇒ t09 | t02 ⇒ t0A | t03 ⇒ t0B | t04 ⇒ t0C | t05 ⇒ t0D | t06 ⇒ t0E | t07 ⇒ t0F
+ | t08 ⇒ t00 | t09 ⇒ t01 | t0A ⇒ t02 | t0B ⇒ t03 | t0C ⇒ t04 | t0D ⇒ t05 | t0E ⇒ t06 | t0F ⇒ t07
+ | t10 ⇒ t18 | t11 ⇒ t19 | t12 ⇒ t1A | t13 ⇒ t1B | t14 ⇒ t1C | t15 ⇒ t1D | t16 ⇒ t1E | t17 ⇒ t1F
+ | t18 ⇒ t10 | t19 ⇒ t11 | t1A ⇒ t12 | t1B ⇒ t13 | t1C ⇒ t14 | t1D ⇒ t15 | t1E ⇒ t16 | t1F ⇒ t17 ]
+ | t09 ⇒ match e2 with
+ [ t00 ⇒ t09 | t01 ⇒ t08 | t02 ⇒ t0B | t03 ⇒ t0A | t04 ⇒ t0D | t05 ⇒ t0C | t06 ⇒ t0F | t07 ⇒ t0E
+ | t08 ⇒ t01 | t09 ⇒ t00 | t0A ⇒ t03 | t0B ⇒ t02 | t0C ⇒ t05 | t0D ⇒ t04 | t0E ⇒ t07 | t0F ⇒ t06
+ | t10 ⇒ t19 | t11 ⇒ t18 | t12 ⇒ t1B | t13 ⇒ t1A | t14 ⇒ t1D | t15 ⇒ t1C | t16 ⇒ t1F | t17 ⇒ t1E
+ | t18 ⇒ t11 | t19 ⇒ t10 | t1A ⇒ t13 | t1B ⇒ t12 | t1C ⇒ t15 | t1D ⇒ t14 | t1E ⇒ t17 | t1F ⇒ t16 ]
+ | t0A ⇒ match e2 with
+ [ t00 ⇒ t0A | t01 ⇒ t0B | t02 ⇒ t08 | t03 ⇒ t09 | t04 ⇒ t0E | t05 ⇒ t0F | t06 ⇒ t0C | t07 ⇒ t0D
+ | t08 ⇒ t02 | t09 ⇒ t03 | t0A ⇒ t00 | t0B ⇒ t01 | t0C ⇒ t06 | t0D ⇒ t07 | t0E ⇒ t04 | t0F ⇒ t05
+ | t10 ⇒ t1A | t11 ⇒ t1B | t12 ⇒ t18 | t13 ⇒ t19 | t14 ⇒ t1E | t15 ⇒ t1F | t16 ⇒ t1C | t17 ⇒ t1D
+ | t18 ⇒ t12 | t19 ⇒ t13 | t1A ⇒ t10 | t1B ⇒ t11 | t1C ⇒ t16 | t1D ⇒ t17 | t1E ⇒ t14 | t1F ⇒ t15 ]
+ | t0B ⇒ match e2 with
+ [ t00 ⇒ t0B | t01 ⇒ t0A | t02 ⇒ t09 | t03 ⇒ t08 | t04 ⇒ t0F | t05 ⇒ t0E | t06 ⇒ t0D | t07 ⇒ t0C
+ | t08 ⇒ t03 | t09 ⇒ t02 | t0A ⇒ t01 | t0B ⇒ t00 | t0C ⇒ t07 | t0D ⇒ t06 | t0E ⇒ t05 | t0F ⇒ t04
+ | t10 ⇒ t1B | t11 ⇒ t1A | t12 ⇒ t19 | t13 ⇒ t18 | t14 ⇒ t1F | t15 ⇒ t1E | t16 ⇒ t1D | t17 ⇒ t1C
+ | t18 ⇒ t13 | t19 ⇒ t12 | t1A ⇒ t11 | t1B ⇒ t10 | t1C ⇒ t17 | t1D ⇒ t16 | t1E ⇒ t15 | t1F ⇒ t14 ]
+ | t0C ⇒ match e2 with
+ [ t00 ⇒ t0C | t01 ⇒ t0D | t02 ⇒ t0E | t03 ⇒ t0F | t04 ⇒ t08 | t05 ⇒ t09 | t06 ⇒ t0A | t07 ⇒ t0B
+ | t08 ⇒ t04 | t09 ⇒ t05 | t0A ⇒ t06 | t0B ⇒ t07 | t0C ⇒ t00 | t0D ⇒ t01 | t0E ⇒ t02 | t0F ⇒ t03
+ | t10 ⇒ t1C | t11 ⇒ t1D | t12 ⇒ t1E | t13 ⇒ t1F | t14 ⇒ t18 | t15 ⇒ t19 | t16 ⇒ t1A | t17 ⇒ t1B
+ | t18 ⇒ t14 | t19 ⇒ t15 | t1A ⇒ t16 | t1B ⇒ t17 | t1C ⇒ t10 | t1D ⇒ t11 | t1E ⇒ t12 | t1F ⇒ t13 ]
+ | t0D ⇒ match e2 with
+ [ t00 ⇒ t0D | t01 ⇒ t0C | t02 ⇒ t0F | t03 ⇒ t0E | t04 ⇒ t09 | t05 ⇒ t08 | t06 ⇒ t0B | t07 ⇒ t0A
+ | t08 ⇒ t05 | t09 ⇒ t04 | t0A ⇒ t07 | t0B ⇒ t06 | t0C ⇒ t01 | t0D ⇒ t00 | t0E ⇒ t03 | t0F ⇒ t02
+ | t10 ⇒ t1D | t11 ⇒ t1C | t12 ⇒ t1F | t13 ⇒ t1E | t14 ⇒ t19 | t15 ⇒ t18 | t16 ⇒ t1B | t17 ⇒ t1A
+ | t18 ⇒ t15 | t19 ⇒ t14 | t1A ⇒ t17 | t1B ⇒ t16 | t1C ⇒ t11 | t1D ⇒ t10 | t1E ⇒ t13 | t1F ⇒ t12 ]
+ | t0E ⇒ match e2 with
+ [ t00 ⇒ t0E | t01 ⇒ t0F | t02 ⇒ t0C | t03 ⇒ t0D | t04 ⇒ t0A | t05 ⇒ t0B | t06 ⇒ t08 | t07 ⇒ t09
+ | t08 ⇒ t06 | t09 ⇒ t07 | t0A ⇒ t04 | t0B ⇒ t05 | t0C ⇒ t02 | t0D ⇒ t03 | t0E ⇒ t00 | t0F ⇒ t01
+ | t10 ⇒ t1E | t11 ⇒ t1F | t12 ⇒ t1C | t13 ⇒ t1D | t14 ⇒ t1A | t15 ⇒ t1B | t16 ⇒ t18 | t17 ⇒ t19
+ | t18 ⇒ t16 | t19 ⇒ t17 | t1A ⇒ t14 | t1B ⇒ t15 | t1C ⇒ t12 | t1D ⇒ t13 | t1E ⇒ t10 | t1F ⇒ t11 ]
+ | t0F ⇒ match e2 with
+ [ t00 ⇒ t0F | t01 ⇒ t0E | t02 ⇒ t0D | t03 ⇒ t0C | t04 ⇒ t0B | t05 ⇒ t0A | t06 ⇒ t09 | t07 ⇒ t08
+ | t08 ⇒ t07 | t09 ⇒ t06 | t0A ⇒ t05 | t0B ⇒ t04 | t0C ⇒ t03 | t0D ⇒ t02 | t0E ⇒ t01 | t0F ⇒ t00
+ | t10 ⇒ t1F | t11 ⇒ t1E | t12 ⇒ t1D | t13 ⇒ t1C | t14 ⇒ t1B | t15 ⇒ t1A | t16 ⇒ t19 | t17 ⇒ t18
+ | t18 ⇒ t17 | t19 ⇒ t16 | t1A ⇒ t15 | t1B ⇒ t14 | t1C ⇒ t13 | t1D ⇒ t12 | t1E ⇒ t11 | t1F ⇒ t10 ]
+ | t10 ⇒ match e2 with
+ [ t00 ⇒ t10 | t01 ⇒ t11 | t02 ⇒ t12 | t03 ⇒ t13 | t04 ⇒ t14 | t05 ⇒ t15 | t06 ⇒ t16 | t07 ⇒ t17
+ | t08 ⇒ t18 | t09 ⇒ t19 | t0A ⇒ t1A | t0B ⇒ t1B | t0C ⇒ t1C | t0D ⇒ t1D | t0E ⇒ t1E | t0F ⇒ t1F
+ | t10 ⇒ t00 | t11 ⇒ t01 | t12 ⇒ t02 | t13 ⇒ t03 | t14 ⇒ t04 | t15 ⇒ t05 | t16 ⇒ t06 | t17 ⇒ t07
+ | t18 ⇒ t08 | t19 ⇒ t09 | t1A ⇒ t0A | t1B ⇒ t0B | t1C ⇒ t0C | t1D ⇒ t0D | t1E ⇒ t0E | t1F ⇒ t0F ]
+ | t11 ⇒ match e2 with
+ [ t00 ⇒ t11 | t01 ⇒ t10 | t02 ⇒ t13 | t03 ⇒ t12 | t04 ⇒ t15 | t05 ⇒ t14 | t06 ⇒ t17 | t07 ⇒ t16
+ | t08 ⇒ t19 | t09 ⇒ t18 | t0A ⇒ t1B | t0B ⇒ t1A | t0C ⇒ t1D | t0D ⇒ t1C | t0E ⇒ t1F | t0F ⇒ t1E
+ | t10 ⇒ t01 | t11 ⇒ t00 | t12 ⇒ t03 | t13 ⇒ t02 | t14 ⇒ t05 | t15 ⇒ t04 | t16 ⇒ t07 | t17 ⇒ t06
+ | t18 ⇒ t09 | t19 ⇒ t08 | t1A ⇒ t0B | t1B ⇒ t0A | t1C ⇒ t0D | t1D ⇒ t0C | t1E ⇒ t0F | t1F ⇒ t0E ]
+ | t12 ⇒ match e2 with
+ [ t00 ⇒ t12 | t01 ⇒ t13 | t02 ⇒ t10 | t03 ⇒ t11 | t04 ⇒ t16 | t05 ⇒ t17 | t06 ⇒ t14 | t07 ⇒ t15
+ | t08 ⇒ t1A | t09 ⇒ t1B | t0A ⇒ t18 | t0B ⇒ t19 | t0C ⇒ t1E | t0D ⇒ t1F | t0E ⇒ t1C | t0F ⇒ t1D
+ | t10 ⇒ t02 | t11 ⇒ t03 | t12 ⇒ t00 | t13 ⇒ t01 | t14 ⇒ t06 | t15 ⇒ t07 | t16 ⇒ t04 | t17 ⇒ t05
+ | t18 ⇒ t0A | t19 ⇒ t0B | t1A ⇒ t08 | t1B ⇒ t09 | t1C ⇒ t0E | t1D ⇒ t0F | t1E ⇒ t0C | t1F ⇒ t0D ]
+ | t13 ⇒ match e2 with
+ [ t00 ⇒ t13 | t01 ⇒ t12 | t02 ⇒ t11 | t03 ⇒ t10 | t04 ⇒ t17 | t05 ⇒ t16 | t06 ⇒ t15 | t07 ⇒ t14
+ | t08 ⇒ t1B | t09 ⇒ t1A | t0A ⇒ t19 | t0B ⇒ t18 | t0C ⇒ t1F | t0D ⇒ t1E | t0E ⇒ t1D | t0F ⇒ t1C
+ | t10 ⇒ t03 | t11 ⇒ t02 | t12 ⇒ t01 | t13 ⇒ t00 | t14 ⇒ t07 | t15 ⇒ t06 | t16 ⇒ t05 | t17 ⇒ t04
+ | t18 ⇒ t0B | t19 ⇒ t0A | t1A ⇒ t09 | t1B ⇒ t08 | t1C ⇒ t0F | t1D ⇒ t0E | t1E ⇒ t0D | t1F ⇒ t0C ]
+ | t14 ⇒ match e2 with
+ [ t00 ⇒ t14 | t01 ⇒ t15 | t02 ⇒ t16 | t03 ⇒ t17 | t04 ⇒ t10 | t05 ⇒ t11 | t06 ⇒ t12 | t07 ⇒ t13
+ | t08 ⇒ t1C | t09 ⇒ t1D | t0A ⇒ t1E | t0B ⇒ t1F | t0C ⇒ t18 | t0D ⇒ t19 | t0E ⇒ t1A | t0F ⇒ t1B
+ | t10 ⇒ t04 | t11 ⇒ t05 | t12 ⇒ t06 | t13 ⇒ t07 | t14 ⇒ t00 | t15 ⇒ t01 | t16 ⇒ t02 | t17 ⇒ t03
+ | t18 ⇒ t0C | t19 ⇒ t0D | t1A ⇒ t0E | t1B ⇒ t0F | t1C ⇒ t08 | t1D ⇒ t09 | t1E ⇒ t0A | t1F ⇒ t0B ]
+ | t15 ⇒ match e2 with
+ [ t00 ⇒ t15 | t01 ⇒ t14 | t02 ⇒ t17 | t03 ⇒ t16 | t04 ⇒ t11 | t05 ⇒ t10 | t06 ⇒ t13 | t07 ⇒ t12
+ | t08 ⇒ t1D | t09 ⇒ t1C | t0A ⇒ t1F | t0B ⇒ t1E | t0C ⇒ t19 | t0D ⇒ t18 | t0E ⇒ t1B | t0F ⇒ t1A
+ | t10 ⇒ t05 | t11 ⇒ t04 | t12 ⇒ t07 | t13 ⇒ t06 | t14 ⇒ t01 | t15 ⇒ t00 | t16 ⇒ t03 | t17 ⇒ t02
+ | t18 ⇒ t0D | t19 ⇒ t0C | t1A ⇒ t0F | t1B ⇒ t0E | t1C ⇒ t09 | t1D ⇒ t08 | t1E ⇒ t0B | t1F ⇒ t0A ]
+ | t16 ⇒ match e2 with
+ [ t00 ⇒ t16 | t01 ⇒ t17 | t02 ⇒ t14 | t03 ⇒ t15 | t04 ⇒ t12 | t05 ⇒ t13 | t06 ⇒ t10 | t07 ⇒ t11
+ | t08 ⇒ t1E | t09 ⇒ t1F | t0A ⇒ t1C | t0B ⇒ t1D | t0C ⇒ t1A | t0D ⇒ t1B | t0E ⇒ t18 | t0F ⇒ t19
+ | t10 ⇒ t06 | t11 ⇒ t07 | t12 ⇒ t04 | t13 ⇒ t05 | t14 ⇒ t02 | t15 ⇒ t03 | t16 ⇒ t00 | t17 ⇒ t01
+ | t18 ⇒ t0E | t19 ⇒ t0F | t1A ⇒ t0C | t1B ⇒ t0D | t1C ⇒ t0A | t1D ⇒ t0B | t1E ⇒ t08 | t1F ⇒ t09 ]
+ | t17 ⇒ match e2 with
+ [ t00 ⇒ t17 | t01 ⇒ t16 | t02 ⇒ t15 | t03 ⇒ t14 | t04 ⇒ t13 | t05 ⇒ t12 | t06 ⇒ t11 | t07 ⇒ t10
+ | t08 ⇒ t1F | t09 ⇒ t1E | t0A ⇒ t1D | t0B ⇒ t1C | t0C ⇒ t1B | t0D ⇒ t1A | t0E ⇒ t19 | t0F ⇒ t18
+ | t10 ⇒ t07 | t11 ⇒ t06 | t12 ⇒ t05 | t13 ⇒ t04 | t14 ⇒ t03 | t15 ⇒ t02 | t16 ⇒ t01 | t17 ⇒ t00
+ | t18 ⇒ t0F | t19 ⇒ t0E | t1A ⇒ t0D | t1B ⇒ t0C | t1C ⇒ t0B | t1D ⇒ t0A | t1E ⇒ t09 | t1F ⇒ t08 ]
+ | t18 ⇒ match e2 with
+ [ t00 ⇒ t18 | t01 ⇒ t19 | t02 ⇒ t1A | t03 ⇒ t1B | t04 ⇒ t1C | t05 ⇒ t1D | t06 ⇒ t1E | t07 ⇒ t1F
+ | t08 ⇒ t10 | t09 ⇒ t11 | t0A ⇒ t12 | t0B ⇒ t13 | t0C ⇒ t14 | t0D ⇒ t15 | t0E ⇒ t16 | t0F ⇒ t17
+ | t10 ⇒ t08 | t11 ⇒ t09 | t12 ⇒ t0A | t13 ⇒ t0B | t14 ⇒ t0C | t15 ⇒ t0D | t16 ⇒ t0E | t17 ⇒ t0F
+ | t18 ⇒ t00 | t19 ⇒ t01 | t1A ⇒ t02 | t1B ⇒ t03 | t1C ⇒ t04 | t1D ⇒ t05 | t1E ⇒ t06 | t1F ⇒ t07 ]
+ | t19 ⇒ match e2 with
+ [ t00 ⇒ t19 | t01 ⇒ t18 | t02 ⇒ t1B | t03 ⇒ t1A | t04 ⇒ t1D | t05 ⇒ t1C | t06 ⇒ t1F | t07 ⇒ t1E
+ | t08 ⇒ t11 | t09 ⇒ t10 | t0A ⇒ t13 | t0B ⇒ t12 | t0C ⇒ t15 | t0D ⇒ t14 | t0E ⇒ t17 | t0F ⇒ t16
+ | t10 ⇒ t09 | t11 ⇒ t08 | t12 ⇒ t0B | t13 ⇒ t0A | t14 ⇒ t0D | t15 ⇒ t0C | t16 ⇒ t0F | t17 ⇒ t0E
+ | t18 ⇒ t01 | t19 ⇒ t00 | t1A ⇒ t03 | t1B ⇒ t02 | t1C ⇒ t05 | t1D ⇒ t04 | t1E ⇒ t07 | t1F ⇒ t06 ]
+ | t1A ⇒ match e2 with
+ [ t00 ⇒ t1A | t01 ⇒ t1B | t02 ⇒ t18 | t03 ⇒ t19 | t04 ⇒ t1E | t05 ⇒ t1F | t06 ⇒ t1C | t07 ⇒ t1D
+ | t08 ⇒ t12 | t09 ⇒ t13 | t0A ⇒ t10 | t0B ⇒ t11 | t0C ⇒ t16 | t0D ⇒ t17 | t0E ⇒ t14 | t0F ⇒ t15
+ | t10 ⇒ t0A | t11 ⇒ t0B | t12 ⇒ t08 | t13 ⇒ t09 | t14 ⇒ t0E | t15 ⇒ t0F | t16 ⇒ t0C | t17 ⇒ t0D
+ | t18 ⇒ t02 | t19 ⇒ t03 | t1A ⇒ t00 | t1B ⇒ t01 | t1C ⇒ t06 | t1D ⇒ t07 | t1E ⇒ t04 | t1F ⇒ t05 ]
+ | t1B ⇒ match e2 with
+ [ t00 ⇒ t1B | t01 ⇒ t1A | t02 ⇒ t19 | t03 ⇒ t18 | t04 ⇒ t1F | t05 ⇒ t1E | t06 ⇒ t1D | t07 ⇒ t1C
+ | t08 ⇒ t13 | t09 ⇒ t12 | t0A ⇒ t11 | t0B ⇒ t10 | t0C ⇒ t17 | t0D ⇒ t16 | t0E ⇒ t15 | t0F ⇒ t14
+ | t10 ⇒ t0B | t11 ⇒ t0A | t12 ⇒ t09 | t13 ⇒ t08 | t14 ⇒ t0F | t15 ⇒ t0E | t16 ⇒ t0D | t17 ⇒ t0C
+ | t18 ⇒ t03 | t19 ⇒ t02 | t1A ⇒ t01 | t1B ⇒ t00 | t1C ⇒ t07 | t1D ⇒ t06 | t1E ⇒ t05 | t1F ⇒ t04 ]
+ | t1C ⇒ match e2 with
+ [ t00 ⇒ t1C | t01 ⇒ t1D | t02 ⇒ t1E | t03 ⇒ t1F | t04 ⇒ t18 | t05 ⇒ t19 | t06 ⇒ t1A | t07 ⇒ t1B
+ | t08 ⇒ t14 | t09 ⇒ t15 | t0A ⇒ t16 | t0B ⇒ t17 | t0C ⇒ t10 | t0D ⇒ t11 | t0E ⇒ t12 | t0F ⇒ t13
+ | t10 ⇒ t0C | t11 ⇒ t0D | t12 ⇒ t0E | t13 ⇒ t0F | t14 ⇒ t08 | t15 ⇒ t09 | t16 ⇒ t0A | t17 ⇒ t0B
+ | t18 ⇒ t04 | t19 ⇒ t05 | t1A ⇒ t06 | t1B ⇒ t07 | t1C ⇒ t00 | t1D ⇒ t01 | t1E ⇒ t02 | t1F ⇒ t03 ]
+ | t1D ⇒ match e2 with
+ [ t00 ⇒ t1D | t01 ⇒ t1C | t02 ⇒ t1F | t03 ⇒ t1E | t04 ⇒ t19 | t05 ⇒ t18 | t06 ⇒ t1B | t07 ⇒ t1A
+ | t08 ⇒ t15 | t09 ⇒ t14 | t0A ⇒ t17 | t0B ⇒ t16 | t0C ⇒ t11 | t0D ⇒ t10 | t0E ⇒ t13 | t0F ⇒ t12
+ | t10 ⇒ t0D | t11 ⇒ t0C | t12 ⇒ t0F | t13 ⇒ t0E | t14 ⇒ t09 | t15 ⇒ t08 | t16 ⇒ t0B | t17 ⇒ t0A
+ | t18 ⇒ t05 | t19 ⇒ t04 | t1A ⇒ t07 | t1B ⇒ t06 | t1C ⇒ t01 | t1D ⇒ t00 | t1E ⇒ t03 | t1F ⇒ t02 ]
+ | t1E ⇒ match e2 with
+ [ t00 ⇒ t1E | t01 ⇒ t1F | t02 ⇒ t1C | t03 ⇒ t1D | t04 ⇒ t1A | t05 ⇒ t1B | t06 ⇒ t18 | t07 ⇒ t19
+ | t08 ⇒ t16 | t09 ⇒ t17 | t0A ⇒ t14 | t0B ⇒ t15 | t0C ⇒ t12 | t0D ⇒ t13 | t0E ⇒ t10 | t0F ⇒ t11
+ | t10 ⇒ t0E | t11 ⇒ t0F | t12 ⇒ t0C | t13 ⇒ t0D | t14 ⇒ t0A | t15 ⇒ t0B | t16 ⇒ t08 | t17 ⇒ t09
+ | t18 ⇒ t06 | t19 ⇒ t07 | t1A ⇒ t04 | t1B ⇒ t05 | t1C ⇒ t02 | t1D ⇒ t03 | t1E ⇒ t00 | t1F ⇒ t01 ]
+ | t1F ⇒ match e2 with
+ [ t00 ⇒ t1F | t01 ⇒ t1E | t02 ⇒ t1D | t03 ⇒ t1C | t04 ⇒ t1B | t05 ⇒ t1A | t06 ⇒ t19 | t07 ⇒ t18
+ | t08 ⇒ t17 | t09 ⇒ t16 | t0A ⇒ t15 | t0B ⇒ t14 | t0C ⇒ t13 | t0D ⇒ t12 | t0E ⇒ t11 | t0F ⇒ t10
+ | t10 ⇒ t0F | t11 ⇒ t0E | t12 ⇒ t0D | t13 ⇒ t0C | t14 ⇒ t0B | t15 ⇒ t0A | t16 ⇒ t09 | t17 ⇒ t08
+ | t18 ⇒ t07 | t19 ⇒ t06 | t1A ⇒ t05 | t1B ⇒ t04 | t1C ⇒ t03 | t1D ⇒ t02 | t1E ⇒ t01 | t1F ⇒ t00 ]
+ ].
+
+(* operatore predecessore *)
+ndefinition pred_bit ≝
+λn.match n with
+ [ t00 ⇒ t1F | t01 ⇒ t00 | t02 ⇒ t01 | t03 ⇒ t02 | t04 ⇒ t03 | t05 ⇒ t04 | t06 ⇒ t05 | t07 ⇒ t06
+ | t08 ⇒ t07 | t09 ⇒ t08 | t0A ⇒ t09 | t0B ⇒ t0A | t0C ⇒ t0B | t0D ⇒ t0C | t0E ⇒ t0D | t0F ⇒ t0E
+ | t10 ⇒ t0F | t11 ⇒ t10 | t12 ⇒ t11 | t13 ⇒ t12 | t14 ⇒ t13 | t15 ⇒ t14 | t16 ⇒ t15 | t17 ⇒ t16
+ | t18 ⇒ t17 | t19 ⇒ t18 | t1A ⇒ t19 | t1B ⇒ t1A | t1C ⇒ t1B | t1D ⇒ t1C | t1E ⇒ t1D | t1F ⇒ t0E
+ ].
+
(* operatore successore *)
ndefinition succ_bit ≝
λn.match n with
| false : bool.
(* operatori booleani *)
-
ndefinition eq_bool ≝
λb1,b2:bool.match b1 with
[ true ⇒ match b2 with [ true ⇒ true | false ⇒ false ]
for @{ 'xor_bool $a $b }.
interpretation "xor_bool" 'xor_bool x y = (xor_bool x y).
+(* iteratore sugli esadecimali *)
+ndefinition forall_bool ≝ λP.P true ⊗ P false.
+
ndefinition boolRelation : Type → Type ≝
λA:Type.A → A → bool.
(* ********************************************************************** *)
include "num/bool.ma".
+include "common/comp.ma".
(* ******** *)
(* BOOLEANI *)
##| ##*: #H; ndestruct (*napply (bool_destruct … H)*)
##]
nqed.
+
+nlemma bool_is_comparable : comparable.
+ @ bool
+ ##[ napply false
+ ##| napply forall_bool
+ ##| napply eq_bool
+ ##| napply eqbool_to_eq
+ ##| napply eq_to_eqbool
+ ##| napply neqbool_to_neq
+ ##| napply neq_to_neqbool
+ ##| napply decidable_bool
+ ##| napply symmetric_eqbool
+ ##]
+nqed.
+
+unification hint 0 ≔ ⊢ carr bool_is_comparable ≡ bool.
notation "〈x,y〉" non associative with precedence 80
for @{ mk_comp_num exadecim $x $y }.
+ndefinition byte8_is_comparable ≝ cn_is_comparable exadecim_is_comparable.
ndefinition byte8_is_comparable_ext ≝ cn_is_comparable_ext exadecim_is_comparable_ext.
unification hint 0 ≔ ⊢ carr (comp_base byte8_is_comparable_ext) ≡ comp_num exadecim.
unification hint 0 ≔ ⊢ carr (comp_base byte8_is_comparable_ext) ≡ byte8.
+unification hint 0 ≔ ⊢ carr byte8_is_comparable ≡ comp_num exadecim.
+unification hint 0 ≔ ⊢ carr byte8_is_comparable ≡ byte8.
(* operatore estensione unsigned *)
ndefinition extu_b8 ≝ λe2.〈zeroc ?,e2〉.
nqed.
nlemma cn_is_comparable_ext : comparable_ext → comparable_ext.
- #T; nelim T; #c;
+ #T; nelim T; #c;
#ltc; #lec; #gtc; #gec; #andc; #orc; #xorc;
#getMSBc; #setMSBc; #clrMSBc; #getLSBc; #setLSBc; #clrLSBc;
#rcrc; #shrc; #rorc; #rclc; #shlc; #rolc; #notc;
##]
nqed.
-unification hint 0 ≔ S: comparable;
- T ≟ (carr S),
- X ≟ (cn_is_comparable S)
- (*********************************************) ⊢
- carr X ≡ comp_num T.
-
ndefinition zeroc ≝ λx:comparable_ext.zeroc (comp_base x).
ndefinition forallc ≝ λx:comparable_ext.forallc (comp_base x).
ndefinition eqc ≝ λx:comparable_ext.eqc (comp_base x).
ndefinition neq_to_neqc ≝ λx:comparable_ext.neq_to_neqc (comp_base x).
ndefinition decidable_c ≝ λx:comparable_ext.decidable_c (comp_base x).
ndefinition symmetric_eqc ≝ λx:comparable_ext.symmetric_eqc (comp_base x).
+
+
+unification hint 0 ≔ S: comparable;
+ T ≟ (carr S),
+ X ≟ (cn_is_comparable S)
+ (*********************************************) ⊢
+ carr X ≡ comp_num T.
| o4 ⇒ o3 | o5 ⇒ o2 | o6 ⇒ o1 | o7 ⇒ o0 ]
].
+(* operatore predecessore *)
+ndefinition pred_oct ≝
+λn.match n with
+ [ o0 ⇒ o7 | o1 ⇒ o0 | o2 ⇒ o1 | o3 ⇒ o2 | o4 ⇒ o3 | o5 ⇒ o4 | o6 ⇒ o5 | o7 ⇒ o6 ].
+
(* operatore successore *)
ndefinition succ_oct ≝
λn.match n with
notation "〈x:y〉" non associative with precedence 80
for @{ mk_comp_num byte8 $x $y }.
+ndefinition word16_is_comparable ≝ cn_is_comparable byte8_is_comparable.
ndefinition word16_is_comparable_ext ≝ cn_is_comparable_ext byte8_is_comparable_ext.
unification hint 0 ≔ ⊢ carr (comp_base word16_is_comparable_ext) ≡ comp_num (comp_num exadecim).
unification hint 0 ≔ ⊢ carr (comp_base word16_is_comparable_ext) ≡ comp_num byte8.
unification hint 0 ≔ ⊢ carr (comp_base word16_is_comparable_ext) ≡ word16.
+unification hint 0 ≔ ⊢ carr word16_is_comparable ≡ comp_num (comp_num exadecim).
+unification hint 0 ≔ ⊢ carr word16_is_comparable ≡ comp_num byte8.
+unification hint 0 ≔ ⊢ carr word16_is_comparable ≡ word16.
(* operatore estensione unsigned *)
ndefinition extu_w16 ≝ λb2.〈zeroc ?:b2〉.
notation "〈x.y〉" non associative with precedence 80
for @{ mk_comp_num word16 $x $y }.
+ndefinition word32_is_comparable ≝ cn_is_comparable word16_is_comparable.
ndefinition word32_is_comparable_ext ≝ cn_is_comparable_ext word16_is_comparable_ext.
unification hint 0 ≔ ⊢ carr (comp_base word32_is_comparable_ext) ≡ comp_num (comp_num (comp_num exadecim)).
unification hint 0 ≔ ⊢ carr (comp_base word32_is_comparable_ext) ≡ comp_num (comp_num byte8).
unification hint 0 ≔ ⊢ carr (comp_base word32_is_comparable_ext) ≡ comp_num word16.
unification hint 0 ≔ ⊢ carr (comp_base word32_is_comparable_ext) ≡ word32.
+unification hint 0 ≔ ⊢ carr word32_is_comparable ≡ comp_num (comp_num (comp_num exadecim)).
+unification hint 0 ≔ ⊢ carr word32_is_comparable ≡ comp_num (comp_num byte8).
+unification hint 0 ≔ ⊢ carr word32_is_comparable ≡ comp_num word16.
+unification hint 0 ≔ ⊢ carr word32_is_comparable ≡ word32.
(* operatore estensione unsigned *)
ndefinition extu_w32 ≝ λw2.〈zeroc ?.w2〉.
#u1; #dim1;
#y; nelim y;
#u2; #dim2;
- nchange with (? → eqc ? u1 u2 = true);
+ nchange with (? → (eqc ? u1 u2) = true);
#H; napply (eq_to_eqc ? u1 u2);
napply (SUN_destruct_1 l … H).
nqed.
nlemma eqSUN_to_eq : ∀l.∀x,y:S_UN l.eq_SUN l x y = true → x = y.
#l; #x; #y;
- nchange with ((eqc ? (getelem ? x) (getelem ? y) = true) → x = y);
+ nchange with (((eqc ? (getelem ? x) (getelem ? y)) = true) → x = y);
#H; napply (eqSUN_to_eq_aux l x y (eqc_to_eq … H)).
nqed.
| ne_cons _ t ⇒ ProdT T (farg1_auxT T t)
].
-nlemma farg1_auxDim : ∀h,t,x.eqc ? x h = false → member_natList x (h§§t) = true → member_natList x t = true.
+nlemma farg1_auxDim : ∀h,t,x.(eqc ? x h) = false → member_natList x (h§§t) = true → member_natList x t = true.
#h; #t; #x; #H; #H1;
nnormalize in H1:(%);
nrewrite > H in H1:(%);
[ ne_nil h ⇒ λarg:farg1_auxT T «£h».λx:S_UN «£h».arg
| ne_cons h t ⇒ λarg:farg1_auxT T (h§§t).λx:S_UN (h§§t).
match eqc ? (getelem ? x) h
- return λy.eqc ? (getelem ? x) h = y → ?
+ return λy.(eqc ? (getelem ? x) h) = y → ?
with
- [ true ⇒ λp:(eqc ? (getelem ? x) h = true).fst … arg
- | false ⇒ λp:(eqc ? (getelem ? x) h = false).
+ [ true ⇒ λp:((eqc ? (getelem ? x) h) = true).fst … arg
+ | false ⇒ λp:((eqc ? (getelem ? x) h) = false).
farg1 T t
(snd … arg)
(S_EL t (getelem ? x) (farg1_auxDim h t (getelem ? x) p (getdim ? x)))
[ ne_nil h ⇒ λarg:farg1_auxT (farg1_auxT T lfix) «£h».λx:S_UN «£h».farg1 T lfix arg
| ne_cons h t ⇒ λarg:farg1_auxT (farg1_auxT T lfix) (h§§t).λx:S_UN (h§§t).
match eqc ? (getelem ? x) h
- return λy.eqc ? (getelem ? x) h = y → ?
+ return λy.(eqc ? (getelem ? x) h) = y → ?
with
- [ true ⇒ λp:(eqc ? (getelem ? x) h = true).farg1 T lfix (fst … arg)
- | false ⇒ λp:(eqc ? (getelem ? x) h = false).
+ [ true ⇒ λp:((eqc ? (getelem ? x) h) = true).farg1 T lfix (fst … arg)
+ | false ⇒ λp:((eqc ? (getelem ? x) h) = false).
farg2 T t lfix
(snd … arg)
(S_EL t (getelem ? x) (farg1_auxDim h t (getelem ? x) p (getdim ? x)))
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