(* ********************************************************************** *)
include "utility/utility.ma".
-include "freescale/nat_lemmas.ma".
(* ************************* *)
(* dimensioni degli elementi *)
-freescale/byte8.ma freescale/exadecim.ma
+freescale/byte8.ma freescale/bitrigesim.ma freescale/exadecim.ma
freescale/status.ma freescale/memory_abs.ma freescale/opcode_base.ma freescale/prod.ma
freescale/memory_bits.ma freescale/memory_trees.ma
utility/ascii_lemmas1.ma freescale/theory.ma utility/ascii.ma
freescale/byte8_lemmas.ma freescale/byte8.ma freescale/exadecim_lemmas.ma
-utility/string_lemmas.ma freescale/nat_lemmas.ma utility/ascii_lemmas2.ma utility/string.ma
+utility/string_lemmas.ma utility/ascii_lemmas2.ma utility/string.ma utility/utility_lemmas.ma
freescale/table_HCS08_tests.ma freescale/table_HCS08.ma
-freescale/multivm.ma freescale/load_write.ma freescale/nat_lemmas.ma
+freescale/multivm.ma freescale/load_write.ma
freescale/opcode_base_lemmas.ma freescale/bool_lemmas.ma freescale/opcode_base.ma
-compiler/ast_type_lemmas.ma compiler/ast_type.ma
+compiler/ast_type_lemmas.ma compiler/ast_type.ma utility/utility_lemmas.ma
freescale/table_HC05_tests.ma freescale/table_HC05.ma
freescale/option.ma freescale/bool.ma
freescale/bool.ma freescale/pts.ma
-freescale/nat_lemmas.ma freescale/bool_lemmas.ma freescale/nat.ma
freescale/bool_lemmas.ma freescale/bool.ma freescale/theory.ma
freescale/opcode_base_lemmas_opcode1.ma freescale/bool_lemmas.ma freescale/opcode_base.ma
freescale/memory_func.ma freescale/memory_struct.ma freescale/option.ma freescale/theory.ma freescale/word16.ma
freescale/load_write.ma freescale/model.ma freescale/translation.ma
+freescale/bitrigesim.ma freescale/bool.ma
freescale/table_RS08.ma freescale/opcode.ma
+freescale/oct.ma freescale/bool.ma
freescale/option_lemmas.ma freescale/bool_lemmas.ma freescale/option.ma
freescale/table_RS08_tests.ma freescale/table_RS08.ma
freescale/translation.ma freescale/option.ma freescale/table_HC05.ma freescale/table_HC08.ma freescale/table_HCS08.ma freescale/table_RS08.ma
-freescale/nat.ma freescale/bool.ma freescale/pts.ma
freescale/medium_tests_tools.ma freescale/multivm.ma
utility/utility_lemmas.ma utility/utility.ma
freescale/memory_abs.ma freescale/memory_bits.ma freescale/memory_func.ma freescale/memory_trees.ma
+freescale/bitrigesim_lemmas.ma freescale/bitrigesim.ma freescale/bool_lemmas.ma
test_errori.ma compiler/ast_type_lemmas.ma freescale/byte8_lemmas.ma utility/utility.ma
-freescale/memory_struct.ma freescale/aux_bases.ma freescale/byte8.ma
+freescale/memory_struct.ma freescale/byte8.ma freescale/oct.ma
freescale/model.ma freescale/status.ma
-freescale/aux_bases.ma freescale/byte8.ma freescale/nat.ma
freescale/table_HC05.ma freescale/opcode.ma
+freescale/quatern_lemmas.ma freescale/bool_lemmas.ma freescale/quatern.ma
freescale/exadecim_lemmas.ma freescale/bool_lemmas.ma freescale/exadecim.ma
-compiler/ast_type.ma freescale/nat_lemmas.ma utility/utility.ma
+compiler/ast_type.ma utility/utility.ma
freescale/word16.ma freescale/byte8.ma
utility/ascii.ma freescale/bool.ma
freescale/memory_trees.ma freescale/memory_struct.ma freescale/option.ma freescale/theory.ma freescale/word16.ma
freescale/pts.ma
freescale/opcode_base_lemmas_instrmode2.ma freescale/opcode_base_lemmas_instrmode1.ma
-freescale/aux_bases_lemmas.ma freescale/aux_bases.ma freescale/bool_lemmas.ma
freescale/opcode_base_lemmas1.ma freescale/opcode_base_lemmas_instrmode2.ma freescale/opcode_base_lemmas_opcode2.ma freescale/word16_lemmas.ma
freescale/table_HC08.ma freescale/opcode.ma
freescale/prod.ma freescale/bool.ma
-utility/string.ma freescale/nat.ma freescale/theory.ma utility/ascii.ma
+utility/string.ma freescale/theory.ma utility/ascii.ma utility/utility.ma
freescale/table_HCS08.ma freescale/opcode.ma
freescale/word32.ma freescale/word16.ma
freescale/prod_lemmas.ma freescale/bool_lemmas.ma freescale/prod.ma
-freescale/opcode_base.ma freescale/aux_bases.ma freescale/theory.ma freescale/word16.ma
+freescale/opcode_base.ma freescale/bitrigesim.ma freescale/oct.ma freescale/theory.ma freescale/word16.ma
freescale/word32_lemmas.ma freescale/word16_lemmas.ma freescale/word32.ma
freescale/status_lemmas.ma freescale/opcode_base_lemmas1.ma freescale/option_lemmas.ma freescale/prod_lemmas.ma freescale/status.ma freescale/word16_lemmas.ma
utility/ascii_lemmas2.ma freescale/bool_lemmas.ma utility/ascii_lemmas1.ma
freescale/micro_tests.ma freescale/multivm.ma freescale/status_lemmas.ma
freescale/table_HC08_tests.ma freescale/table_HC08.ma
-utility/utility.ma freescale/nat_lemmas.ma freescale/option.ma freescale/theory.ma
-freescale/opcode_base_lemmas_instrmode1.ma freescale/aux_bases_lemmas.ma freescale/exadecim_lemmas.ma freescale/opcode_base.ma
+utility/utility.ma freescale/option.ma freescale/theory.ma
+freescale/quatern.ma freescale/bool.ma
+freescale/opcode_base_lemmas_instrmode1.ma freescale/bitrigesim_lemmas.ma freescale/exadecim_lemmas.ma freescale/oct_lemmas.ma freescale/opcode_base.ma
freescale/word16_lemmas.ma freescale/byte8_lemmas.ma freescale/word16.ma
-freescale/exadecim.ma freescale/bool.ma freescale/nat.ma freescale/prod.ma
+freescale/exadecim.ma freescale/bool.ma freescale/oct.ma freescale/prod.ma freescale/quatern.ma
freescale/theory.ma freescale/pts.ma
freescale/opcode_base_lemmas_opcode2.ma freescale/opcode_base_lemmas_opcode1.ma
freescale/medium_tests.ma freescale/medium_tests_tools.ma utility/utility.ma
freescale/opcode.ma freescale/opcode_base.ma
+freescale/oct_lemmas.ma freescale/bool_lemmas.ma freescale/oct.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: Cosimo Oliboni, oliboni@cs.unibo.it *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
-(* *)
-(* ********************************************************************** *)
-
-include "freescale/byte8.ma".
-include "freescale/nat.ma".
-
-(* ****** *)
-(* OTTALI *)
-(* ****** *)
-
-ninductive oct : Type ≝
- o0: oct
-| o1: oct
-| o2: oct
-| o3: oct
-| o4: oct
-| o5: oct
-| o6: oct
-| o7: oct.
-
-(* operatore = *)
-ndefinition eq_oct ≝
-λn1,n2:oct.
- match n1 with
- [ o0 ⇒ match n2 with
- [ o0 ⇒ true | o1 ⇒ false | o2 ⇒ false | o3 ⇒ false
- | o4 ⇒ false | o5 ⇒ false | o6 ⇒ false | o7 ⇒ false ]
- | o1 ⇒ match n2 with
- [ o0 ⇒ false | o1 ⇒ true | o2 ⇒ false | o3 ⇒ false
- | o4 ⇒ false | o5 ⇒ false | o6 ⇒ false | o7 ⇒ false ]
- | o2 ⇒ match n2 with
- [ o0 ⇒ false | o1 ⇒ false | o2 ⇒ true | o3 ⇒ false
- | o4 ⇒ false | o5 ⇒ false | o6 ⇒ false | o7 ⇒ false ]
- | o3 ⇒ match n2 with
- [ o0 ⇒ false | o1 ⇒ false | o2 ⇒ false | o3 ⇒ true
- | o4 ⇒ false | o5 ⇒ false | o6 ⇒ false | o7 ⇒ false ]
- | o4 ⇒ match n2 with
- [ o0 ⇒ false | o1 ⇒ false | o2 ⇒ false | o3 ⇒ false
- | o4 ⇒ true | o5 ⇒ false | o6 ⇒ false | o7 ⇒ false ]
- | o5 ⇒ match n2 with
- [ o0 ⇒ false | o1 ⇒ false | o2 ⇒ false | o3 ⇒ false
- | o4 ⇒ false | o5 ⇒ true | o6 ⇒ false | o7 ⇒ false ]
- | o6 ⇒ match n2 with
- [ o0 ⇒ false | o1 ⇒ false | o2 ⇒ false | o3 ⇒ false
- | o4 ⇒ false | o5 ⇒ false | o6 ⇒ true | o7 ⇒ false ]
- | o7 ⇒ match n2 with
- [ o0 ⇒ false | o1 ⇒ false | o2 ⇒ false | o3 ⇒ false
- | o4 ⇒ false | o5 ⇒ false | o6 ⇒ false | o7 ⇒ true ]
- ].
-
-(* ottali → naturali *)
-ndefinition nat_of_oct ≝
-λn:oct.
- match n with
- [ o0 ⇒ 0 | o1 ⇒ 1 | o2 ⇒ 2 | o3 ⇒ 3 | o4 ⇒ 4 | o5 ⇒ 5 | o6 ⇒ 6 | o7 ⇒ 7 ].
-
-(* iteratore sugli ottali *)
-ndefinition forall_oct ≝ λP.
- P o0 ⊗ P o1 ⊗ P o2 ⊗ P o3 ⊗ P o4 ⊗ P o5 ⊗ P o6 ⊗ P o7.
-
-(* ************* *)
-(* BITRIGESIMALI *)
-(* ************* *)
-
-ninductive bitrigesim : Type ≝
- t00: bitrigesim
-| t01: bitrigesim
-| t02: bitrigesim
-| t03: bitrigesim
-| t04: bitrigesim
-| t05: bitrigesim
-| t06: bitrigesim
-| t07: bitrigesim
-| t08: bitrigesim
-| t09: bitrigesim
-| t0A: bitrigesim
-| t0B: bitrigesim
-| t0C: bitrigesim
-| t0D: bitrigesim
-| t0E: bitrigesim
-| t0F: bitrigesim
-| t10: bitrigesim
-| t11: bitrigesim
-| t12: bitrigesim
-| t13: bitrigesim
-| t14: bitrigesim
-| t15: bitrigesim
-| t16: bitrigesim
-| t17: bitrigesim
-| t18: bitrigesim
-| t19: bitrigesim
-| t1A: bitrigesim
-| t1B: bitrigesim
-| t1C: bitrigesim
-| t1D: bitrigesim
-| t1E: bitrigesim
-| t1F: bitrigesim.
-
-(* operatore = *)
-ndefinition eq_bitrig ≝
-λt1,t2:bitrigesim.
- match t1 with
- [ t00 ⇒ match t2 with
- [ t00 ⇒ true | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t01 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ true | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t02 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ true | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t03 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ true | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t04 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ true | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t05 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ true | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t06 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ true | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t07 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ true
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t08 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ true | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t09 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ true | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t0A ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ true | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t0B ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ true | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t0C ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ true | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t0D ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ true | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t0E ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ true | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t0F ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ true
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t10 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ true | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t11 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ true | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t12 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ true | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t13 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ true | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t14 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ true | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t15 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ true | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t16 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ true | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t17 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ true
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t18 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ true | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t19 ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ true | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t1A ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ true | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t1B ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ true | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t1C ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ true | t1D ⇒ false | t1E ⇒ false | t1F ⇒ false ]
- | t1D ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ true | t1E ⇒ false | t1F ⇒ false ]
- | t1E ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ true | t1F ⇒ false ]
- | t1F ⇒ match t2 with
- [ t00 ⇒ false | t01 ⇒ false | t02 ⇒ false | t03 ⇒ false | t04 ⇒ false | t05 ⇒ false | t06 ⇒ false | t07 ⇒ false
- | t08 ⇒ false | t09 ⇒ false | t0A ⇒ false | t0B ⇒ false | t0C ⇒ false | t0D ⇒ false | t0E ⇒ false | t0F ⇒ false
- | t10 ⇒ false | t11 ⇒ false | t12 ⇒ false | t13 ⇒ false | t14 ⇒ false | t15 ⇒ false | t16 ⇒ false | t17 ⇒ false
- | t18 ⇒ false | t19 ⇒ false | t1A ⇒ false | t1B ⇒ false | t1C ⇒ false | t1D ⇒ false | t1E ⇒ false | t1F ⇒ true ]
- ].
-
-(* bitrigesimali → naturali *)
-ndefinition nat_of_bitrigesim ≝
-λt:bitrigesim.
- match t with
- [ t00 ⇒ 0 | t01 ⇒ 1 | t02 ⇒ 2 | t03 ⇒ 3 | t04 ⇒ 4 | t05 ⇒ 5 | t06 ⇒ 6 | t07 ⇒ 7
- | t08 ⇒ 8 | t09 ⇒ 9 | t0A ⇒ 10 | t0B ⇒ 11 | t0C ⇒ 12 | t0D ⇒ 13 | t0E ⇒ 14 | t0F ⇒ 15
- | t10 ⇒ 16 | t11 ⇒ 17 | t12 ⇒ 18 | t13 ⇒ 19 | t14 ⇒ 20 | t15 ⇒ 21 | t16 ⇒ 22 | t17 ⇒ 23
- | t18 ⇒ 24 | t19 ⇒ 25 | t1A ⇒ 26 | t1B ⇒ 27 | t1C ⇒ 28 | t1D ⇒ 29 | t1E ⇒ 30 | t1F ⇒ 31 ].
-
-ndefinition byte8_of_bitrigesim ≝
-λt:bitrigesim.
- match t with
- [ t00 ⇒ 〈x0,x0〉 | t01 ⇒ 〈x0,x1〉 | t02 ⇒ 〈x0,x2〉 | t03 ⇒ 〈x0,x3〉
- | t04 ⇒ 〈x0,x4〉 | t05 ⇒ 〈x0,x5〉 | t06 ⇒ 〈x0,x6〉 | t07 ⇒ 〈x0,x7〉
- | t08 ⇒ 〈x0,x8〉 | t09 ⇒ 〈x0,x9〉 | t0A ⇒ 〈x0,xA〉 | t0B ⇒ 〈x0,xB〉
- | t0C ⇒ 〈x0,xC〉 | t0D ⇒ 〈x0,xD〉 | t0E ⇒ 〈x0,xE〉 | t0F ⇒ 〈x0,xF〉
- | t10 ⇒ 〈x1,x0〉 | t11 ⇒ 〈x1,x1〉 | t12 ⇒ 〈x1,x2〉 | t13 ⇒ 〈x1,x3〉
- | t14 ⇒ 〈x1,x4〉 | t15 ⇒ 〈x1,x5〉 | t16 ⇒ 〈x1,x6〉 | t17 ⇒ 〈x1,x7〉
- | t18 ⇒ 〈x1,x8〉 | t19 ⇒ 〈x1,x9〉 | t1A ⇒ 〈x1,xA〉 | t1B ⇒ 〈x1,xB〉
- | t1C ⇒ 〈x1,xC〉 | t1D ⇒ 〈x1,xD〉 | t1E ⇒ 〈x1,xE〉 | t1F ⇒ 〈x1,xF〉 ].
-
-(* iteratore sui bitrigesimali *)
-ndefinition forall_bitrigesim ≝ λP.
- P t00 ⊗ P t01 ⊗ P t02 ⊗ P t03 ⊗ P t04 ⊗ P t05 ⊗ P t06 ⊗ P t07 ⊗
- P t08 ⊗ P t09 ⊗ P t0A ⊗ P t0B ⊗ P t0C ⊗ P t0D ⊗ P t0E ⊗ P t0F ⊗
- 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.
+++ /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: Cosimo Oliboni, oliboni@cs.unibo.it *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
-(* *)
-(* ********************************************************************** *)
-
-include "freescale/bool_lemmas.ma".
-include "freescale/aux_bases.ma".
-
-(* ****** *)
-(* OTTALI *)
-(* ****** *)
-
-ndefinition oct_destruct_aux ≝
-Πn1,n2:oct.ΠP:Prop.n1 = n2 →
- match n1 with
- [ o0 ⇒ match n2 with [ o0 ⇒ P → P | _ ⇒ P ]
- | o1 ⇒ match n2 with [ o1 ⇒ P → P | _ ⇒ P ]
- | o2 ⇒ match n2 with [ o2 ⇒ P → P | _ ⇒ P ]
- | o3 ⇒ match n2 with [ o3 ⇒ P → P | _ ⇒ P ]
- | o4 ⇒ match n2 with [ o4 ⇒ P → P | _ ⇒ P ]
- | o5 ⇒ match n2 with [ o5 ⇒ P → P | _ ⇒ P ]
- | o6 ⇒ match n2 with [ o6 ⇒ P → P | _ ⇒ P ]
- | o7 ⇒ match n2 with [ o7 ⇒ P → P | _ ⇒ P ]
- ].
-
-ndefinition oct_destruct : oct_destruct_aux.
- #n1; #n2; #P;
- nelim n1;
- ##[ ##1: nelim n2; nnormalize; #H;
- ##[ ##1: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match o0 with [ o0 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
- ##| ##2: nelim n2; nnormalize; #H;
- ##[ ##2: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match o1 with [ o1 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
- ##| ##3: nelim n2; nnormalize; #H;
- ##[ ##3: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match o2 with [ o2 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
- ##| ##4: nelim n2; nnormalize; #H;
- ##[ ##4: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match o3 with [ o3 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
- ##| ##5: nelim n2; nnormalize; #H;
- ##[ ##5: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match o4 with [ o4 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
- ##| ##6: nelim n2; nnormalize; #H;
- ##[ ##6: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match o5 with [ o5 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
- ##| ##7: nelim n2; nnormalize; #H;
- ##[ ##7: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match o6 with [ o6 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
- ##| ##8: nelim n2; nnormalize; #H;
- ##[ ##8: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match o7 with [ o7 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
- ##]
-nqed.
-
-nlemma symmetric_eqoct : symmetricT oct bool eq_oct.
- #n1; #n2;
- nelim n1;
- nelim n2;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma eqoct_to_eq : ∀n1,n2.eq_oct n1 n2 = true → n1 = n2.
- #n1; #n2;
- ncases n1;
- ncases n2;
- nnormalize;
- ##[ ##1,10,19,28,37,46,55,64: #H; napply refl_eq
- ##| ##*: #H; napply (bool_destruct … H)
- ##]
-nqed.
-
-nlemma eq_to_eqoct : ∀n1,n2.n1 = n2 → eq_oct n1 n2 = true.
- #n1; #n2;
- ncases n1;
- ncases n2;
- nnormalize;
- ##[ ##1,10,19,28,37,46,55,64: #H; napply refl_eq
- ##| ##*: #H; napply (oct_destruct … H)
- ##]
-nqed.
-
-(* ************* *)
-(* BITRIGESIMALI *)
-(* ************* *)
-
-ndefinition bitrigesim_destruct1 :
-Πt2:bitrigesim.ΠP:Prop.t00 = t2 → match t2 with [ t00 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##1: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t00 with [ t00 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct2 :
-Πt2:bitrigesim.ΠP:Prop.t01 = t2 → match t2 with [ t01 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##2: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t01 with [ t01 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct3 :
-Πt2:bitrigesim.ΠP:Prop.t02 = t2 → match t2 with [ t02 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##3: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t02 with [ t02 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct4 :
-Πt2:bitrigesim.ΠP:Prop.t03 = t2 → match t2 with [ t03 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##4: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t03 with [ t03 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct5 :
-Πt2:bitrigesim.ΠP:Prop.t04 = t2 → match t2 with [ t04 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##5: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t04 with [ t04 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct6 :
-Πt2:bitrigesim.ΠP:Prop.t05 = t2 → match t2 with [ t05 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##6: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t05 with [ t05 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct7 :
-Πt2:bitrigesim.ΠP:Prop.t06 = t2 → match t2 with [ t06 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##7: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t06 with [ t06 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct8 :
-Πt2:bitrigesim.ΠP:Prop.t07 = t2 → match t2 with [ t07 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##8: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t07 with [ t07 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct9 :
-Πt2:bitrigesim.ΠP:Prop.t08 = t2 → match t2 with [ t08 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##9: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t08 with [ t08 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct10 :
-Πt2:bitrigesim.ΠP:Prop.t09 = t2 → match t2 with [ t09 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##10: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t09 with [ t09 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct11 :
-Πt2:bitrigesim.ΠP:Prop.t0A = t2 → match t2 with [ t0A ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##11: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t0A with [ t0A ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct12 :
-Πt2:bitrigesim.ΠP:Prop.t0B = t2 → match t2 with [ t0B ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##12: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t0B with [ t0B ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct13 :
-Πt2:bitrigesim.ΠP:Prop.t0C = t2 → match t2 with [ t0C ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##13: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t0C with [ t0C ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct14 :
-Πt2:bitrigesim.ΠP:Prop.t0D = t2 → match t2 with [ t0D ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##14: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t0D with [ t0D ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct15 :
-Πt2:bitrigesim.ΠP:Prop.t0E = t2 → match t2 with [ t0E ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##15: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t0E with [ t0E ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct16 :
-Πt2:bitrigesim.ΠP:Prop.t0F = t2 → match t2 with [ t0F ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##16: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t0F with [ t0F ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct17 :
-Πt2:bitrigesim.ΠP:Prop.t10 = t2 → match t2 with [ t10 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##17: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t10 with [ t10 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct18 :
-Πt2:bitrigesim.ΠP:Prop.t11 = t2 → match t2 with [ t11 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##18: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t11 with [ t11 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct19 :
-Πt2:bitrigesim.ΠP:Prop.t12 = t2 → match t2 with [ t12 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##19: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t12 with [ t12 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct20 :
-Πt2:bitrigesim.ΠP:Prop.t13 = t2 → match t2 with [ t13 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##20: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t13 with [ t13 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct21 :
-Πt2:bitrigesim.ΠP:Prop.t14 = t2 → match t2 with [ t14 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##21: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t14 with [ t14 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct22 :
-Πt2:bitrigesim.ΠP:Prop.t15 = t2 → match t2 with [ t15 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##22: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t15 with [ t15 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct23 :
-Πt2:bitrigesim.ΠP:Prop.t16 = t2 → match t2 with [ t16 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##23: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t16 with [ t16 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct24 :
-Πt2:bitrigesim.ΠP:Prop.t17 = t2 → match t2 with [ t17 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##24: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t17 with [ t17 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct25 :
-Πt2:bitrigesim.ΠP:Prop.t18 = t2 → match t2 with [ t18 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##25: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t18 with [ t18 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct26 :
-Πt2:bitrigesim.ΠP:Prop.t19 = t2 → match t2 with [ t19 ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##26: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t19 with [ t19 ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct27 :
-Πt2:bitrigesim.ΠP:Prop.t1A = t2 → match t2 with [ t1A ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##27: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t1A with [ t1A ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct28 :
-Πt2:bitrigesim.ΠP:Prop.t1B = t2 → match t2 with [ t1B ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##28: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t1B with [ t1B ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct29 :
-Πt2:bitrigesim.ΠP:Prop.t1C = t2 → match t2 with [ t1C ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##29: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t1C with [ t1C ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct30 :
-Πt2:bitrigesim.ΠP:Prop.t1D = t2 → match t2 with [ t1D ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##30: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t1D with [ t1D ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct31 :
-Πt2:bitrigesim.ΠP:Prop.t1E = t2 → match t2 with [ t1E ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##31: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t1E with [ t1E ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct32 :
-Πt2:bitrigesim.ΠP:Prop.t1F = t2 → match t2 with [ t1F ⇒ P → P | _ ⇒ P ].
- #t2; #P;
- ncases t2;
- nnormalize; #H;
- ##[ ##32: napply (λx:P.x)
- ##| ##*: napply (False_ind …);
- nchange with (match t1F with [ t1F ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition bitrigesim_destruct_aux ≝
-Πt1,t2:bitrigesim.ΠP:Prop.t1 = t2 →
- match t1 with
- [ t00 ⇒ match t2 with [ t00 ⇒ P → P | _ ⇒ P ]
- | t01 ⇒ match t2 with [ t01 ⇒ P → P | _ ⇒ P ]
- | t02 ⇒ match t2 with [ t02 ⇒ P → P | _ ⇒ P ]
- | t03 ⇒ match t2 with [ t03 ⇒ P → P | _ ⇒ P ]
- | t04 ⇒ match t2 with [ t04 ⇒ P → P | _ ⇒ P ]
- | t05 ⇒ match t2 with [ t05 ⇒ P → P | _ ⇒ P ]
- | t06 ⇒ match t2 with [ t06 ⇒ P → P | _ ⇒ P ]
- | t07 ⇒ match t2 with [ t07 ⇒ P → P | _ ⇒ P ]
- | t08 ⇒ match t2 with [ t08 ⇒ P → P | _ ⇒ P ]
- | t09 ⇒ match t2 with [ t09 ⇒ P → P | _ ⇒ P ]
- | t0A ⇒ match t2 with [ t0A ⇒ P → P | _ ⇒ P ]
- | t0B ⇒ match t2 with [ t0B ⇒ P → P | _ ⇒ P ]
- | t0C ⇒ match t2 with [ t0C ⇒ P → P | _ ⇒ P ]
- | t0D ⇒ match t2 with [ t0D ⇒ P → P | _ ⇒ P ]
- | t0E ⇒ match t2 with [ t0E ⇒ P → P | _ ⇒ P ]
- | t0F ⇒ match t2 with [ t0F ⇒ P → P | _ ⇒ P ]
- | t10 ⇒ match t2 with [ t10 ⇒ P → P | _ ⇒ P ]
- | t11 ⇒ match t2 with [ t11 ⇒ P → P | _ ⇒ P ]
- | t12 ⇒ match t2 with [ t12 ⇒ P → P | _ ⇒ P ]
- | t13 ⇒ match t2 with [ t13 ⇒ P → P | _ ⇒ P ]
- | t14 ⇒ match t2 with [ t14 ⇒ P → P | _ ⇒ P ]
- | t15 ⇒ match t2 with [ t15 ⇒ P → P | _ ⇒ P ]
- | t16 ⇒ match t2 with [ t16 ⇒ P → P | _ ⇒ P ]
- | t17 ⇒ match t2 with [ t17 ⇒ P → P | _ ⇒ P ]
- | t18 ⇒ match t2 with [ t18 ⇒ P → P | _ ⇒ P ]
- | t19 ⇒ match t2 with [ t19 ⇒ P → P | _ ⇒ P ]
- | t1A ⇒ match t2 with [ t1A ⇒ P → P | _ ⇒ P ]
- | t1B ⇒ match t2 with [ t1B ⇒ P → P | _ ⇒ P ]
- | t1C ⇒ match t2 with [ t1C ⇒ P → P | _ ⇒ P ]
- | t1D ⇒ match t2 with [ t1D ⇒ P → P | _ ⇒ P ]
- | t1E ⇒ match t2 with [ t1E ⇒ P → P | _ ⇒ P ]
- | t1F ⇒ match t2 with [ t1F ⇒ P → P | _ ⇒ P ]
- ].
-
-ndefinition bitrigesim_destruct : bitrigesim_destruct_aux.
- #t1;
- ncases t1;
- ##[ ##1: napply bitrigesim_destruct1
- ##| ##2: napply bitrigesim_destruct2
- ##| ##3: napply bitrigesim_destruct3
- ##| ##4: napply bitrigesim_destruct4
- ##| ##5: napply bitrigesim_destruct5
- ##| ##6: napply bitrigesim_destruct6
- ##| ##7: napply bitrigesim_destruct7
- ##| ##8: napply bitrigesim_destruct8
- ##| ##9: napply bitrigesim_destruct9
- ##| ##10: napply bitrigesim_destruct10
- ##| ##11: napply bitrigesim_destruct11
- ##| ##12: napply bitrigesim_destruct12
- ##| ##13: napply bitrigesim_destruct13
- ##| ##14: napply bitrigesim_destruct14
- ##| ##15: napply bitrigesim_destruct15
- ##| ##16: napply bitrigesim_destruct16
- ##| ##17: napply bitrigesim_destruct17
- ##| ##18: napply bitrigesim_destruct18
- ##| ##19: napply bitrigesim_destruct19
- ##| ##20: napply bitrigesim_destruct20
- ##| ##21: napply bitrigesim_destruct21
- ##| ##22: napply bitrigesim_destruct22
- ##| ##23: napply bitrigesim_destruct23
- ##| ##24: napply bitrigesim_destruct24
- ##| ##25: napply bitrigesim_destruct25
- ##| ##26: napply bitrigesim_destruct26
- ##| ##27: napply bitrigesim_destruct27
- ##| ##28: napply bitrigesim_destruct28
- ##| ##29: napply bitrigesim_destruct29
- ##| ##30: napply bitrigesim_destruct30
- ##| ##31: napply bitrigesim_destruct31
- ##| ##32: napply bitrigesim_destruct32
- ##]
-nqed.
-
-nlemma symmetric_eqbitrig : symmetricT bitrigesim bool eq_bitrig.
- #t1;
- nelim t1;
- ##[ ##1: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##2: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##3: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##4: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##5: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##6: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##7: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##8: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##9: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##10: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##11: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##12: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##13: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##14: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##15: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##16: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##17: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##18: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##19: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##20: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##21: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##22: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##23: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##24: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##25: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##26: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##27: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##28: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##29: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##30: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##31: #t2; nelim t2; nnormalize; napply refl_eq
- ##| ##32: #t2; nelim t2; nnormalize; napply refl_eq
- ##]
-nqed.
-
-nlemma eqbitrig_to_eq1 : ∀t2.eq_bitrig t00 t2 = true → t00 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##1: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq2 : ∀t2.eq_bitrig t01 t2 = true → t01 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##2: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq3 : ∀t2.eq_bitrig t02 t2 = true → t02 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##3: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq4 : ∀t2.eq_bitrig t03 t2 = true → t03 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##4: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq5 : ∀t2.eq_bitrig t04 t2 = true → t04 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##5: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq6 : ∀t2.eq_bitrig t05 t2 = true → t05 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##6: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq7 : ∀t2.eq_bitrig t06 t2 = true → t06 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##7: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq8 : ∀t2.eq_bitrig t07 t2 = true → t07 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##8: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq9 : ∀t2.eq_bitrig t08 t2 = true → t08 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##9: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq10 : ∀t2.eq_bitrig t09 t2 = true → t09 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##10: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq11 : ∀t2.eq_bitrig t0A t2 = true → t0A = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##11: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq12 : ∀t2.eq_bitrig t0B t2 = true → t0B = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##12: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq13 : ∀t2.eq_bitrig t0C t2 = true → t0C = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##13: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq14 : ∀t2.eq_bitrig t0D t2 = true → t0D = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##14: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq15 : ∀t2.eq_bitrig t0E t2 = true → t0E = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##15: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq16 : ∀t2.eq_bitrig t0F t2 = true → t0F = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##16: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq17 : ∀t2.eq_bitrig t10 t2 = true → t10 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##17: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq18 : ∀t2.eq_bitrig t11 t2 = true → t11 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##18: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq19 : ∀t2.eq_bitrig t12 t2 = true → t12 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##19: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq20 : ∀t2.eq_bitrig t13 t2 = true → t13 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##20: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq21 : ∀t2.eq_bitrig t14 t2 = true → t14 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##21: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq22 : ∀t2.eq_bitrig t15 t2 = true → t15 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##22: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq23 : ∀t2.eq_bitrig t16 t2 = true → t16 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##23: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq24 : ∀t2.eq_bitrig t17 t2 = true → t17 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##24: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq25 : ∀t2.eq_bitrig t18 t2 = true → t18 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##25: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq26 : ∀t2.eq_bitrig t19 t2 = true → t19 = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##26: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq27 : ∀t2.eq_bitrig t1A t2 = true → t1A = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##27: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq28 : ∀t2.eq_bitrig t1B t2 = true → t1B = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##28: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq29 : ∀t2.eq_bitrig t1C t2 = true → t1C = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##29: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq30 : ∀t2.eq_bitrig t1D t2 = true → t1D = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##30: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq31 : ∀t2.eq_bitrig t1E t2 = true → t1E = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##31: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq32 : ∀t2.eq_bitrig t1F t2 = true → t1F = t2.
- #t2; ncases t2; nnormalize; #H; ##[ ##32: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
-nqed.
-
-nlemma eqbitrig_to_eq : ∀t1,t2.eq_bitrig t1 t2 = true → t1 = t2.
- #t1;
- ncases t1;
- ##[ ##1: napply eqbitrig_to_eq1
- ##| ##2: napply eqbitrig_to_eq2
- ##| ##3: napply eqbitrig_to_eq3
- ##| ##4: napply eqbitrig_to_eq4
- ##| ##5: napply eqbitrig_to_eq5
- ##| ##6: napply eqbitrig_to_eq6
- ##| ##7: napply eqbitrig_to_eq7
- ##| ##8: napply eqbitrig_to_eq8
- ##| ##9: napply eqbitrig_to_eq9
- ##| ##10: napply eqbitrig_to_eq10
- ##| ##11: napply eqbitrig_to_eq11
- ##| ##12: napply eqbitrig_to_eq12
- ##| ##13: napply eqbitrig_to_eq13
- ##| ##14: napply eqbitrig_to_eq14
- ##| ##15: napply eqbitrig_to_eq15
- ##| ##16: napply eqbitrig_to_eq16
- ##| ##17: napply eqbitrig_to_eq17
- ##| ##18: napply eqbitrig_to_eq18
- ##| ##19: napply eqbitrig_to_eq19
- ##| ##20: napply eqbitrig_to_eq20
- ##| ##21: napply eqbitrig_to_eq21
- ##| ##22: napply eqbitrig_to_eq22
- ##| ##23: napply eqbitrig_to_eq23
- ##| ##24: napply eqbitrig_to_eq24
- ##| ##25: napply eqbitrig_to_eq25
- ##| ##26: napply eqbitrig_to_eq26
- ##| ##27: napply eqbitrig_to_eq27
- ##| ##28: napply eqbitrig_to_eq28
- ##| ##29: napply eqbitrig_to_eq29
- ##| ##30: napply eqbitrig_to_eq30
- ##| ##31: napply eqbitrig_to_eq31
- ##| ##32: napply eqbitrig_to_eq32
- ##]
-nqed.
-
-nlemma eq_to_eqbitrig1 : ∀t2.t00 = t2 → eq_bitrig t00 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##1: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig2 : ∀t2.t01 = t2 → eq_bitrig t01 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##2: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig3 : ∀t2.t02 = t2 → eq_bitrig t02 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##3: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig4 : ∀t2.t03 = t2 → eq_bitrig t03 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##4: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig5 : ∀t2.t04 = t2 → eq_bitrig t04 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##5: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig6 : ∀t2.t05 = t2 → eq_bitrig t05 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##6: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig7 : ∀t2.t06 = t2 → eq_bitrig t06 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##7: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig8 : ∀t2.t07 = t2 → eq_bitrig t07 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##8: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig9 : ∀t2.t08 = t2 → eq_bitrig t08 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##9: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig10 : ∀t2.t09 = t2 → eq_bitrig t09 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##10: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig11 : ∀t2.t0A = t2 → eq_bitrig t0A t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##11: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig12 : ∀t2.t0B = t2 → eq_bitrig t0B t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##12: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig13 : ∀t2.t0C = t2 → eq_bitrig t0C t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##13: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig14 : ∀t2.t0D = t2 → eq_bitrig t0D t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##14: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig15 : ∀t2.t0E = t2 → eq_bitrig t0E t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##15: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig16 : ∀t2.t0F = t2 → eq_bitrig t0F t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##16: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig17 : ∀t2.t10 = t2 → eq_bitrig t10 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##17: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig18 : ∀t2.t11 = t2 → eq_bitrig t11 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##18: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig19 : ∀t2.t12 = t2 → eq_bitrig t12 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##19: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig20 : ∀t2.t13 = t2 → eq_bitrig t13 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##20: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig21 : ∀t2.t14 = t2 → eq_bitrig t14 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##21: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-nlemma eq_to_eqbitrig22 : ∀t2.t15 = t2 → eq_bitrig t15 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##22: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig23 : ∀t2.t16 = t2 → eq_bitrig t16 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##23: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig24 : ∀t2.t17 = t2 → eq_bitrig t17 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##24: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig25 : ∀t2.t18 = t2 → eq_bitrig t18 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##25: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig26 : ∀t2.t19 = t2 → eq_bitrig t19 t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##26: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig27 : ∀t2.t1A = t2 → eq_bitrig t1A t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##27: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig28 : ∀t2.t1B = t2 → eq_bitrig t1B t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##28: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig29 : ∀t2.t1C = t2 → eq_bitrig t1C t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##29: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig30 : ∀t2.t1D = t2 → eq_bitrig t1D t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##30: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig31 : ∀t2.t1E = t2 → eq_bitrig t1E t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##31: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig32 : ∀t2.t1F = t2 → eq_bitrig t1F t2 = true.
- #t2; ncases t2; nnormalize; #H; ##[ ##32: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
-nqed.
-
-nlemma eq_to_eqbitrig : ∀t1,t2.t1 = t2 → eq_bitrig t1 t2 = true.
- #t1;
- ncases t1;
- ##[ ##1: napply eq_to_eqbitrig1
- ##| ##2: napply eq_to_eqbitrig2
- ##| ##3: napply eq_to_eqbitrig3
- ##| ##4: napply eq_to_eqbitrig4
- ##| ##5: napply eq_to_eqbitrig5
- ##| ##6: napply eq_to_eqbitrig6
- ##| ##7: napply eq_to_eqbitrig7
- ##| ##8: napply eq_to_eqbitrig8
- ##| ##9: napply eq_to_eqbitrig9
- ##| ##10: napply eq_to_eqbitrig10
- ##| ##11: napply eq_to_eqbitrig11
- ##| ##12: napply eq_to_eqbitrig12
- ##| ##13: napply eq_to_eqbitrig13
- ##| ##14: napply eq_to_eqbitrig14
- ##| ##15: napply eq_to_eqbitrig15
- ##| ##16: napply eq_to_eqbitrig16
- ##| ##17: napply eq_to_eqbitrig17
- ##| ##18: napply eq_to_eqbitrig18
- ##| ##19: napply eq_to_eqbitrig19
- ##| ##20: napply eq_to_eqbitrig20
- ##| ##21: napply eq_to_eqbitrig21
- ##| ##22: napply eq_to_eqbitrig22
- ##| ##23: napply eq_to_eqbitrig23
- ##| ##24: napply eq_to_eqbitrig24
- ##| ##25: napply eq_to_eqbitrig25
- ##| ##26: napply eq_to_eqbitrig26
- ##| ##27: napply eq_to_eqbitrig27
- ##| ##28: napply eq_to_eqbitrig28
- ##| ##29: napply eq_to_eqbitrig29
- ##| ##30: napply eq_to_eqbitrig30
- ##| ##31: napply eq_to_eqbitrig31
- ##| ##32: napply eq_to_eqbitrig32
- ##]
-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: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* *)
+(* ********************************************************************** *)
+
+include "freescale/bool.ma".
+
+(* ************* *)
+(* BITRIGESIMALI *)
+(* ************* *)
+
+ninductive bitrigesim : Type ≝
+ t00: bitrigesim
+| t01: bitrigesim
+| t02: bitrigesim
+| t03: bitrigesim
+| t04: bitrigesim
+| t05: bitrigesim
+| t06: bitrigesim
+| t07: bitrigesim
+| t08: bitrigesim
+| t09: bitrigesim
+| t0A: bitrigesim
+| t0B: bitrigesim
+| t0C: bitrigesim
+| t0D: bitrigesim
+| t0E: bitrigesim
+| t0F: bitrigesim
+| t10: bitrigesim
+| t11: bitrigesim
+| t12: bitrigesim
+| t13: bitrigesim
+| t14: bitrigesim
+| t15: bitrigesim
+| t16: bitrigesim
+| t17: bitrigesim
+| t18: bitrigesim
+| t19: bitrigesim
+| t1A: bitrigesim
+| t1B: bitrigesim
+| t1C: bitrigesim
+| t1D: bitrigesim
+| t1E: bitrigesim
+| t1F: bitrigesim.
+
+(* operatore = *)
+ndefinition eq_bit ≝
+λt1,t2:bitrigesim.
+ match t1 with
+ [ t00 ⇒ match t2 with [ t00 ⇒ true | _ ⇒ false ]
+ | t01 ⇒ match t2 with [ t01 ⇒ true | _ ⇒ false ]
+ | t02 ⇒ match t2 with [ t02 ⇒ true | _ ⇒ false ]
+ | t03 ⇒ match t2 with [ t03 ⇒ true | _ ⇒ false ]
+ | t04 ⇒ match t2 with [ t04 ⇒ true | _ ⇒ false ]
+ | t05 ⇒ match t2 with [ t05 ⇒ true | _ ⇒ false ]
+ | t06 ⇒ match t2 with [ t06 ⇒ true | _ ⇒ false ]
+ | t07 ⇒ match t2 with [ t07 ⇒ true | _ ⇒ false ]
+ | t08 ⇒ match t2 with [ t08 ⇒ true | _ ⇒ false ]
+ | t09 ⇒ match t2 with [ t09 ⇒ true | _ ⇒ false ]
+ | t0A ⇒ match t2 with [ t0A ⇒ true | _ ⇒ false ]
+ | t0B ⇒ match t2 with [ t0B ⇒ true | _ ⇒ false ]
+ | t0C ⇒ match t2 with [ t0C ⇒ true | _ ⇒ false ]
+ | t0D ⇒ match t2 with [ t0D ⇒ true | _ ⇒ false ]
+ | t0E ⇒ match t2 with [ t0E ⇒ true | _ ⇒ false ]
+ | t0F ⇒ match t2 with [ t0F ⇒ true | _ ⇒ false ]
+ | t10 ⇒ match t2 with [ t10 ⇒ true | _ ⇒ false ]
+ | t11 ⇒ match t2 with [ t11 ⇒ true | _ ⇒ false ]
+ | t12 ⇒ match t2 with [ t12 ⇒ true | _ ⇒ false ]
+ | t13 ⇒ match t2 with [ t13 ⇒ true | _ ⇒ false ]
+ | t14 ⇒ match t2 with [ t14 ⇒ true | _ ⇒ false ]
+ | t15 ⇒ match t2 with [ t15 ⇒ true | _ ⇒ false ]
+ | t16 ⇒ match t2 with [ t16 ⇒ true | _ ⇒ false ]
+ | t17 ⇒ match t2 with [ t17 ⇒ true | _ ⇒ false ]
+ | t18 ⇒ match t2 with [ t18 ⇒ true | _ ⇒ false ]
+ | t19 ⇒ match t2 with [ t19 ⇒ true | _ ⇒ false ]
+ | t1A ⇒ match t2 with [ t1A ⇒ true | _ ⇒ false ]
+ | t1B ⇒ match t2 with [ t1B ⇒ true | _ ⇒ false ]
+ | t1C ⇒ match t2 with [ t1C ⇒ true | _ ⇒ false ]
+ | t1D ⇒ match t2 with [ t1D ⇒ true | _ ⇒ false ]
+ | t1E ⇒ match t2 with [ t1E ⇒ true | _ ⇒ false ]
+ | t1F ⇒ match t2 with [ t1F ⇒ true | _ ⇒ false ]
+ ].
+
+(* iteratore sui bitrigesimali *)
+ndefinition forall_bit ≝ λP.
+ P t00 ⊗ P t01 ⊗ P t02 ⊗ P t03 ⊗ P t04 ⊗ P t05 ⊗ P t06 ⊗ P t07 ⊗
+ P t08 ⊗ P t09 ⊗ P t0A ⊗ P t0B ⊗ P t0C ⊗ P t0D ⊗ P t0E ⊗ P t0F ⊗
+ 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 successore *)
+ndefinition succ_bit ≝
+λn.match n with
+ [ 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 ⇒ t00
+ ].
+
+(* bitrigesimali ricorsivi *)
+ninductive rec_bitrigesim : bitrigesim → Type ≝
+ bi_O : rec_bitrigesim t00
+| bi_S : ∀n.rec_bitrigesim n → rec_bitrigesim (succ_bit n).
+
+(* bitrigesimali → bitrigesimali ricorsivi *)
+ndefinition bit_to_recbit ≝
+λn.match n return λx.rec_bitrigesim x with
+ [ t00 ⇒ bi_O
+ | t01 ⇒ bi_S ? bi_O
+ | t02 ⇒ bi_S ? (bi_S ? bi_O)
+ | t03 ⇒ bi_S ? (bi_S ? (bi_S ? bi_O))
+ | t04 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O)))
+ | t05 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O))))
+ | t06 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O)))))
+ | t07 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O))))))
+ | t08 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ bi_O)))))))
+ | t09 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? bi_O))))))))
+ | t0A ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? bi_O)))))))))
+ | t0B ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? bi_O))))))))))
+ | t0C ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O)))))))))))
+ | t0D ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O))))))))))))
+ | t0E ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O)))))))))))))
+ | t0F ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O))))))))))))))
+ | t10 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ bi_O)))))))))))))))
+ | t11 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? bi_O))))))))))))))))
+ | t12 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? bi_O)))))))))))))))))
+ | t13 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? bi_O))))))))))))))))))
+ | t14 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O)))))))))))))))))))
+ | t15 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O))))))))))))))))))))
+ | t16 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O)))))))))))))))))))))
+ | t17 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O))))))))))))))))))))))
+ | t18 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ bi_O)))))))))))))))))))))))
+ | t19 ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? bi_O))))))))))))))))))))))))
+ | t1A ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? bi_O)))))))))))))))))))))))))
+ | t1B ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? bi_O))))))))))))))))))))))))))
+ | t1C ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O)))))))))))))))))))))))))))
+ | t1D ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O))))))))))))))))))))))))))))
+ | t1E ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O)))))))))))))))))))))))))))))
+ | t1F ⇒ bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ?
+ (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? (bi_S ? bi_O))))))))))))))))))))))))))))))
+ ].
--- /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: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* *)
+(* ********************************************************************** *)
+
+include "freescale/bool_lemmas.ma".
+include "freescale/bitrigesim.ma".
+
+(* ************* *)
+(* BITRIGESIMALI *)
+(* ************* *)
+
+ndefinition bitrigesim_destruct1 :
+Πt2:bitrigesim.ΠP:Prop.t00 = t2 → match t2 with [ t00 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##1: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t00 with [ t00 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct2 :
+Πt2:bitrigesim.ΠP:Prop.t01 = t2 → match t2 with [ t01 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##2: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t01 with [ t01 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct3 :
+Πt2:bitrigesim.ΠP:Prop.t02 = t2 → match t2 with [ t02 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##3: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t02 with [ t02 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct4 :
+Πt2:bitrigesim.ΠP:Prop.t03 = t2 → match t2 with [ t03 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##4: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t03 with [ t03 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct5 :
+Πt2:bitrigesim.ΠP:Prop.t04 = t2 → match t2 with [ t04 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##5: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t04 with [ t04 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct6 :
+Πt2:bitrigesim.ΠP:Prop.t05 = t2 → match t2 with [ t05 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##6: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t05 with [ t05 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct7 :
+Πt2:bitrigesim.ΠP:Prop.t06 = t2 → match t2 with [ t06 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##7: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t06 with [ t06 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct8 :
+Πt2:bitrigesim.ΠP:Prop.t07 = t2 → match t2 with [ t07 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##8: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t07 with [ t07 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct9 :
+Πt2:bitrigesim.ΠP:Prop.t08 = t2 → match t2 with [ t08 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##9: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t08 with [ t08 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct10 :
+Πt2:bitrigesim.ΠP:Prop.t09 = t2 → match t2 with [ t09 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##10: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t09 with [ t09 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct11 :
+Πt2:bitrigesim.ΠP:Prop.t0A = t2 → match t2 with [ t0A ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##11: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t0A with [ t0A ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct12 :
+Πt2:bitrigesim.ΠP:Prop.t0B = t2 → match t2 with [ t0B ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##12: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t0B with [ t0B ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct13 :
+Πt2:bitrigesim.ΠP:Prop.t0C = t2 → match t2 with [ t0C ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##13: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t0C with [ t0C ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct14 :
+Πt2:bitrigesim.ΠP:Prop.t0D = t2 → match t2 with [ t0D ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##14: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t0D with [ t0D ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct15 :
+Πt2:bitrigesim.ΠP:Prop.t0E = t2 → match t2 with [ t0E ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##15: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t0E with [ t0E ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct16 :
+Πt2:bitrigesim.ΠP:Prop.t0F = t2 → match t2 with [ t0F ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##16: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t0F with [ t0F ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct17 :
+Πt2:bitrigesim.ΠP:Prop.t10 = t2 → match t2 with [ t10 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##17: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t10 with [ t10 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct18 :
+Πt2:bitrigesim.ΠP:Prop.t11 = t2 → match t2 with [ t11 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##18: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t11 with [ t11 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct19 :
+Πt2:bitrigesim.ΠP:Prop.t12 = t2 → match t2 with [ t12 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##19: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t12 with [ t12 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct20 :
+Πt2:bitrigesim.ΠP:Prop.t13 = t2 → match t2 with [ t13 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##20: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t13 with [ t13 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct21 :
+Πt2:bitrigesim.ΠP:Prop.t14 = t2 → match t2 with [ t14 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##21: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t14 with [ t14 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct22 :
+Πt2:bitrigesim.ΠP:Prop.t15 = t2 → match t2 with [ t15 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##22: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t15 with [ t15 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct23 :
+Πt2:bitrigesim.ΠP:Prop.t16 = t2 → match t2 with [ t16 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##23: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t16 with [ t16 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct24 :
+Πt2:bitrigesim.ΠP:Prop.t17 = t2 → match t2 with [ t17 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##24: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t17 with [ t17 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct25 :
+Πt2:bitrigesim.ΠP:Prop.t18 = t2 → match t2 with [ t18 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##25: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t18 with [ t18 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct26 :
+Πt2:bitrigesim.ΠP:Prop.t19 = t2 → match t2 with [ t19 ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##26: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t19 with [ t19 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct27 :
+Πt2:bitrigesim.ΠP:Prop.t1A = t2 → match t2 with [ t1A ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##27: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t1A with [ t1A ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct28 :
+Πt2:bitrigesim.ΠP:Prop.t1B = t2 → match t2 with [ t1B ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##28: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t1B with [ t1B ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct29 :
+Πt2:bitrigesim.ΠP:Prop.t1C = t2 → match t2 with [ t1C ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##29: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t1C with [ t1C ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct30 :
+Πt2:bitrigesim.ΠP:Prop.t1D = t2 → match t2 with [ t1D ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##30: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t1D with [ t1D ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct31 :
+Πt2:bitrigesim.ΠP:Prop.t1E = t2 → match t2 with [ t1E ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##31: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t1E with [ t1E ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct32 :
+Πt2:bitrigesim.ΠP:Prop.t1F = t2 → match t2 with [ t1F ⇒ P → P | _ ⇒ P ].
+ #t2; #P;
+ ncases t2;
+ nnormalize; #H;
+ ##[ ##32: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match t1F with [ t1F ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition bitrigesim_destruct_aux ≝
+Πt1,t2:bitrigesim.ΠP:Prop.t1 = t2 →
+ match t1 with
+ [ t00 ⇒ match t2 with [ t00 ⇒ P → P | _ ⇒ P ]
+ | t01 ⇒ match t2 with [ t01 ⇒ P → P | _ ⇒ P ]
+ | t02 ⇒ match t2 with [ t02 ⇒ P → P | _ ⇒ P ]
+ | t03 ⇒ match t2 with [ t03 ⇒ P → P | _ ⇒ P ]
+ | t04 ⇒ match t2 with [ t04 ⇒ P → P | _ ⇒ P ]
+ | t05 ⇒ match t2 with [ t05 ⇒ P → P | _ ⇒ P ]
+ | t06 ⇒ match t2 with [ t06 ⇒ P → P | _ ⇒ P ]
+ | t07 ⇒ match t2 with [ t07 ⇒ P → P | _ ⇒ P ]
+ | t08 ⇒ match t2 with [ t08 ⇒ P → P | _ ⇒ P ]
+ | t09 ⇒ match t2 with [ t09 ⇒ P → P | _ ⇒ P ]
+ | t0A ⇒ match t2 with [ t0A ⇒ P → P | _ ⇒ P ]
+ | t0B ⇒ match t2 with [ t0B ⇒ P → P | _ ⇒ P ]
+ | t0C ⇒ match t2 with [ t0C ⇒ P → P | _ ⇒ P ]
+ | t0D ⇒ match t2 with [ t0D ⇒ P → P | _ ⇒ P ]
+ | t0E ⇒ match t2 with [ t0E ⇒ P → P | _ ⇒ P ]
+ | t0F ⇒ match t2 with [ t0F ⇒ P → P | _ ⇒ P ]
+ | t10 ⇒ match t2 with [ t10 ⇒ P → P | _ ⇒ P ]
+ | t11 ⇒ match t2 with [ t11 ⇒ P → P | _ ⇒ P ]
+ | t12 ⇒ match t2 with [ t12 ⇒ P → P | _ ⇒ P ]
+ | t13 ⇒ match t2 with [ t13 ⇒ P → P | _ ⇒ P ]
+ | t14 ⇒ match t2 with [ t14 ⇒ P → P | _ ⇒ P ]
+ | t15 ⇒ match t2 with [ t15 ⇒ P → P | _ ⇒ P ]
+ | t16 ⇒ match t2 with [ t16 ⇒ P → P | _ ⇒ P ]
+ | t17 ⇒ match t2 with [ t17 ⇒ P → P | _ ⇒ P ]
+ | t18 ⇒ match t2 with [ t18 ⇒ P → P | _ ⇒ P ]
+ | t19 ⇒ match t2 with [ t19 ⇒ P → P | _ ⇒ P ]
+ | t1A ⇒ match t2 with [ t1A ⇒ P → P | _ ⇒ P ]
+ | t1B ⇒ match t2 with [ t1B ⇒ P → P | _ ⇒ P ]
+ | t1C ⇒ match t2 with [ t1C ⇒ P → P | _ ⇒ P ]
+ | t1D ⇒ match t2 with [ t1D ⇒ P → P | _ ⇒ P ]
+ | t1E ⇒ match t2 with [ t1E ⇒ P → P | _ ⇒ P ]
+ | t1F ⇒ match t2 with [ t1F ⇒ P → P | _ ⇒ P ]
+ ].
+
+ndefinition bitrigesim_destruct : bitrigesim_destruct_aux.
+ #t1;
+ ncases t1;
+ ##[ ##1: napply bitrigesim_destruct1
+ ##| ##2: napply bitrigesim_destruct2
+ ##| ##3: napply bitrigesim_destruct3
+ ##| ##4: napply bitrigesim_destruct4
+ ##| ##5: napply bitrigesim_destruct5
+ ##| ##6: napply bitrigesim_destruct6
+ ##| ##7: napply bitrigesim_destruct7
+ ##| ##8: napply bitrigesim_destruct8
+ ##| ##9: napply bitrigesim_destruct9
+ ##| ##10: napply bitrigesim_destruct10
+ ##| ##11: napply bitrigesim_destruct11
+ ##| ##12: napply bitrigesim_destruct12
+ ##| ##13: napply bitrigesim_destruct13
+ ##| ##14: napply bitrigesim_destruct14
+ ##| ##15: napply bitrigesim_destruct15
+ ##| ##16: napply bitrigesim_destruct16
+ ##| ##17: napply bitrigesim_destruct17
+ ##| ##18: napply bitrigesim_destruct18
+ ##| ##19: napply bitrigesim_destruct19
+ ##| ##20: napply bitrigesim_destruct20
+ ##| ##21: napply bitrigesim_destruct21
+ ##| ##22: napply bitrigesim_destruct22
+ ##| ##23: napply bitrigesim_destruct23
+ ##| ##24: napply bitrigesim_destruct24
+ ##| ##25: napply bitrigesim_destruct25
+ ##| ##26: napply bitrigesim_destruct26
+ ##| ##27: napply bitrigesim_destruct27
+ ##| ##28: napply bitrigesim_destruct28
+ ##| ##29: napply bitrigesim_destruct29
+ ##| ##30: napply bitrigesim_destruct30
+ ##| ##31: napply bitrigesim_destruct31
+ ##| ##32: napply bitrigesim_destruct32
+ ##]
+nqed.
+
+nlemma symmetric_eqbit : symmetricT bitrigesim bool eq_bit.
+ #t1;
+ nelim t1;
+ ##[ ##1: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##2: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##3: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##4: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##5: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##6: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##7: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##8: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##9: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##10: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##11: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##12: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##13: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##14: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##15: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##16: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##17: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##18: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##19: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##20: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##21: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##22: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##23: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##24: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##25: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##26: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##27: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##28: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##29: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##30: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##31: #t2; nelim t2; nnormalize; napply refl_eq
+ ##| ##32: #t2; nelim t2; nnormalize; napply refl_eq
+ ##]
+nqed.
+
+nlemma eqbit_to_eq1 : ∀t2.eq_bit t00 t2 = true → t00 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##1: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq2 : ∀t2.eq_bit t01 t2 = true → t01 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##2: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq3 : ∀t2.eq_bit t02 t2 = true → t02 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##3: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq4 : ∀t2.eq_bit t03 t2 = true → t03 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##4: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq5 : ∀t2.eq_bit t04 t2 = true → t04 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##5: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq6 : ∀t2.eq_bit t05 t2 = true → t05 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##6: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq7 : ∀t2.eq_bit t06 t2 = true → t06 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##7: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq8 : ∀t2.eq_bit t07 t2 = true → t07 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##8: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq9 : ∀t2.eq_bit t08 t2 = true → t08 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##9: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq10 : ∀t2.eq_bit t09 t2 = true → t09 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##10: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq11 : ∀t2.eq_bit t0A t2 = true → t0A = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##11: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq12 : ∀t2.eq_bit t0B t2 = true → t0B = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##12: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq13 : ∀t2.eq_bit t0C t2 = true → t0C = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##13: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq14 : ∀t2.eq_bit t0D t2 = true → t0D = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##14: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq15 : ∀t2.eq_bit t0E t2 = true → t0E = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##15: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq16 : ∀t2.eq_bit t0F t2 = true → t0F = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##16: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq17 : ∀t2.eq_bit t10 t2 = true → t10 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##17: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq18 : ∀t2.eq_bit t11 t2 = true → t11 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##18: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq19 : ∀t2.eq_bit t12 t2 = true → t12 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##19: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq20 : ∀t2.eq_bit t13 t2 = true → t13 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##20: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq21 : ∀t2.eq_bit t14 t2 = true → t14 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##21: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq22 : ∀t2.eq_bit t15 t2 = true → t15 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##22: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq23 : ∀t2.eq_bit t16 t2 = true → t16 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##23: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq24 : ∀t2.eq_bit t17 t2 = true → t17 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##24: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq25 : ∀t2.eq_bit t18 t2 = true → t18 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##25: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq26 : ∀t2.eq_bit t19 t2 = true → t19 = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##26: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq27 : ∀t2.eq_bit t1A t2 = true → t1A = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##27: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq28 : ∀t2.eq_bit t1B t2 = true → t1B = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##28: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq29 : ∀t2.eq_bit t1C t2 = true → t1C = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##29: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq30 : ∀t2.eq_bit t1D t2 = true → t1D = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##30: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq31 : ∀t2.eq_bit t1E t2 = true → t1E = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##31: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq32 : ∀t2.eq_bit t1F t2 = true → t1F = t2.
+ #t2; ncases t2; nnormalize; #H; ##[ ##32: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]
+nqed.
+
+nlemma eqbit_to_eq : ∀t1,t2.eq_bit t1 t2 = true → t1 = t2.
+ #t1;
+ ncases t1;
+ ##[ ##1: napply eqbit_to_eq1
+ ##| ##2: napply eqbit_to_eq2
+ ##| ##3: napply eqbit_to_eq3
+ ##| ##4: napply eqbit_to_eq4
+ ##| ##5: napply eqbit_to_eq5
+ ##| ##6: napply eqbit_to_eq6
+ ##| ##7: napply eqbit_to_eq7
+ ##| ##8: napply eqbit_to_eq8
+ ##| ##9: napply eqbit_to_eq9
+ ##| ##10: napply eqbit_to_eq10
+ ##| ##11: napply eqbit_to_eq11
+ ##| ##12: napply eqbit_to_eq12
+ ##| ##13: napply eqbit_to_eq13
+ ##| ##14: napply eqbit_to_eq14
+ ##| ##15: napply eqbit_to_eq15
+ ##| ##16: napply eqbit_to_eq16
+ ##| ##17: napply eqbit_to_eq17
+ ##| ##18: napply eqbit_to_eq18
+ ##| ##19: napply eqbit_to_eq19
+ ##| ##20: napply eqbit_to_eq20
+ ##| ##21: napply eqbit_to_eq21
+ ##| ##22: napply eqbit_to_eq22
+ ##| ##23: napply eqbit_to_eq23
+ ##| ##24: napply eqbit_to_eq24
+ ##| ##25: napply eqbit_to_eq25
+ ##| ##26: napply eqbit_to_eq26
+ ##| ##27: napply eqbit_to_eq27
+ ##| ##28: napply eqbit_to_eq28
+ ##| ##29: napply eqbit_to_eq29
+ ##| ##30: napply eqbit_to_eq30
+ ##| ##31: napply eqbit_to_eq31
+ ##| ##32: napply eqbit_to_eq32
+ ##]
+nqed.
+
+nlemma eq_to_eqbit1 : ∀t2.t00 = t2 → eq_bit t00 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##1: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit2 : ∀t2.t01 = t2 → eq_bit t01 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##2: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit3 : ∀t2.t02 = t2 → eq_bit t02 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##3: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit4 : ∀t2.t03 = t2 → eq_bit t03 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##4: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit5 : ∀t2.t04 = t2 → eq_bit t04 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##5: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit6 : ∀t2.t05 = t2 → eq_bit t05 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##6: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit7 : ∀t2.t06 = t2 → eq_bit t06 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##7: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit8 : ∀t2.t07 = t2 → eq_bit t07 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##8: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit9 : ∀t2.t08 = t2 → eq_bit t08 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##9: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit10 : ∀t2.t09 = t2 → eq_bit t09 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##10: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit11 : ∀t2.t0A = t2 → eq_bit t0A t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##11: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit12 : ∀t2.t0B = t2 → eq_bit t0B t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##12: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit13 : ∀t2.t0C = t2 → eq_bit t0C t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##13: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit14 : ∀t2.t0D = t2 → eq_bit t0D t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##14: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit15 : ∀t2.t0E = t2 → eq_bit t0E t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##15: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit16 : ∀t2.t0F = t2 → eq_bit t0F t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##16: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit17 : ∀t2.t10 = t2 → eq_bit t10 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##17: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit18 : ∀t2.t11 = t2 → eq_bit t11 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##18: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit19 : ∀t2.t12 = t2 → eq_bit t12 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##19: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit20 : ∀t2.t13 = t2 → eq_bit t13 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##20: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit21 : ∀t2.t14 = t2 → eq_bit t14 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##21: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit22 : ∀t2.t15 = t2 → eq_bit t15 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##22: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit23 : ∀t2.t16 = t2 → eq_bit t16 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##23: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit24 : ∀t2.t17 = t2 → eq_bit t17 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##24: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit25 : ∀t2.t18 = t2 → eq_bit t18 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##25: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit26 : ∀t2.t19 = t2 → eq_bit t19 t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##26: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit27 : ∀t2.t1A = t2 → eq_bit t1A t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##27: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit28 : ∀t2.t1B = t2 → eq_bit t1B t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##28: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit29 : ∀t2.t1C = t2 → eq_bit t1C t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##29: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit30 : ∀t2.t1D = t2 → eq_bit t1D t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##30: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit31 : ∀t2.t1E = t2 → eq_bit t1E t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##31: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit32 : ∀t2.t1F = t2 → eq_bit t1F t2 = true.
+ #t2; ncases t2; nnormalize; #H; ##[ ##32: napply refl_eq ##| ##*: napply (bitrigesim_destruct … H) ##]
+nqed.
+
+nlemma eq_to_eqbit : ∀t1,t2.t1 = t2 → eq_bit t1 t2 = true.
+ #t1;
+ ncases t1;
+ ##[ ##1: napply eq_to_eqbit1
+ ##| ##2: napply eq_to_eqbit2
+ ##| ##3: napply eq_to_eqbit3
+ ##| ##4: napply eq_to_eqbit4
+ ##| ##5: napply eq_to_eqbit5
+ ##| ##6: napply eq_to_eqbit6
+ ##| ##7: napply eq_to_eqbit7
+ ##| ##8: napply eq_to_eqbit8
+ ##| ##9: napply eq_to_eqbit9
+ ##| ##10: napply eq_to_eqbit10
+ ##| ##11: napply eq_to_eqbit11
+ ##| ##12: napply eq_to_eqbit12
+ ##| ##13: napply eq_to_eqbit13
+ ##| ##14: napply eq_to_eqbit14
+ ##| ##15: napply eq_to_eqbit15
+ ##| ##16: napply eq_to_eqbit16
+ ##| ##17: napply eq_to_eqbit17
+ ##| ##18: napply eq_to_eqbit18
+ ##| ##19: napply eq_to_eqbit19
+ ##| ##20: napply eq_to_eqbit20
+ ##| ##21: napply eq_to_eqbit21
+ ##| ##22: napply eq_to_eqbit22
+ ##| ##23: napply eq_to_eqbit23
+ ##| ##24: napply eq_to_eqbit24
+ ##| ##25: napply eq_to_eqbit25
+ ##| ##26: napply eq_to_eqbit26
+ ##| ##27: napply eq_to_eqbit27
+ ##| ##28: napply eq_to_eqbit28
+ ##| ##29: napply eq_to_eqbit29
+ ##| ##30: napply eq_to_eqbit30
+ ##| ##31: napply eq_to_eqbit31
+ ##| ##32: napply eq_to_eqbit32
+ ##]
+nqed.
nelim b2;
nnormalize;
#H;
- ##[ ##2: napply (False_ind (λx.?) ?);
+ ##[ ##2: napply False_ind;
nchange with (match true with [ true ⇒ False | false ⇒ True]);
nrewrite > H;
nnormalize;
napply I
- ##| ##3: napply (False_ind (λx.?) ?);
+ ##| ##3: napply False_ind;
nchange with (match true with [ true ⇒ False | false ⇒ True]);
nrewrite < H;
nnormalize;
(* ********************************************************************** *)
include "freescale/exadecim.ma".
+include "freescale/bitrigesim.ma".
(* **** *)
(* BYTE *)
| false ⇒ mk_byte8 bh' bl' ]]].
(* operatore rotazione destra n-volte *)
-nlet rec ror_b8_n (b:byte8) (n:nat) on n ≝
- match n with
- [ O ⇒ b
- | S n' ⇒ ror_b8_n (ror_b8 b) n' ].
+nlet rec ror_b8_n (b:byte8) (n:oct) (r:rec_oct n) on r ≝
+ match r with
+ [ oc_O ⇒ b
+ | oc_S t n' ⇒ ror_b8_n (ror_b8 b) t n' ].
(* operatore rotazione sinistra con carry *)
ndefinition rcl_b8 ≝
| false ⇒ mk_byte8 bh' bl' ]]].
(* operatore rotazione sinistra n-volte *)
-nlet rec rol_b8_n (b:byte8) (n:nat) on n ≝
- match n with
- [ O ⇒ b
- | S n' ⇒ rol_b8_n (rol_b8 b) n' ].
+nlet rec rol_b8_n (b:byte8) (n:oct) (r:rec_oct n) on r ≝
+ match r with
+ [ oc_O ⇒ b
+ | oc_S t n' ⇒ rol_b8_n (rol_b8 b) t n' ].
(* operatore not/complemento a 1 *)
ndefinition not_b8 ≝
(* operatore Most Significant Bit *)
ndefinition MSB_b8 ≝ λb:byte8.eq_ex x8 (and_ex x8 (b8h b)).
-(* byte → naturali *)
-ndefinition nat_of_byte8 ≝ λb:byte8.(16*(nat_of_exadecim (b8h b))) + (nat_of_exadecim (b8l b)).
-
(* operatore predecessore *)
ndefinition pred_b8 ≝
λb:byte8.match eq_ex (b8l b) x0 with
].
(* iteratore sui byte *)
-ndefinition forall_byte8 ≝
+ndefinition forall_b8 ≝
λP.
- forall_exadecim (λbh.
- forall_exadecim (λbl.
+ forall_ex (λbh.
+ forall_ex (λbl.
P (mk_byte8 bh bl))).
+
+(* byte ricorsivi *)
+ninductive rec_byte8 : byte8 → Type ≝
+ b8_O : rec_byte8 〈x0,x0〉
+| b8_S : ∀n.rec_byte8 n → rec_byte8 (succ_b8 n).
+
+(* byte → byte ricorsivi *)
+ndefinition b8_to_recb8_aux1 : Πn.rec_byte8 〈n,x0〉 → rec_byte8 〈succ_ex n,x0〉 ≝
+λn.λrecb:rec_byte8 〈n,x0〉.
+ b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (
+ b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? recb))))))))))))))).
+
+(* ... cifra esadecimale superiore *)
+nlet rec b8_to_recb8_aux2 (n:exadecim) (r:rec_exadecim n) on r ≝
+ match r return λx.λy:rec_exadecim x.rec_byte8 〈x,x0〉 with
+ [ ex_O ⇒ b8_O
+ | ex_S t n' ⇒ b8_to_recb8_aux1 ? (b8_to_recb8_aux2 t n')
+ ].
+
+(* ... cifra esadecimale inferiore *)
+ndefinition b8_to_recb8_aux3 : Πn1,n2.rec_byte8 〈n1,x0〉 → rec_byte8 〈n1,n2〉 ≝
+λn1,n2.λrecb:rec_byte8 〈n1,x0〉.
+ match n2 return λx.rec_byte8 〈n1,x〉 with
+ [ x0 ⇒ recb
+ | x1 ⇒ b8_S ? recb
+ | x2 ⇒ b8_S ? (b8_S ? recb)
+ | x3 ⇒ b8_S ? (b8_S ? (b8_S ? recb))
+ | x4 ⇒ b8_S ? (b8_S ? (b8_S ? (b8_S ? recb)))
+ | x5 ⇒ b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? recb))))
+ | x6 ⇒ b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? recb)))))
+ | x7 ⇒ b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? recb))))))
+ | x8 ⇒ b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? recb)))))))
+ | x9 ⇒ b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? recb))))))))
+ | xA ⇒ b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? recb)))))))))
+ | xB ⇒ b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? recb))))))))))
+ | xC ⇒ b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? recb)))))))))))
+ | xD ⇒ b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? recb))))))))))))
+ | xE ⇒ b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? recb)))))))))))))
+ | xF ⇒ b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? (b8_S ? recb))))))))))))))
+ ].
+
+ndefinition b8_to_recb8 ≝
+λn.b8_to_recb8_aux3 (b8h n) (b8l n) (b8_to_recb8_aux2 (b8h n) (ex_to_recex (b8h n))).
+
+(* ottali → esadecimali *)
+ndefinition b8_of_bit ≝
+λn.match n with
+ [ t00 ⇒ 〈x0,x0〉 | t01 ⇒ 〈x0,x1〉 | t02 ⇒ 〈x0,x2〉 | t03 ⇒ 〈x0,x3〉
+ | t04 ⇒ 〈x0,x4〉 | t05 ⇒ 〈x0,x5〉 | t06 ⇒ 〈x0,x6〉 | t07 ⇒ 〈x0,x7〉
+ | t08 ⇒ 〈x0,x8〉 | t09 ⇒ 〈x0,x9〉 | t0A ⇒ 〈x0,xA〉 | t0B ⇒ 〈x0,xB〉
+ | t0C ⇒ 〈x0,xC〉 | t0D ⇒ 〈x0,xD〉 | t0E ⇒ 〈x0,xE〉 | t0F ⇒ 〈x0,xF〉
+ | t10 ⇒ 〈x1,x0〉 | t11 ⇒ 〈x1,x1〉 | t12 ⇒ 〈x1,x2〉 | t13 ⇒ 〈x1,x3〉
+ | t14 ⇒ 〈x1,x4〉 | t15 ⇒ 〈x1,x5〉 | t16 ⇒ 〈x1,x6〉 | t17 ⇒ 〈x1,x7〉
+ | t18 ⇒ 〈x1,x8〉 | t19 ⇒ 〈x1,x9〉 | t1A ⇒ 〈x1,xA〉 | t1B ⇒ 〈x1,xB〉
+ | t1C ⇒ 〈x1,xC〉 | t1D ⇒ 〈x1,xD〉 | t1E ⇒ 〈x1,xE〉 | t1F ⇒ 〈x1,xF〉
+ ].
(* ********************************************************************** *)
include "freescale/bool.ma".
+include "freescale/quatern.ma".
+include "freescale/oct.ma".
include "freescale/prod.ma".
-include "freescale/nat.ma".
(* *********** *)
(* ESADECIMALI *)
(* *********** *)
-(* non riesce a terminare l'esecuzione !!! *)
-
ninductive exadecim : Type ≝
x0: exadecim
| x1: exadecim
ndefinition eq_ex ≝
λe1,e2:exadecim.
match e1 with
- [ x0 ⇒ match e2 with
- [ x0 ⇒ true | x1 ⇒ false | x2 ⇒ false | x3 ⇒ false
- | x4 ⇒ false | x5 ⇒ false | x6 ⇒ false | x7 ⇒ false
- | x8 ⇒ false | x9 ⇒ false | xA ⇒ false | xB ⇒ false
- | xC ⇒ false | xD ⇒ false | xE ⇒ false | xF ⇒ false ]
- | x1 ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ true | x2 ⇒ false | x3 ⇒ false
- | x4 ⇒ false | x5 ⇒ false | x6 ⇒ false | x7 ⇒ false
- | x8 ⇒ false | x9 ⇒ false | xA ⇒ false | xB ⇒ false
- | xC ⇒ false | xD ⇒ false | xE ⇒ false | xF ⇒ false ]
- | x2 ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ false | x2 ⇒ true | x3 ⇒ false
- | x4 ⇒ false | x5 ⇒ false | x6 ⇒ false | x7 ⇒ false
- | x8 ⇒ false | x9 ⇒ false | xA ⇒ false | xB ⇒ false
- | xC ⇒ false | xD ⇒ false | xE ⇒ false | xF ⇒ false ]
- | x3 ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ false | x2 ⇒ false | x3 ⇒ true
- | x4 ⇒ false | x5 ⇒ false | x6 ⇒ false | x7 ⇒ false
- | x8 ⇒ false | x9 ⇒ false | xA ⇒ false | xB ⇒ false
- | xC ⇒ false | xD ⇒ false | xE ⇒ false | xF ⇒ false ]
- | x4 ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ false | x2 ⇒ false | x3 ⇒ false
- | x4 ⇒ true | x5 ⇒ false | x6 ⇒ false | x7 ⇒ false
- | x8 ⇒ false | x9 ⇒ false | xA ⇒ false | xB ⇒ false
- | xC ⇒ false | xD ⇒ false | xE ⇒ false | xF ⇒ false ]
- | x5 ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ false | x2 ⇒ false | x3 ⇒ false
- | x4 ⇒ false | x5 ⇒ true | x6 ⇒ false | x7 ⇒ false
- | x8 ⇒ false | x9 ⇒ false | xA ⇒ false | xB ⇒ false
- | xC ⇒ false | xD ⇒ false | xE ⇒ false | xF ⇒ false ]
- | x6 ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ false | x2 ⇒ false | x3 ⇒ false
- | x4 ⇒ false | x5 ⇒ false | x6 ⇒ true | x7 ⇒ false
- | x8 ⇒ false | x9 ⇒ false | xA ⇒ false | xB ⇒ false
- | xC ⇒ false | xD ⇒ false | xE ⇒ false | xF ⇒ false ]
- | x7 ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ false | x2 ⇒ false | x3 ⇒ false
- | x4 ⇒ false | x5 ⇒ false | x6 ⇒ false | x7 ⇒ true
- | x8 ⇒ false | x9 ⇒ false | xA ⇒ false | xB ⇒ false
- | xC ⇒ false | xD ⇒ false | xE ⇒ false | xF ⇒ false ]
- | x8 ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ false | x2 ⇒ false | x3 ⇒ false
- | x4 ⇒ false | x5 ⇒ false | x6 ⇒ false | x7 ⇒ false
- | x8 ⇒ true | x9 ⇒ false | xA ⇒ false | xB ⇒ false
- | xC ⇒ false | xD ⇒ false | xE ⇒ false | xF ⇒ false ]
- | x9 ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ false | x2 ⇒ false | x3 ⇒ false
- | x4 ⇒ false | x5 ⇒ false | x6 ⇒ false | x7 ⇒ false
- | x8 ⇒ false | x9 ⇒ true | xA ⇒ false | xB ⇒ false
- | xC ⇒ false | xD ⇒ false | xE ⇒ false | xF ⇒ false ]
- | xA ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ false | x2 ⇒ false | x3 ⇒ false
- | x4 ⇒ false | x5 ⇒ false | x6 ⇒ false | x7 ⇒ false
- | x8 ⇒ false | x9 ⇒ false | xA ⇒ true | xB ⇒ false
- | xC ⇒ false | xD ⇒ false | xE ⇒ false | xF ⇒ false ]
- | xB ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ false | x2 ⇒ false | x3 ⇒ false
- | x4 ⇒ false | x5 ⇒ false | x6 ⇒ false | x7 ⇒ false
- | x8 ⇒ false | x9 ⇒ false | xA ⇒ false | xB ⇒ true
- | xC ⇒ false | xD ⇒ false | xE ⇒ false | xF ⇒ false ]
- | xC ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ false | x2 ⇒ false | x3 ⇒ false
- | x4 ⇒ false | x5 ⇒ false | x6 ⇒ false | x7 ⇒ false
- | x8 ⇒ false | x9 ⇒ false | xA ⇒ false | xB ⇒ false
- | xC ⇒ true | xD ⇒ false | xE ⇒ false | xF ⇒ false ]
- | xD ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ false | x2 ⇒ false | x3 ⇒ false
- | x4 ⇒ false | x5 ⇒ false | x6 ⇒ false | x7 ⇒ false
- | x8 ⇒ false | x9 ⇒ false | xA ⇒ false | xB ⇒ false
- | xC ⇒ false | xD ⇒ true | xE ⇒ false | xF ⇒ false ]
- | xE ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ false | x2 ⇒ false | x3 ⇒ false
- | x4 ⇒ false | x5 ⇒ false | x6 ⇒ false | x7 ⇒ false
- | x8 ⇒ false | x9 ⇒ false | xA ⇒ false | xB ⇒ false
- | xC ⇒ false | xD ⇒ false | xE ⇒ true | xF ⇒ false ]
- | xF ⇒ match e2 with
- [ x0 ⇒ false | x1 ⇒ false | x2 ⇒ false | x3 ⇒ false
- | x4 ⇒ false | x5 ⇒ false | x6 ⇒ false | x7 ⇒ false
- | x8 ⇒ false | x9 ⇒ false | xA ⇒ false | xB ⇒ false
- | xC ⇒ false | xD ⇒ false | xE ⇒ false | xF ⇒ true ]
+ [ x0 ⇒ match e2 with [ x0 ⇒ true | _ ⇒ false ]
+ | x1 ⇒ match e2 with [ x1 ⇒ true | _ ⇒ false ]
+ | x2 ⇒ match e2 with [ x2 ⇒ true | _ ⇒ false ]
+ | x3 ⇒ match e2 with [ x3 ⇒ true | _ ⇒ false ]
+ | x4 ⇒ match e2 with [ x4 ⇒ true | _ ⇒ false ]
+ | x5 ⇒ match e2 with [ x5 ⇒ true | _ ⇒ false ]
+ | x6 ⇒ match e2 with [ x6 ⇒ true | _ ⇒ false ]
+ | x7 ⇒ match e2 with [ x7 ⇒ true | _ ⇒ false ]
+ | x8 ⇒ match e2 with [ x8 ⇒ true | _ ⇒ false ]
+ | x9 ⇒ match e2 with [ x9 ⇒ true | _ ⇒ false ]
+ | xA ⇒ match e2 with [ xA ⇒ true | _ ⇒ false ]
+ | xB ⇒ match e2 with [ xB ⇒ true | _ ⇒ false ]
+ | xC ⇒ match e2 with [ xC ⇒ true | _ ⇒ false ]
+ | xD ⇒ match e2 with [ xD ⇒ true | _ ⇒ false ]
+ | xE ⇒ match e2 with [ xE ⇒ true | _ ⇒ false ]
+ | xF ⇒ match e2 with [ xF ⇒ true | _ ⇒ false ]
].
(* operatore < *)
| xC ⇒ x6 | xD ⇒ xE | xE ⇒ x7 | xF ⇒ xF ].
(* operatore rotazione destra n-volte *)
-nlet rec ror_ex_n (e:exadecim) (n:nat) on n ≝
- match n with
- [ O ⇒ e
- | S n' ⇒ ror_ex_n (ror_ex e) n' ].
+nlet rec ror_ex_n (e:exadecim) (n:quatern) (r:rec_quatern n) on r ≝
+ match r with
+ [ qu_O ⇒ e
+ | qu_S t n' ⇒ ror_ex_n (ror_ex e) t n' ].
(* operatore rotazione sinistra con carry *)
ndefinition rcl_ex ≝
| xC ⇒ x9 | xD ⇒ xB | xE ⇒ xD | xF ⇒ xF ].
(* operatore rotazione sinistra n-volte *)
-nlet rec rol_ex_n (e:exadecim) (n:nat) on n ≝
- match n with
- [ O ⇒ e
- | S n' ⇒ rol_ex_n (rol_ex e) n' ].
+nlet rec rol_ex_n (e:exadecim) (n:quatern) (r:rec_quatern n) on r ≝
+ match r with
+ [ qu_O ⇒ e
+ | qu_S t n' ⇒ rol_ex_n (rol_ex e) t n' ].
(* operatore not/complemento a 1 *)
ndefinition not_ex ≝
| x8 ⇒ true | x9 ⇒ true | xA ⇒ true | xB ⇒ true
| xC ⇒ true | xD ⇒ true | xE ⇒ true | xF ⇒ true ].
-(* esadecimali → naturali *)
-ndefinition nat_of_exadecim : exadecim → nat ≝
-λe:exadecim.
- match e with
- [ x0 ⇒ 0 | x1 ⇒ 1 | x2 ⇒ 2 | x3 ⇒ 3 | x4 ⇒ 4 | x5 ⇒ 5 | x6 ⇒ 6 | x7 ⇒ 7
- | x8 ⇒ 8 | x9 ⇒ 9 | xA ⇒ 10 | xB ⇒ 11 | xC ⇒ 12 | xD ⇒ 13 | xE ⇒ 14 | xF ⇒ 15 ].
-
(* operatore predecessore *)
ndefinition pred_ex ≝
λe:exadecim.
| xC ⇒ x4 | xD ⇒ x3 | xE ⇒ x2 | xF ⇒ x1 ].
(* iteratore sugli esadecimali *)
-ndefinition forall_exadecim ≝ λP.
+ndefinition forall_ex ≝ λP.
P x0 ⊗ P x1 ⊗ P x2 ⊗ P x3 ⊗ P x4 ⊗ P x5 ⊗ P x6 ⊗ P x7 ⊗
P x8 ⊗ P x9 ⊗ P xA ⊗ P xB ⊗ P xC ⊗ P xD ⊗ P xE ⊗ P xF.
+
+(* esadecimali ricorsivi *)
+ninductive rec_exadecim : exadecim → Type ≝
+ ex_O : rec_exadecim x0
+| ex_S : ∀n.rec_exadecim n → rec_exadecim (succ_ex n).
+
+(* esadecimali → esadecimali ricorsivi *)
+ndefinition ex_to_recex ≝
+λn.match n return λx.rec_exadecim x with
+ [ x0 ⇒ ex_O
+ | x1 ⇒ ex_S ? ex_O
+ | x2 ⇒ ex_S ? (ex_S ? ex_O)
+ | x3 ⇒ ex_S ? (ex_S ? (ex_S ? ex_O))
+ | x4 ⇒ ex_S ? (ex_S ? (ex_S ? (ex_S ? ex_O)))
+ | x5 ⇒ ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? ex_O))))
+ | x6 ⇒ ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? ex_O)))))
+ | x7 ⇒ ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? ex_O))))))
+ | x8 ⇒ ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? ex_O)))))))
+ | x9 ⇒ ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? ex_O))))))))
+ | xA ⇒ ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? ex_O)))))))))
+ | xB ⇒ ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? ex_O))))))))))
+ | xC ⇒ ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? ex_O)))))))))))
+ | xD ⇒ ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? ex_O))))))))))))
+ | xE ⇒ ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? ex_O)))))))))))))
+ | xF ⇒ ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? (ex_S ? ex_O))))))))))))))
+ ].
+
+(* quaternari → esadecimali *)
+ndefinition ex_of_qu ≝
+λn.match n with
+ [ q0 ⇒ x0 | q1 ⇒ x1 | q2 ⇒ x2 | q3 ⇒ x3 ].
+
+(* ottali → esadecimali *)
+ndefinition ex_of_oct ≝
+λn.match n with
+ [ o0 ⇒ x0 | o1 ⇒ x1 | o2 ⇒ x2 | o3 ⇒ x3 | o4 ⇒ x4 | o5 ⇒ x5 | o6 ⇒ x6 | o7 ⇒ x7 ].
ndefinition exadecim_destruct1 : Πe2.ΠP:Prop.ΠH:x0 = e2.match e2 with [ x0 ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##1: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match x0 with [ x0 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct2 : Πe2.ΠP:Prop.ΠH:x1 = e2.match e2 with [ x1 ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##2: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match x1 with [ x1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct3 : Πe2.ΠP:Prop.ΠH:x2 = e2.match e2 with [ x2 ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##3: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match x2 with [ x2 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct4 : Πe2.ΠP:Prop.ΠH:x3 = e2.match e2 with [ x3 ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##4: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match x3 with [ x3 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct5 : Πe2.ΠP:Prop.ΠH:x4 = e2.match e2 with [ x4 ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##5: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match x4 with [ x4 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct6 : Πe2.ΠP:Prop.ΠH:x5 = e2.match e2 with [ x5 ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##6: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match x5 with [ x5 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct7 : Πe2.ΠP:Prop.ΠH:x6 = e2.match e2 with [ x6 ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##7: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match x6 with [ x6 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct8 : Πe2.ΠP:Prop.ΠH:x7 = e2.match e2 with [ x7 ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##8: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match x7 with [ x7 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct9 : Πe2.ΠP:Prop.ΠH:x8 = e2.match e2 with [ x8 ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##9: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match x8 with [ x8 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct10 : Πe2.ΠP:Prop.ΠH:x9 = e2.match e2 with [ x9 ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##10: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match x9 with [ x9 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct11 : Πe2.ΠP:Prop.ΠH:xA = e2.match e2 with [ xA ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##11: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match xA with [ xA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct12 : Πe2.ΠP:Prop.ΠH:xB = e2.match e2 with [ xB ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##12: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match xB with [ xB ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct13 : Πe2.ΠP:Prop.ΠH:xC = e2.match e2 with [ xC ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##13: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match xC with [ xC ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct14 : Πe2.ΠP:Prop.ΠH:xD = e2.match e2 with [ xD ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##14: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match xD with [ xD ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct15 : Πe2.ΠP:Prop.ΠH:xE = e2.match e2 with [ xE ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##15: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match xE with [ xE ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition exadecim_destruct16 : Πe2.ΠP:Prop.ΠH:xF = e2.match e2 with [ xF ⇒ P → P | _ ⇒ P ].
#e2; #P; ncases e2; nnormalize; #H;
##[ ##16: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match xF with [ xF ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
(* *)
(* ********************************************************************** *)
-include "freescale/aux_bases.ma".
+include "freescale/oct.ma".
include "freescale/byte8.ma".
(* **************************** *)
(* ********************************************************************** *)
include "freescale/load_write.ma".
-include "freescale/nat_lemmas.ma".
(* ************************************************ *)
(* LOGICHE AUSILIARE CHE ACCOMUNANO PIU' OPERAZIONI *)
+++ /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: Cosimo Oliboni, oliboni@cs.unibo.it *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
-(* *)
-(* ********************************************************************** *)
-
-include "freescale/pts.ma".
-include "freescale/bool.ma".
-
-(* ******** *)
-(* NATURALI *)
-(* ******** *)
-
-inductive nat : Type ≝
- O : nat
-| S : nat → nat.
-
-interpretation "Natural numbers" 'N = nat.
-
-default "natural numbers" cic:/matita/freescale/nat/nat.ind.
-
-alias num (instance 0) = "natural number".
-
-nlet rec eq_nat (n1,n2:nat) on n1 ≝
- match n1 with
- [ O ⇒ match n2 with [ O ⇒ true | S _ ⇒ false ]
- | S n1' ⇒ match n2 with [ O ⇒ false | S n2' ⇒ eq_nat n1' n2' ]
- ].
-
-nlet rec le_nat n m ≝
- match n with
- [ O ⇒ true
- | (S p) ⇒ match m with
- [ O ⇒ false | (S q) ⇒ le_nat p q ]
- ].
-
-nlet rec plus (n1,n2:nat) on n1 ≝
- match n1 with
- [ O ⇒ n2
- | (S n1') ⇒ S (plus n1' n2) ].
-
-interpretation "natural plus" 'plus x y = (plus x y).
-
-nlet rec times (n1,n2:nat) on n1 ≝
- match n1 with
- [ O ⇒ O
- | (S n1') ⇒ n2 + (times n1' n2) ].
-
-interpretation "natural times" 'times x y = (times x y).
-
-nlet rec minus n m ≝
- match n with
- [ O ⇒ O
- | (S p) ⇒
- match m with
- [O ⇒ (S p)
- | (S q) ⇒ minus p q ]].
-
-interpretation "natural minus" 'minus x y = (minus x y).
-
-nlet rec div_aux p m n : nat ≝
-match (le_nat m n) with
-[ true ⇒ O
-| false ⇒
- match p with
- [ O ⇒ O
- | (S q) ⇒ S (div_aux q (m-(S n)) n)]].
-
-ndefinition div : nat → nat → nat ≝
-λn,m.match m with
- [ O ⇒ S n
- | (S p) ⇒ div_aux n n p].
-
-interpretation "natural divide" 'divide x y = (div 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: Cosimo Oliboni, oliboni@cs.unibo.it *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
-(* *)
-(* ********************************************************************** *)
-
-include "freescale/bool_lemmas.ma".
-include "freescale/nat.ma".
-
-(* ******** *)
-(* NATURALI *)
-(* ******** *)
-
-nlemma nat_destruct_S_S : ∀n1,n2:nat.S n1 = S n2 → n1 = n2.
- #n1; #n2; #H;
- nchange with (match S n2 with [ O ⇒ False | S a ⇒ n1 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma nat_destruct_0_S : ∀n:nat.O = S n → False.
- #n; #H;
- nchange with (match S n with [ O ⇒ True | S a ⇒ False ]);
- nrewrite < H;
- nnormalize;
- napply I.
-nqed.
-
-nlemma nat_destruct_S_0 : ∀n:nat.S n = O → False.
- #n; #H;
- nchange with (match S n with [ O ⇒ True | S a ⇒ False ]);
- nrewrite > H;
- nnormalize;
- napply I.
-nqed.
-
-nlemma symmetric_eqnat : symmetricT nat bool eq_nat.
- nnormalize;
- #n1;
- nelim n1;
- ##[ ##1: #n2;
- nelim n2;
- nnormalize;
- ##[ ##1: napply refl_eq
- ##| ##2: #n3; #H; napply refl_eq
- ##]
- ##| ##2: #n2; #H; #n3;
- nnormalize;
- ncases n3;
- nnormalize;
- ##[ ##1: napply refl_eq
- ##| ##2: #n4; napply (H n4)
- ##]
- ##]
-nqed.
-
-nlemma eq_to_eqnat : ∀n1,n2:nat.n1 = n2 → eq_nat n1 n2 = true.
- #n1;
- nelim n1;
- ##[ ##1: #n2;
- nelim n2;
- nnormalize;
- ##[ ##1: #H; napply refl_eq
- ##| ##2: #n3; #H; #H1; nelim (nat_destruct_0_S ? H1)
- ##]
- ##| ##2: #n2; #H; #n3; #H1;
- ncases n3 in H1:(%) ⊢ %;
- nnormalize;
- ##[ ##1: #H1; nelim (nat_destruct_S_0 ? H1)
- ##| ##2: #n4; #H1;
- napply (H n4 (nat_destruct_S_S … H1))
- ##]
- ##]
-nqed.
-
-nlemma eqnat_to_eq : ∀n1,n2:nat.(eq_nat n1 n2 = true → n1 = n2).
- #n1;
- nelim n1;
- ##[ ##1: #n2;
- nelim n2;
- nnormalize;
- ##[ ##1: #H; napply refl_eq
- ##| ##2: #n3; #H; #H1; napply (bool_destruct … (O = S n3) H1)
- ##]
- ##| ##2: #n2; #H; #n3; #H1;
- ncases n3 in H1:(%) ⊢ %;
- nnormalize;
- ##[ ##1: #H1; napply (bool_destruct … (S n2 = O) H1)
- ##| ##2: #n4; #H1;
- nrewrite > (H n4 H1);
- napply refl_eq
- ##]
- ##]
-nqed.
-
-nlemma Sn_p_n_to_S_npn : ∀n1,n2.(S n1) + n2 = S (n1 + n2).
- #n1;
- nelim n1;
- ##[ ##1: nnormalize; #n2; napply refl_eq
- ##| ##2: #n; #H; #n2; nrewrite > (H n2);
- ncases n in H:(%) ⊢ %;
- ##[ ##1: nnormalize; #H; napply refl_eq
- ##| ##2: #n3; nnormalize; #H; napply refl_eq
- ##]
- ##]
-nqed.
-
-nlemma n_p_Sn_to_S_npn : ∀n1,n2.n1 + (S n2) = S (n1 + n2).
- #n1;
- nelim n1;
- ##[ ##1: nnormalize; #n2; napply refl_eq
- ##| ##2: #n; #H; #n2;
- nrewrite > (Sn_p_n_to_S_npn n (S n2));
- nrewrite > (H n2);
- napply refl_eq
- ##]
-nqed.
-
-nlemma Opn_to_n : ∀n.O + n = n.
- #n; nnormalize; napply refl_eq.
-nqed.
-
-nlemma npO_to_n : ∀n.n + O = n.
- #n;
- nelim n;
- ##[ ##1: nnormalize; napply refl_eq
- ##| ##2: #n1; #H;
- nrewrite > (Sn_p_n_to_S_npn n1 O);
- nrewrite > H;
- napply refl_eq
- ##]
-nqed.
-
-nlemma symmetric_plusnat : symmetricT nat nat plus.
- #n1;
- nelim n1;
- ##[ ##1: #n2; nrewrite > (npO_to_n n2); nnormalize; napply refl_eq
- ##| ##2: #n2; #H; #n3;
- nrewrite > (Sn_p_n_to_S_npn n2 n3);
- nrewrite > (n_p_Sn_to_S_npn n3 n2);
- nrewrite > (H n3);
- 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: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* *)
+(* ********************************************************************** *)
+
+include "freescale/bool.ma".
+
+(* ****** *)
+(* OTTALI *)
+(* ****** *)
+
+ninductive oct : Type ≝
+ o0: oct
+| o1: oct
+| o2: oct
+| o3: oct
+| o4: oct
+| o5: oct
+| o6: oct
+| o7: oct.
+
+(* operatore = *)
+ndefinition eq_oct ≝
+λn1,n2:oct.
+ match n1 with
+ [ o0 ⇒ match n2 with [ o0 ⇒ true | _ ⇒ false ]
+ | o1 ⇒ match n2 with [ o1 ⇒ true | _ ⇒ false ]
+ | o2 ⇒ match n2 with [ o2 ⇒ true | _ ⇒ false ]
+ | o3 ⇒ match n2 with [ o3 ⇒ true | _ ⇒ false ]
+ | o4 ⇒ match n2 with [ o4 ⇒ true | _ ⇒ false ]
+ | o5 ⇒ match n2 with [ o5 ⇒ true | _ ⇒ false ]
+ | o6 ⇒ match n2 with [ o6 ⇒ true | _ ⇒ false ]
+ | o7 ⇒ match n2 with [ o7 ⇒ true | _ ⇒ false ]
+ ].
+
+(* iteratore sugli ottali *)
+ndefinition forall_oct ≝ λP.
+ P o0 ⊗ P o1 ⊗ P o2 ⊗ P o3 ⊗ P o4 ⊗ P o5 ⊗ P o6 ⊗ P o7.
+
+(* operatore successore *)
+ndefinition succ_oct ≝
+λn.match n with
+ [ o0 ⇒ o1 | o1 ⇒ o2 | o2 ⇒ o3 | o3 ⇒ o4 | o4 ⇒ o5 | o5 ⇒ o6 | o6 ⇒ o7 | o7 ⇒ o0 ].
+
+(* ottali ricorsivi *)
+ninductive rec_oct : oct → Type ≝
+ oc_O : rec_oct o0
+| oc_S : ∀n.rec_oct n → rec_oct (succ_oct n).
+
+(* ottali → ottali ricorsivi *)
+ndefinition oct_to_recoct ≝
+λn.match n return λx.rec_oct x with
+ [ o0 ⇒ oc_O
+ | o1 ⇒ oc_S ? oc_O
+ | o2 ⇒ oc_S ? (oc_S ? oc_O)
+ | o3 ⇒ oc_S ? (oc_S ? (oc_S ? oc_O))
+ | o4 ⇒ oc_S ? (oc_S ? (oc_S ? (oc_S ? oc_O)))
+ | o5 ⇒ oc_S ? (oc_S ? (oc_S ? (oc_S ? (oc_S ? oc_O))))
+ | o6 ⇒ oc_S ? (oc_S ? (oc_S ? (oc_S ? (oc_S ? (oc_S ? oc_O)))))
+ | o7 ⇒ oc_S ? (oc_S ? (oc_S ? (oc_S ? (oc_S ? (oc_S ? (oc_S ? oc_O))))))
+ ].
--- /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: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* *)
+(* ********************************************************************** *)
+
+include "freescale/bool_lemmas.ma".
+include "freescale/oct.ma".
+
+(* ****** *)
+(* OTTALI *)
+(* ****** *)
+
+ndefinition oct_destruct_aux ≝
+Πn1,n2:oct.ΠP:Prop.n1 = n2 →
+ match n1 with
+ [ o0 ⇒ match n2 with [ o0 ⇒ P → P | _ ⇒ P ]
+ | o1 ⇒ match n2 with [ o1 ⇒ P → P | _ ⇒ P ]
+ | o2 ⇒ match n2 with [ o2 ⇒ P → P | _ ⇒ P ]
+ | o3 ⇒ match n2 with [ o3 ⇒ P → P | _ ⇒ P ]
+ | o4 ⇒ match n2 with [ o4 ⇒ P → P | _ ⇒ P ]
+ | o5 ⇒ match n2 with [ o5 ⇒ P → P | _ ⇒ P ]
+ | o6 ⇒ match n2 with [ o6 ⇒ P → P | _ ⇒ P ]
+ | o7 ⇒ match n2 with [ o7 ⇒ P → P | _ ⇒ P ]
+ ].
+
+ndefinition oct_destruct : oct_destruct_aux.
+ #n1; #n2; #P;
+ nelim n1;
+ ##[ ##1: nelim n2; nnormalize; #H;
+ ##[ ##1: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match o0 with [ o0 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+ ##| ##2: nelim n2; nnormalize; #H;
+ ##[ ##2: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match o1 with [ o1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+ ##| ##3: nelim n2; nnormalize; #H;
+ ##[ ##3: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match o2 with [ o2 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+ ##| ##4: nelim n2; nnormalize; #H;
+ ##[ ##4: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match o3 with [ o3 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+ ##| ##5: nelim n2; nnormalize; #H;
+ ##[ ##5: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match o4 with [ o4 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+ ##| ##6: nelim n2; nnormalize; #H;
+ ##[ ##6: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match o5 with [ o5 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+ ##| ##7: nelim n2; nnormalize; #H;
+ ##[ ##7: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match o6 with [ o6 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+ ##| ##8: nelim n2; nnormalize; #H;
+ ##[ ##8: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match o7 with [ o7 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+ ##]
+nqed.
+
+nlemma symmetric_eqoct : symmetricT oct bool eq_oct.
+ #n1; #n2;
+ nelim n1;
+ nelim n2;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma eqoct_to_eq : ∀n1,n2.eq_oct n1 n2 = true → n1 = n2.
+ #n1; #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,10,19,28,37,46,55,64: #H; napply refl_eq
+ ##| ##*: #H; napply (bool_destruct … H)
+ ##]
+nqed.
+
+nlemma eq_to_eqoct : ∀n1,n2.n1 = n2 → eq_oct n1 n2 = true.
+ #n1; #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,10,19,28,37,46,55,64: #H; napply refl_eq
+ ##| ##*: #H; napply (oct_destruct … H)
+ ##]
+nqed.
(* *)
(* ********************************************************************** *)
-include "freescale/aux_bases.ma".
+include "freescale/oct.ma".
+include "freescale/bitrigesim.ma".
include "freescale/word16.ma".
include "freescale/theory.ma".
| MODE_SRT : bitrigesim → instr_mode
.
-ndefinition eq_instrmode ≝
+ndefinition eq_im ≝
λi1,i2:instr_mode.
match i1 with
[ MODE_INH ⇒ match i2 with [ MODE_INH ⇒ true | _ ⇒ false ]
| MODE_DIRn n1 ⇒ match i2 with [ MODE_DIRn n2 ⇒ eq_oct n1 n2 | _ ⇒ false ]
| MODE_DIRn_and_IMM1 n1 ⇒ match i2 with [ MODE_DIRn_and_IMM1 n2 ⇒ eq_oct n1 n2 | _ ⇒ false ]
| MODE_TNY e1 ⇒ match i2 with [ MODE_TNY e2 ⇒ eq_ex e1 e2 | _ ⇒ false ]
- | MODE_SRT t1 ⇒ match i2 with [ MODE_SRT t2 ⇒ eq_bitrig t1 t2 | _ ⇒ false ]
+ | MODE_SRT t1 ⇒ match i2 with [ MODE_SRT t2 ⇒ eq_bit t1 t2 | _ ⇒ false ]
].
(* enumerazione delle istruzioni di tutte le ALU *)
nelim m1;
##[ ##1: nelim m2; nnormalize; #H;
##[ ##1: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match HC05 with [ HC05 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
##| ##2: nelim m2; nnormalize; #H;
##[ ##2: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match HC08 with [ HC08 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
##| ##3: nelim m2; nnormalize; #H;
##[ ##3: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match HCS08 with [ HCS08 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
##| ##4: nelim m2; nnormalize; #H;
##[ ##4: napply (λx:P.x)
- ##| ##*: napply (False_ind (λ_.?) ?);
+ ##| ##*: napply False_ind;
nchange with (match RS08 with [ RS08 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
(* *)
(* ********************************************************************** *)
-include "freescale/aux_bases_lemmas.ma".
+include "freescale/oct_lemmas.ma".
+include "freescale/bitrigesim_lemmas.ma".
include "freescale/exadecim_lemmas.ma".
include "freescale/opcode_base.ma".
nnormalize;
##[ ##1: #H; napply (λx:P.x)
##| ##2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INH with [ MODE_INH ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INH with [ MODE_INH ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##2: #H; napply (λx:P.x)
##| ##1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHA with [ MODE_INHA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHA with [ MODE_INHA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##3: #H; napply (λx:P.x)
##| ##1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHX with [ MODE_INHX ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHX with [ MODE_INHX ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##4: #H; napply (λx:P.x)
##| ##1,2,3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHH with [ MODE_INHH ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHH with [ MODE_INHH ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##5: #H; napply (λx:P.x)
##| ##1,2,3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHX0ADD with [ MODE_INHX0ADD ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHX0ADD with [ MODE_INHX0ADD ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##6: #H; napply (λx:P.x)
##| ##1,2,3,4,5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHX1ADD with [ MODE_INHX1ADD ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHX1ADD with [ MODE_INHX1ADD ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##7: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHX2ADD with [ MODE_INHX2ADD ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHX2ADD with [ MODE_INHX2ADD ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##8: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IMM1 with [ MODE_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IMM1 with [ MODE_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##9: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IMM1EXT with [ MODE_IMM1EXT ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IMM1EXT with [ MODE_IMM1EXT ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##10: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IMM2 with [ MODE_IMM2 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IMM2 with [ MODE_IMM2 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##11: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_DIR1 with [ MODE_DIR1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_DIR1 with [ MODE_DIR1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##12: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_DIR2 with [ MODE_DIR2 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_DIR2 with [ MODE_DIR2 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##13: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX0 with [ MODE_IX0 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX0 with [ MODE_IX0 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##14: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX1 with [ MODE_IX1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX1 with [ MODE_IX1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##15: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX2 with [ MODE_IX2 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX2 with [ MODE_IX2 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##16: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_SP1 with [ MODE_SP1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_SP1 with [ MODE_SP1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##17: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_SP2 with [ MODE_SP2 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_SP2 with [ MODE_SP2 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##18: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_DIR1_to_DIR1 with [ MODE_DIR1_to_DIR1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_DIR1_to_DIR1 with [ MODE_DIR1_to_DIR1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##19: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IMM1_to_DIR1 with [ MODE_IMM1_to_DIR1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IMM1_to_DIR1 with [ MODE_IMM1_to_DIR1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##20: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX0p_to_DIR1 with [ MODE_IX0p_to_DIR1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX0p_to_DIR1 with [ MODE_IX0p_to_DIR1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##21: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_DIR1_to_IX0p with [ MODE_DIR1_to_IX0p ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_DIR1_to_IX0p with [ MODE_DIR1_to_IX0p ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##22: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHA_and_IMM1 with [ MODE_INHA_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHA_and_IMM1 with [ MODE_INHA_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##23: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHX_and_IMM1 with [ MODE_INHX_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_INHX_and_IMM1 with [ MODE_INHX_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##24: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IMM1_and_IMM1 with [ MODE_IMM1_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IMM1_and_IMM1 with [ MODE_IMM1_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##25: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_DIR1_and_IMM1 with [ MODE_DIR1_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_DIR1_and_IMM1 with [ MODE_DIR1_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##26: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX0_and_IMM1 with [ MODE_IX0_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX0_and_IMM1 with [ MODE_IX0_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##27: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX0p_and_IMM1 with [ MODE_IX0p_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX0p_and_IMM1 with [ MODE_IX0p_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##28: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX1_and_IMM1 with [ MODE_IX1_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX1_and_IMM1 with [ MODE_IX1_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##29: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX1p_and_IMM1 with [ MODE_IX1p_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_IX1p_and_IMM1 with [ MODE_IX1p_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nnormalize;
##[ ##30: #H; napply (λx:P.x)
##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_SP1_and_IMM1 with [ MODE_SP1_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_SP1_and_IMM1 with [ MODE_SP1_and_IMM1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ncases i2;
nnormalize;
##[ ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_DIRn n1 with [ MODE_DIRn a ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##32,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_DIRn n1 with [ MODE_DIRn n1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31: #n2;
ncases i2;
nnormalize;
##[ ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_DIRn_and_IMM1 n1 with [ MODE_DIRn_and_IMM1 a ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,33,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_DIRn_and_IMM1 n1 with [ MODE_DIRn_and_IMM1 n1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##32: #n2;
ncases i2;
nnormalize;
##[ ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_TNY n1 with [ MODE_TNY a ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,34: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_TNY n1 with [ MODE_TNY n1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##33: #n2;
ncases i2;
nnormalize;
##[ ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_SRT n1 with [ MODE_SRT a ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##31,32,33: #n; #H;
- napply (False_ind (λ_.?) ?);
+ napply False_ind;
nchange with (match MODE_SRT n1 with [ MODE_SRT n1 ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##34: #n2;
(* MATTONI BASE PER DEFINIRE LE TABELLE DELLE MCU *)
(* ********************************************** *)
-nlemma symmetric_eqinstrmode : symmetricT instr_mode bool eq_instrmode.
+nlemma symmetric_eqim : symmetricT instr_mode bool eq_im.
#i1; #i2;
ncases i1;
##[ ##1: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply refl_eq
nnormalize; napply refl_eq
##| ##34: ncases i2; #n1;
##[ ##34: #n2;
- nchange with (eq_bitrig n2 n1 = eq_bitrig n1 n2);
- nrewrite > (symmetric_eqbitrig n1 n2);
+ nchange with (eq_bit n2 n1 = eq_bit n1 n2);
+ nrewrite > (symmetric_eqbit n1 n2);
##| ##31,32,33: #n2; nnormalize
##]
nnormalize; napply refl_eq
##]
nqed.
-nlemma eqinstrmode_to_eq1 : ∀i2.eq_instrmode MODE_INH i2 = true → MODE_INH = i2.
+nlemma eqim_to_eq1 : ∀i2.eq_im MODE_INH i2 = true → MODE_INH = i2.
#i2; ncases i2; nnormalize;
##[ ##1: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq2 : ∀i2.eq_instrmode MODE_INHA i2 = true → MODE_INHA = i2.
+nlemma eqim_to_eq2 : ∀i2.eq_im MODE_INHA i2 = true → MODE_INHA = i2.
#i2; ncases i2; nnormalize;
##[ ##2: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq3 : ∀i2.eq_instrmode MODE_INHX i2 = true → MODE_INHX = i2.
+nlemma eqim_to_eq3 : ∀i2.eq_im MODE_INHX i2 = true → MODE_INHX = i2.
#i2; ncases i2; nnormalize;
##[ ##3: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq4 : ∀i2.eq_instrmode MODE_INHH i2 = true → MODE_INHH = i2.
+nlemma eqim_to_eq4 : ∀i2.eq_im MODE_INHH i2 = true → MODE_INHH = i2.
#i2; ncases i2; nnormalize;
##[ ##4: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq5 : ∀i2.eq_instrmode MODE_INHX0ADD i2 = true → MODE_INHX0ADD = i2.
+nlemma eqim_to_eq5 : ∀i2.eq_im MODE_INHX0ADD i2 = true → MODE_INHX0ADD = i2.
#i2; ncases i2; nnormalize;
##[ ##5: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq6 : ∀i2.eq_instrmode MODE_INHX1ADD i2 = true → MODE_INHX1ADD = i2.
+nlemma eqim_to_eq6 : ∀i2.eq_im MODE_INHX1ADD i2 = true → MODE_INHX1ADD = i2.
#i2; ncases i2; nnormalize;
##[ ##6: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq7 : ∀i2.eq_instrmode MODE_INHX2ADD i2 = true → MODE_INHX2ADD = i2.
+nlemma eqim_to_eq7 : ∀i2.eq_im MODE_INHX2ADD i2 = true → MODE_INHX2ADD = i2.
#i2; ncases i2; nnormalize;
##[ ##7: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq8 : ∀i2.eq_instrmode MODE_IMM1 i2 = true → MODE_IMM1 = i2.
+nlemma eqim_to_eq8 : ∀i2.eq_im MODE_IMM1 i2 = true → MODE_IMM1 = i2.
#i2; ncases i2; nnormalize;
##[ ##8: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq9 : ∀i2.eq_instrmode MODE_IMM1EXT i2 = true → MODE_IMM1EXT = i2.
+nlemma eqim_to_eq9 : ∀i2.eq_im MODE_IMM1EXT i2 = true → MODE_IMM1EXT = i2.
#i2; ncases i2; nnormalize;
##[ ##9: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq10 : ∀i2.eq_instrmode MODE_IMM2 i2 = true → MODE_IMM2 = i2.
+nlemma eqim_to_eq10 : ∀i2.eq_im MODE_IMM2 i2 = true → MODE_IMM2 = i2.
#i2; ncases i2; nnormalize;
##[ ##10: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq11 : ∀i2.eq_instrmode MODE_DIR1 i2 = true → MODE_DIR1 = i2.
+nlemma eqim_to_eq11 : ∀i2.eq_im MODE_DIR1 i2 = true → MODE_DIR1 = i2.
#i2; ncases i2; nnormalize;
##[ ##11: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq12 : ∀i2.eq_instrmode MODE_DIR2 i2 = true → MODE_DIR2 = i2.
+nlemma eqim_to_eq12 : ∀i2.eq_im MODE_DIR2 i2 = true → MODE_DIR2 = i2.
#i2; ncases i2; nnormalize;
##[ ##12: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq13 : ∀i2.eq_instrmode MODE_IX0 i2 = true → MODE_IX0 = i2.
+nlemma eqim_to_eq13 : ∀i2.eq_im MODE_IX0 i2 = true → MODE_IX0 = i2.
#i2; ncases i2; nnormalize;
##[ ##13: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq14 : ∀i2.eq_instrmode MODE_IX1 i2 = true → MODE_IX1 = i2.
+nlemma eqim_to_eq14 : ∀i2.eq_im MODE_IX1 i2 = true → MODE_IX1 = i2.
#i2; ncases i2; nnormalize;
##[ ##14: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq15 : ∀i2.eq_instrmode MODE_IX2 i2 = true → MODE_IX2 = i2.
+nlemma eqim_to_eq15 : ∀i2.eq_im MODE_IX2 i2 = true → MODE_IX2 = i2.
#i2; ncases i2; nnormalize;
##[ ##15: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq16 : ∀i2.eq_instrmode MODE_SP1 i2 = true → MODE_SP1 = i2.
+nlemma eqim_to_eq16 : ∀i2.eq_im MODE_SP1 i2 = true → MODE_SP1 = i2.
#i2; ncases i2; nnormalize;
##[ ##16: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq17 : ∀i2.eq_instrmode MODE_SP2 i2 = true → MODE_SP2 = i2.
+nlemma eqim_to_eq17 : ∀i2.eq_im MODE_SP2 i2 = true → MODE_SP2 = i2.
#i2; ncases i2; nnormalize;
##[ ##17: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq18 : ∀i2.eq_instrmode MODE_DIR1_to_DIR1 i2 = true → MODE_DIR1_to_DIR1 = i2.
+nlemma eqim_to_eq18 : ∀i2.eq_im MODE_DIR1_to_DIR1 i2 = true → MODE_DIR1_to_DIR1 = i2.
#i2; ncases i2; nnormalize;
##[ ##18: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq19 : ∀i2.eq_instrmode MODE_IMM1_to_DIR1 i2 = true → MODE_IMM1_to_DIR1 = i2.
+nlemma eqim_to_eq19 : ∀i2.eq_im MODE_IMM1_to_DIR1 i2 = true → MODE_IMM1_to_DIR1 = i2.
#i2; ncases i2; nnormalize;
##[ ##19: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq20 : ∀i2.eq_instrmode MODE_IX0p_to_DIR1 i2 = true → MODE_IX0p_to_DIR1 = i2.
+nlemma eqim_to_eq20 : ∀i2.eq_im MODE_IX0p_to_DIR1 i2 = true → MODE_IX0p_to_DIR1 = i2.
#i2; ncases i2; nnormalize;
##[ ##20: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq21 : ∀i2.eq_instrmode MODE_DIR1_to_IX0p i2 = true → MODE_DIR1_to_IX0p = i2.
+nlemma eqim_to_eq21 : ∀i2.eq_im MODE_DIR1_to_IX0p i2 = true → MODE_DIR1_to_IX0p = i2.
#i2; ncases i2; nnormalize;
##[ ##21: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq22 : ∀i2.eq_instrmode MODE_INHA_and_IMM1 i2 = true → MODE_INHA_and_IMM1 = i2.
+nlemma eqim_to_eq22 : ∀i2.eq_im MODE_INHA_and_IMM1 i2 = true → MODE_INHA_and_IMM1 = i2.
#i2; ncases i2; nnormalize;
##[ ##22: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq23 : ∀i2.eq_instrmode MODE_INHX_and_IMM1 i2 = true → MODE_INHX_and_IMM1 = i2.
+nlemma eqim_to_eq23 : ∀i2.eq_im MODE_INHX_and_IMM1 i2 = true → MODE_INHX_and_IMM1 = i2.
#i2; ncases i2; nnormalize;
##[ ##23: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq24 : ∀i2.eq_instrmode MODE_IMM1_and_IMM1 i2 = true → MODE_IMM1_and_IMM1 = i2.
+nlemma eqim_to_eq24 : ∀i2.eq_im MODE_IMM1_and_IMM1 i2 = true → MODE_IMM1_and_IMM1 = i2.
#i2; ncases i2; nnormalize;
##[ ##24: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq25 : ∀i2.eq_instrmode MODE_DIR1_and_IMM1 i2 = true → MODE_DIR1_and_IMM1 = i2.
+nlemma eqim_to_eq25 : ∀i2.eq_im MODE_DIR1_and_IMM1 i2 = true → MODE_DIR1_and_IMM1 = i2.
#i2; ncases i2; nnormalize;
##[ ##25: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq26 : ∀i2.eq_instrmode MODE_IX0_and_IMM1 i2 = true → MODE_IX0_and_IMM1 = i2.
+nlemma eqim_to_eq26 : ∀i2.eq_im MODE_IX0_and_IMM1 i2 = true → MODE_IX0_and_IMM1 = i2.
#i2; ncases i2; nnormalize;
##[ ##26: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq27 : ∀i2.eq_instrmode MODE_IX0p_and_IMM1 i2 = true → MODE_IX0p_and_IMM1 = i2.
+nlemma eqim_to_eq27 : ∀i2.eq_im MODE_IX0p_and_IMM1 i2 = true → MODE_IX0p_and_IMM1 = i2.
#i2; ncases i2; nnormalize;
##[ ##27: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq28 : ∀i2.eq_instrmode MODE_IX1_and_IMM1 i2 = true → MODE_IX1_and_IMM1 = i2.
+nlemma eqim_to_eq28 : ∀i2.eq_im MODE_IX1_and_IMM1 i2 = true → MODE_IX1_and_IMM1 = i2.
#i2; ncases i2; nnormalize;
##[ ##28: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq29 : ∀i2.eq_instrmode MODE_IX1p_and_IMM1 i2 = true → MODE_IX1p_and_IMM1 = i2.
+nlemma eqim_to_eq29 : ∀i2.eq_im MODE_IX1p_and_IMM1 i2 = true → MODE_IX1p_and_IMM1 = i2.
#i2; ncases i2; nnormalize;
##[ ##29: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq30 : ∀i2.eq_instrmode MODE_SP1_and_IMM1 i2 = true → MODE_SP1_and_IMM1 = i2.
+nlemma eqim_to_eq30 : ∀i2.eq_im MODE_SP1_and_IMM1 i2 = true → MODE_SP1_and_IMM1 = i2.
#i2; ncases i2; nnormalize;
##[ ##30: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq31 : ∀n1,i2.eq_instrmode (MODE_DIRn n1) i2 = true → MODE_DIRn n1 = i2.
+nlemma eqim_to_eq31 : ∀n1,i2.eq_im (MODE_DIRn n1) i2 = true → MODE_DIRn n1 = i2.
#n1; #i2; ncases i2;
##[ ##31: #n2; #H;
nchange in H:(%) with (eq_oct n1 n2 = true);
##]
nqed.
-nlemma eqinstrmode_to_eq32 : ∀n1,i2.eq_instrmode (MODE_DIRn_and_IMM1 n1) i2 = true → MODE_DIRn_and_IMM1 n1 = i2.
+nlemma eqim_to_eq32 : ∀n1,i2.eq_im (MODE_DIRn_and_IMM1 n1) i2 = true → MODE_DIRn_and_IMM1 n1 = i2.
#n1; #i2; ncases i2;
##[ ##32: #n2; #H;
nchange in H:(%) with (eq_oct n1 n2 = true);
##]
nqed.
-nlemma eqinstrmode_to_eq33 : ∀n1,i2.eq_instrmode (MODE_TNY n1) i2 = true → MODE_TNY n1 = i2.
+nlemma eqim_to_eq33 : ∀n1,i2.eq_im (MODE_TNY n1) i2 = true → MODE_TNY n1 = i2.
#n1; #i2; ncases i2;
##[ ##33: #n2; #H;
nchange in H:(%) with (eq_ex n1 n2 = true);
##]
nqed.
-nlemma eqinstrmode_to_eq34 : ∀n1,i2.eq_instrmode (MODE_SRT n1) i2 = true → MODE_SRT n1 = i2.
+nlemma eqim_to_eq34 : ∀n1,i2.eq_im (MODE_SRT n1) i2 = true → MODE_SRT n1 = i2.
#n1; #i2; ncases i2;
##[ ##34: #n2; #H;
- nchange in H:(%) with (eq_bitrig n1 n2 = true);
- nrewrite > (eqbitrig_to_eq … H);
+ nchange in H:(%) with (eq_bit n1 n2 = true);
+ nrewrite > (eqbit_to_eq … H);
napply refl_eq
##| ##31,32,33: nnormalize; #n2; #H; napply (bool_destruct … H)
##| ##*: nnormalize; #H; napply (bool_destruct … H)
##]
nqed.
-nlemma eqinstrmode_to_eq : ∀i1,i2.eq_instrmode i1 i2 = true → i1 = i2.
+nlemma eqim_to_eq : ∀i1,i2.eq_im i1 i2 = true → i1 = i2.
#i1; ncases i1;
- ##[ ##1: napply eqinstrmode_to_eq1 ##| ##2: napply eqinstrmode_to_eq2
- ##| ##3: napply eqinstrmode_to_eq3 ##| ##4: napply eqinstrmode_to_eq4
- ##| ##5: napply eqinstrmode_to_eq5 ##| ##6: napply eqinstrmode_to_eq6
- ##| ##7: napply eqinstrmode_to_eq7 ##| ##8: napply eqinstrmode_to_eq8
- ##| ##9: napply eqinstrmode_to_eq9 ##| ##10: napply eqinstrmode_to_eq10
- ##| ##11: napply eqinstrmode_to_eq11 ##| ##12: napply eqinstrmode_to_eq12
- ##| ##13: napply eqinstrmode_to_eq13 ##| ##14: napply eqinstrmode_to_eq14
- ##| ##15: napply eqinstrmode_to_eq15 ##| ##16: napply eqinstrmode_to_eq16
- ##| ##17: napply eqinstrmode_to_eq17 ##| ##18: napply eqinstrmode_to_eq18
- ##| ##19: napply eqinstrmode_to_eq19 ##| ##20: napply eqinstrmode_to_eq20
- ##| ##21: napply eqinstrmode_to_eq21 ##| ##22: napply eqinstrmode_to_eq22
- ##| ##23: napply eqinstrmode_to_eq23 ##| ##24: napply eqinstrmode_to_eq24
- ##| ##25: napply eqinstrmode_to_eq25 ##| ##26: napply eqinstrmode_to_eq26
- ##| ##27: napply eqinstrmode_to_eq27 ##| ##28: napply eqinstrmode_to_eq28
- ##| ##29: napply eqinstrmode_to_eq29 ##| ##30: napply eqinstrmode_to_eq30
- ##| ##31: napply eqinstrmode_to_eq31 ##| ##32: napply eqinstrmode_to_eq32
- ##| ##33: napply eqinstrmode_to_eq33 ##| ##34: napply eqinstrmode_to_eq34
- ##]
-nqed.
-
-nlemma eq_to_eqinstrmode1 : ∀i2.MODE_INH = i2 → eq_instrmode MODE_INH i2 = true.
+ ##[ ##1: napply eqim_to_eq1 ##| ##2: napply eqim_to_eq2
+ ##| ##3: napply eqim_to_eq3 ##| ##4: napply eqim_to_eq4
+ ##| ##5: napply eqim_to_eq5 ##| ##6: napply eqim_to_eq6
+ ##| ##7: napply eqim_to_eq7 ##| ##8: napply eqim_to_eq8
+ ##| ##9: napply eqim_to_eq9 ##| ##10: napply eqim_to_eq10
+ ##| ##11: napply eqim_to_eq11 ##| ##12: napply eqim_to_eq12
+ ##| ##13: napply eqim_to_eq13 ##| ##14: napply eqim_to_eq14
+ ##| ##15: napply eqim_to_eq15 ##| ##16: napply eqim_to_eq16
+ ##| ##17: napply eqim_to_eq17 ##| ##18: napply eqim_to_eq18
+ ##| ##19: napply eqim_to_eq19 ##| ##20: napply eqim_to_eq20
+ ##| ##21: napply eqim_to_eq21 ##| ##22: napply eqim_to_eq22
+ ##| ##23: napply eqim_to_eq23 ##| ##24: napply eqim_to_eq24
+ ##| ##25: napply eqim_to_eq25 ##| ##26: napply eqim_to_eq26
+ ##| ##27: napply eqim_to_eq27 ##| ##28: napply eqim_to_eq28
+ ##| ##29: napply eqim_to_eq29 ##| ##30: napply eqim_to_eq30
+ ##| ##31: napply eqim_to_eq31 ##| ##32: napply eqim_to_eq32
+ ##| ##33: napply eqim_to_eq33 ##| ##34: napply eqim_to_eq34
+ ##]
+nqed.
+
+nlemma eq_to_eqim1 : ∀i2.MODE_INH = i2 → eq_im MODE_INH i2 = true.
#t2; ncases t2; nnormalize;
##[ ##1: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode2 : ∀i2.MODE_INHA = i2 → eq_instrmode MODE_INHA i2 = true.
+nlemma eq_to_eqim2 : ∀i2.MODE_INHA = i2 → eq_im MODE_INHA i2 = true.
#t2; ncases t2; nnormalize;
##[ ##2: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode3 : ∀i2.MODE_INHX = i2 → eq_instrmode MODE_INHX i2 = true.
+nlemma eq_to_eqim3 : ∀i2.MODE_INHX = i2 → eq_im MODE_INHX i2 = true.
#t2; ncases t2; nnormalize;
##[ ##3: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode4 : ∀i2.MODE_INHH = i2 → eq_instrmode MODE_INHH i2 = true.
+nlemma eq_to_eqim4 : ∀i2.MODE_INHH = i2 → eq_im MODE_INHH i2 = true.
#t2; ncases t2; nnormalize;
##[ ##4: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode5 : ∀i2.MODE_INHX0ADD = i2 → eq_instrmode MODE_INHX0ADD i2 = true.
+nlemma eq_to_eqim5 : ∀i2.MODE_INHX0ADD = i2 → eq_im MODE_INHX0ADD i2 = true.
#t2; ncases t2; nnormalize;
##[ ##5: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode6 : ∀i2.MODE_INHX1ADD = i2 → eq_instrmode MODE_INHX1ADD i2 = true.
+nlemma eq_to_eqim6 : ∀i2.MODE_INHX1ADD = i2 → eq_im MODE_INHX1ADD i2 = true.
#t2; ncases t2; nnormalize;
##[ ##6: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode7 : ∀i2.MODE_INHX2ADD = i2 → eq_instrmode MODE_INHX2ADD i2 = true.
+nlemma eq_to_eqim7 : ∀i2.MODE_INHX2ADD = i2 → eq_im MODE_INHX2ADD i2 = true.
#t2; ncases t2; nnormalize;
##[ ##7: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode8 : ∀i2.MODE_IMM1 = i2 → eq_instrmode MODE_IMM1 i2 = true.
+nlemma eq_to_eqim8 : ∀i2.MODE_IMM1 = i2 → eq_im MODE_IMM1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##8: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode9 : ∀i2.MODE_IMM1EXT = i2 → eq_instrmode MODE_IMM1EXT i2 = true.
+nlemma eq_to_eqim9 : ∀i2.MODE_IMM1EXT = i2 → eq_im MODE_IMM1EXT i2 = true.
#t2; ncases t2; nnormalize;
##[ ##9: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode10 : ∀i2.MODE_IMM2 = i2 → eq_instrmode MODE_IMM2 i2 = true.
+nlemma eq_to_eqim10 : ∀i2.MODE_IMM2 = i2 → eq_im MODE_IMM2 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##10: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode11 : ∀i2.MODE_DIR1 = i2 → eq_instrmode MODE_DIR1 i2 = true.
+nlemma eq_to_eqim11 : ∀i2.MODE_DIR1 = i2 → eq_im MODE_DIR1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##11: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode12 : ∀i2.MODE_DIR2 = i2 → eq_instrmode MODE_DIR2 i2 = true.
+nlemma eq_to_eqim12 : ∀i2.MODE_DIR2 = i2 → eq_im MODE_DIR2 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##12: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode13 : ∀i2.MODE_IX0 = i2 → eq_instrmode MODE_IX0 i2 = true.
+nlemma eq_to_eqim13 : ∀i2.MODE_IX0 = i2 → eq_im MODE_IX0 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##13: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode14 : ∀i2.MODE_IX1 = i2 → eq_instrmode MODE_IX1 i2 = true.
+nlemma eq_to_eqim14 : ∀i2.MODE_IX1 = i2 → eq_im MODE_IX1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##14: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode15 : ∀i2.MODE_IX2 = i2 → eq_instrmode MODE_IX2 i2 = true.
+nlemma eq_to_eqim15 : ∀i2.MODE_IX2 = i2 → eq_im MODE_IX2 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##15: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode16 : ∀i2.MODE_SP1 = i2 → eq_instrmode MODE_SP1 i2 = true.
+nlemma eq_to_eqim16 : ∀i2.MODE_SP1 = i2 → eq_im MODE_SP1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##16: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode17 : ∀i2.MODE_SP2 = i2 → eq_instrmode MODE_SP2 i2 = true.
+nlemma eq_to_eqim17 : ∀i2.MODE_SP2 = i2 → eq_im MODE_SP2 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##17: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode18 : ∀i2.MODE_DIR1_to_DIR1 = i2 → eq_instrmode MODE_DIR1_to_DIR1 i2 = true.
+nlemma eq_to_eqim18 : ∀i2.MODE_DIR1_to_DIR1 = i2 → eq_im MODE_DIR1_to_DIR1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##18: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode19 : ∀i2.MODE_IMM1_to_DIR1 = i2 → eq_instrmode MODE_IMM1_to_DIR1 i2 = true.
+nlemma eq_to_eqim19 : ∀i2.MODE_IMM1_to_DIR1 = i2 → eq_im MODE_IMM1_to_DIR1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##19: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode20 : ∀i2.MODE_IX0p_to_DIR1 = i2 → eq_instrmode MODE_IX0p_to_DIR1 i2 = true.
+nlemma eq_to_eqim20 : ∀i2.MODE_IX0p_to_DIR1 = i2 → eq_im MODE_IX0p_to_DIR1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##20: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode21 : ∀i2.MODE_DIR1_to_IX0p = i2 → eq_instrmode MODE_DIR1_to_IX0p i2 = true.
+nlemma eq_to_eqim21 : ∀i2.MODE_DIR1_to_IX0p = i2 → eq_im MODE_DIR1_to_IX0p i2 = true.
#t2; ncases t2; nnormalize;
##[ ##21: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode22 : ∀i2.MODE_INHA_and_IMM1 = i2 → eq_instrmode MODE_INHA_and_IMM1 i2 = true.
+nlemma eq_to_eqim22 : ∀i2.MODE_INHA_and_IMM1 = i2 → eq_im MODE_INHA_and_IMM1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##22: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode23 : ∀i2.MODE_INHX_and_IMM1 = i2 → eq_instrmode MODE_INHX_and_IMM1 i2 = true.
+nlemma eq_to_eqim23 : ∀i2.MODE_INHX_and_IMM1 = i2 → eq_im MODE_INHX_and_IMM1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##23: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode24 : ∀i2.MODE_IMM1_and_IMM1 = i2 → eq_instrmode MODE_IMM1_and_IMM1 i2 = true.
+nlemma eq_to_eqim24 : ∀i2.MODE_IMM1_and_IMM1 = i2 → eq_im MODE_IMM1_and_IMM1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##24: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode25 : ∀i2.MODE_DIR1_and_IMM1 = i2 → eq_instrmode MODE_DIR1_and_IMM1 i2 = true.
+nlemma eq_to_eqim25 : ∀i2.MODE_DIR1_and_IMM1 = i2 → eq_im MODE_DIR1_and_IMM1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##25: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode26 : ∀i2.MODE_IX0_and_IMM1 = i2 → eq_instrmode MODE_IX0_and_IMM1 i2 = true.
+nlemma eq_to_eqim26 : ∀i2.MODE_IX0_and_IMM1 = i2 → eq_im MODE_IX0_and_IMM1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##26: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode27 : ∀i2.MODE_IX0p_and_IMM1 = i2 → eq_instrmode MODE_IX0p_and_IMM1 i2 = true.
+nlemma eq_to_eqim27 : ∀i2.MODE_IX0p_and_IMM1 = i2 → eq_im MODE_IX0p_and_IMM1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##27: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode28 : ∀i2.MODE_IX1_and_IMM1 = i2 → eq_instrmode MODE_IX1_and_IMM1 i2 = true.
+nlemma eq_to_eqim28 : ∀i2.MODE_IX1_and_IMM1 = i2 → eq_im MODE_IX1_and_IMM1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##28: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode29 : ∀i2.MODE_IX1p_and_IMM1 = i2 → eq_instrmode MODE_IX1p_and_IMM1 i2 = true.
+nlemma eq_to_eqim29 : ∀i2.MODE_IX1p_and_IMM1 = i2 → eq_im MODE_IX1p_and_IMM1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##29: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode30 : ∀i2.MODE_SP1_and_IMM1 = i2 → eq_instrmode MODE_SP1_and_IMM1 i2 = true.
+nlemma eq_to_eqim30 : ∀i2.MODE_SP1_and_IMM1 = i2 → eq_im MODE_SP1_and_IMM1 i2 = true.
#t2; ncases t2; nnormalize;
##[ ##30: #H; napply refl_eq
##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode31 : ∀n1,i2.MODE_DIRn n1 = i2 → eq_instrmode (MODE_DIRn n1) i2 = true.
+nlemma eq_to_eqim31 : ∀n1,i2.MODE_DIRn n1 = i2 → eq_im (MODE_DIRn n1) i2 = true.
#n1; #t2; ncases t2;
##[ ##31: #n2; #H;
nchange with (eq_oct n1 n2 = true);
##]
nqed.
-nlemma eq_to_eqinstrmode32 : ∀n1,i2.MODE_DIRn_and_IMM1 n1 = i2 → eq_instrmode (MODE_DIRn_and_IMM1 n1) i2 = true.
+nlemma eq_to_eqim32 : ∀n1,i2.MODE_DIRn_and_IMM1 n1 = i2 → eq_im (MODE_DIRn_and_IMM1 n1) i2 = true.
#n1; #t2; ncases t2;
##[ ##32: #n2; #H;
nchange with (eq_oct n1 n2 = true);
##]
nqed.
-nlemma eq_to_eqinstrmode33 : ∀n1,i2.MODE_TNY n1 = i2 → eq_instrmode (MODE_TNY n1) i2 = true.
+nlemma eq_to_eqim33 : ∀n1,i2.MODE_TNY n1 = i2 → eq_im (MODE_TNY n1) i2 = true.
#n1; #t2; ncases t2;
##[ ##33: #n2; #H;
nchange with (eq_ex n1 n2 = true);
##]
nqed.
-nlemma eq_to_eqinstrmode34 : ∀n1,i2.MODE_SRT n1 = i2 → eq_instrmode (MODE_SRT n1) i2 = true.
+nlemma eq_to_eqim34 : ∀n1,i2.MODE_SRT n1 = i2 → eq_im (MODE_SRT n1) i2 = true.
#n1; #t2; ncases t2;
##[ ##34: #n2; #H;
- nchange with (eq_bitrig n1 n2 = true);
+ nchange with (eq_bit n1 n2 = true);
nrewrite > (instr_mode_destruct_MODE_SRT … H);
- nrewrite > (eq_to_eqbitrig n2 n2 (refl_eq …));
+ nrewrite > (eq_to_eqbit n2 n2 (refl_eq …));
napply refl_eq
##| ##31,32,33: #n; #H; nnormalize; napply (instr_mode_destruct … H)
##| ##*: #H; nnormalize; napply (instr_mode_destruct … H)
##]
nqed.
-nlemma eq_to_eqinstrmode : ∀i1,i2.i1 = i2 → eq_instrmode i1 i2 = true.
+nlemma eq_to_eqim : ∀i1,i2.i1 = i2 → eq_im i1 i2 = true.
#i1; ncases i1;
- ##[ ##1: napply eq_to_eqinstrmode1 ##| ##2: napply eq_to_eqinstrmode2
- ##| ##3: napply eq_to_eqinstrmode3 ##| ##4: napply eq_to_eqinstrmode4
- ##| ##5: napply eq_to_eqinstrmode5 ##| ##6: napply eq_to_eqinstrmode6
- ##| ##7: napply eq_to_eqinstrmode7 ##| ##8: napply eq_to_eqinstrmode8
- ##| ##9: napply eq_to_eqinstrmode9 ##| ##10: napply eq_to_eqinstrmode10
- ##| ##11: napply eq_to_eqinstrmode11 ##| ##12: napply eq_to_eqinstrmode12
- ##| ##13: napply eq_to_eqinstrmode13 ##| ##14: napply eq_to_eqinstrmode14
- ##| ##15: napply eq_to_eqinstrmode15 ##| ##16: napply eq_to_eqinstrmode16
- ##| ##17: napply eq_to_eqinstrmode17 ##| ##18: napply eq_to_eqinstrmode18
- ##| ##19: napply eq_to_eqinstrmode19 ##| ##20: napply eq_to_eqinstrmode20
- ##| ##21: napply eq_to_eqinstrmode21 ##| ##22: napply eq_to_eqinstrmode22
- ##| ##23: napply eq_to_eqinstrmode23 ##| ##24: napply eq_to_eqinstrmode24
- ##| ##25: napply eq_to_eqinstrmode25 ##| ##26: napply eq_to_eqinstrmode26
- ##| ##27: napply eq_to_eqinstrmode27 ##| ##28: napply eq_to_eqinstrmode28
- ##| ##29: napply eq_to_eqinstrmode29 ##| ##30: napply eq_to_eqinstrmode30
- ##| ##31: napply eq_to_eqinstrmode31 ##| ##32: napply eq_to_eqinstrmode32
- ##| ##33: napply eq_to_eqinstrmode33 ##| ##34: napply eq_to_eqinstrmode34
+ ##[ ##1: napply eq_to_eqim1 ##| ##2: napply eq_to_eqim2
+ ##| ##3: napply eq_to_eqim3 ##| ##4: napply eq_to_eqim4
+ ##| ##5: napply eq_to_eqim5 ##| ##6: napply eq_to_eqim6
+ ##| ##7: napply eq_to_eqim7 ##| ##8: napply eq_to_eqim8
+ ##| ##9: napply eq_to_eqim9 ##| ##10: napply eq_to_eqim10
+ ##| ##11: napply eq_to_eqim11 ##| ##12: napply eq_to_eqim12
+ ##| ##13: napply eq_to_eqim13 ##| ##14: napply eq_to_eqim14
+ ##| ##15: napply eq_to_eqim15 ##| ##16: napply eq_to_eqim16
+ ##| ##17: napply eq_to_eqim17 ##| ##18: napply eq_to_eqim18
+ ##| ##19: napply eq_to_eqim19 ##| ##20: napply eq_to_eqim20
+ ##| ##21: napply eq_to_eqim21 ##| ##22: napply eq_to_eqim22
+ ##| ##23: napply eq_to_eqim23 ##| ##24: napply eq_to_eqim24
+ ##| ##25: napply eq_to_eqim25 ##| ##26: napply eq_to_eqim26
+ ##| ##27: napply eq_to_eqim27 ##| ##28: napply eq_to_eqim28
+ ##| ##29: napply eq_to_eqim29 ##| ##30: napply eq_to_eqim30
+ ##| ##31: napply eq_to_eqim31 ##| ##32: napply eq_to_eqim32
+ ##| ##33: napply eq_to_eqim33 ##| ##34: napply eq_to_eqim34
##]
nqed.
ndefinition opcode_destruct1 : Πop2.ΠP:Prop.ADC = op2 → match op2 with [ ADC ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##1: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match ADC with [ ADC ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct2 : Πop2.ΠP:Prop.ADD = op2 → match op2 with [ ADD ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##2: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match ADD with [ ADD ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct3 : Πop2.ΠP:Prop.AIS = op2 → match op2 with [ AIS ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##3: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match AIS with [ AIS ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct4 : Πop2.ΠP:Prop.AIX = op2 → match op2 with [ AIX ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##4: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match AIX with [ AIX ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct5 : Πop2.ΠP:Prop.AND = op2 → match op2 with [ AND ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##5: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match AND with [ AND ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct6 : Πop2.ΠP:Prop.ASL = op2 → match op2 with [ ASL ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##6: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match ASL with [ ASL ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct7 : Πop2.ΠP:Prop.ASR = op2 → match op2 with [ ASR ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##7: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match ASR with [ ASR ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct8 : Πop2.ΠP:Prop.BCC = op2 → match op2 with [ BCC ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##8: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BCC with [ BCC ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct9 : Πop2.ΠP:Prop.BCLRn = op2 → match op2 with [ BCLRn ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##9: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BCLRn with [ BCLRn ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct10 : Πop2.ΠP:Prop.BCS = op2 → match op2 with [ BCS ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##10: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BCS with [ BCS ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct11 : Πop2.ΠP:Prop.BEQ = op2 → match op2 with [ BEQ ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##11: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BEQ with [ BEQ ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct12 : Πop2.ΠP:Prop.BGE = op2 → match op2 with [ BGE ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##12: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BGE with [ BGE ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct13 : Πop2.ΠP:Prop.BGND = op2 → match op2 with [ BGND ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##13: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BGND with [ BGND ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct14 : Πop2.ΠP:Prop.BGT = op2 → match op2 with [ BGT ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##14: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BGT with [ BGT ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct15 : Πop2.ΠP:Prop.BHCC = op2 → match op2 with [ BHCC ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##15: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BHCC with [ BHCC ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct16 : Πop2.ΠP:Prop.BHCS = op2 → match op2 with [ BHCS ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##16: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BHCS with [ BHCS ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct17 : Πop2.ΠP:Prop.BHI = op2 → match op2 with [ BHI ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##17: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BHI with [ BHI ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct18 : Πop2.ΠP:Prop.BIH = op2 → match op2 with [ BIH ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##18: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BIH with [ BIH ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct19 : Πop2.ΠP:Prop.BIL = op2 → match op2 with [ BIL ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##19: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BIL with [ BIL ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct20 : Πop2.ΠP:Prop.BIT = op2 → match op2 with [ BIT ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##20: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BIT with [ BIT ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct21 : Πop2.ΠP:Prop.BLE = op2 → match op2 with [ BLE ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##21: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BLE with [ BLE ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct22 : Πop2.ΠP:Prop.BLS = op2 → match op2 with [ BLS ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##22: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BLS with [ BLS ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct23 : Πop2.ΠP:Prop.BLT = op2 → match op2 with [ BLT ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##23: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BLT with [ BLT ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct24 : Πop2.ΠP:Prop.BMC = op2 → match op2 with [ BMC ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##24: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BMC with [ BMC ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct25 : Πop2.ΠP:Prop.BMI = op2 → match op2 with [ BMI ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##25: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BMI with [ BMI ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct26 : Πop2.ΠP:Prop.BMS = op2 → match op2 with [ BMS ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##26: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BMS with [ BMS ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct27 : Πop2.ΠP:Prop.BNE = op2 → match op2 with [ BNE ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##27: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BNE with [ BNE ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct28 : Πop2.ΠP:Prop.BPL = op2 → match op2 with [ BPL ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##28: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BPL with [ BPL ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct29 : Πop2.ΠP:Prop.BRA = op2 → match op2 with [ BRA ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##29: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BRA with [ BRA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct30 : Πop2.ΠP:Prop.BRCLRn = op2 → match op2 with [ BRCLRn ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##30: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BRCLRn with [ BRCLRn ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct31 : Πop2.ΠP:Prop.BRN = op2 → match op2 with [ BRN ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##31: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BRN with [ BRN ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct32 : Πop2.ΠP:Prop.BRSETn = op2 → match op2 with [ BRSETn ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##32: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BRSETn with [ BRSETn ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct33 : Πop2.ΠP:Prop.BSETn = op2 → match op2 with [ BSETn ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##33: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BSETn with [ BSETn ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct34 : Πop2.ΠP:Prop.BSR = op2 → match op2 with [ BSR ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##34: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match BSR with [ BSR ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct35 : Πop2.ΠP:Prop.CBEQA = op2 → match op2 with [ CBEQA ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##35: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match CBEQA with [ CBEQA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct36 : Πop2.ΠP:Prop.CBEQX = op2 → match op2 with [ CBEQX ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##36: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match CBEQX with [ CBEQX ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct37 : Πop2.ΠP:Prop.CLC = op2 → match op2 with [ CLC ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##37: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match CLC with [ CLC ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct38 : Πop2.ΠP:Prop.CLI = op2 → match op2 with [ CLI ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##38: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match CLI with [ CLI ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct39 : Πop2.ΠP:Prop.CLR = op2 → match op2 with [ CLR ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##39: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match CLR with [ CLR ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct40 : Πop2.ΠP:Prop.CMP = op2 → match op2 with [ CMP ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##40: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match CMP with [ CMP ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct41 : Πop2.ΠP:Prop.COM = op2 → match op2 with [ COM ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##41: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match COM with [ COM ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct42 : Πop2.ΠP:Prop.CPHX = op2 → match op2 with [ CPHX ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##42: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match CPHX with [ CPHX ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct43 : Πop2.ΠP:Prop.CPX = op2 → match op2 with [ CPX ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##43: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match CPX with [ CPX ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct44 : Πop2.ΠP:Prop.DAA = op2 → match op2 with [ DAA ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##44: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match DAA with [ DAA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct45 : Πop2.ΠP:Prop.DBNZ = op2 → match op2 with [ DBNZ ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##45: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match DBNZ with [ DBNZ ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct46 : Πop2.ΠP:Prop.DEC = op2 → match op2 with [ DEC ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##46: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match DEC with [ DEC ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct47 : Πop2.ΠP:Prop.DIV = op2 → match op2 with [ DIV ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##47: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match DIV with [ DIV ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct48 : Πop2.ΠP:Prop.EOR = op2 → match op2 with [ EOR ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##48: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match EOR with [ EOR ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct49 : Πop2.ΠP:Prop.INC = op2 → match op2 with [ INC ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##49: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match INC with [ INC ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct50 : Πop2.ΠP:Prop.JMP = op2 → match op2 with [ JMP ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##50: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match JMP with [ JMP ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct51 : Πop2.ΠP:Prop.JSR = op2 → match op2 with [ JSR ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##51: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match JSR with [ JSR ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct52 : Πop2.ΠP:Prop.LDA = op2 → match op2 with [ LDA ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##52: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match LDA with [ LDA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct53 : Πop2.ΠP:Prop.LDHX = op2 → match op2 with [ LDHX ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##53: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match LDHX with [ LDHX ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct54 : Πop2.ΠP:Prop.LDX = op2 → match op2 with [ LDX ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##54: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match LDX with [ LDX ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct55 : Πop2.ΠP:Prop.LSR = op2 → match op2 with [ LSR ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##55: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match LSR with [ LSR ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct56 : Πop2.ΠP:Prop.MOV = op2 → match op2 with [ MOV ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##56: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match MOV with [ MOV ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct57 : Πop2.ΠP:Prop.MUL = op2 → match op2 with [ MUL ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##57: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match MUL with [ MUL ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct58 : Πop2.ΠP:Prop.NEG = op2 → match op2 with [ NEG ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##58: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match NEG with [ NEG ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct59 : Πop2.ΠP:Prop.NOP = op2 → match op2 with [ NOP ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##59: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match NOP with [ NOP ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct60 : Πop2.ΠP:Prop.NSA = op2 → match op2 with [ NSA ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##60: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match NSA with [ NSA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct61 : Πop2.ΠP:Prop.ORA = op2 → match op2 with [ ORA ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##61: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match ORA with [ ORA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct62 : Πop2.ΠP:Prop.PSHA = op2 → match op2 with [ PSHA ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##62: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match PSHA with [ PSHA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct63 : Πop2.ΠP:Prop.PSHH = op2 → match op2 with [ PSHH ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##63: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match PSHH with [ PSHH ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct64 : Πop2.ΠP:Prop.PSHX = op2 → match op2 with [ PSHX ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##64: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match PSHX with [ PSHX ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct65 : Πop2.ΠP:Prop.PULA = op2 → match op2 with [ PULA ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##65: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match PULA with [ PULA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct66 : Πop2.ΠP:Prop.PULH = op2 → match op2 with [ PULH ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##66: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match PULH with [ PULH ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct67 : Πop2.ΠP:Prop.PULX = op2 → match op2 with [ PULX ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##67: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match PULX with [ PULX ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct68 : Πop2.ΠP:Prop.ROL = op2 → match op2 with [ ROL ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##68: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match ROL with [ ROL ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct69 : Πop2.ΠP:Prop.ROR = op2 → match op2 with [ ROR ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##69: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match ROR with [ ROR ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct70 : Πop2.ΠP:Prop.RSP = op2 → match op2 with [ RSP ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##70: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match RSP with [ RSP ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct71 : Πop2.ΠP:Prop.RTI = op2 → match op2 with [ RTI ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##71: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match RTI with [ RTI ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct72 : Πop2.ΠP:Prop.RTS = op2 → match op2 with [ RTS ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##72: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match RTS with [ RTS ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct73 : Πop2.ΠP:Prop.SBC = op2 → match op2 with [ SBC ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##73: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match SBC with [ SBC ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct74 : Πop2.ΠP:Prop.SEC = op2 → match op2 with [ SEC ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##74: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match SEC with [ SEC ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct75 : Πop2.ΠP:Prop.SEI = op2 → match op2 with [ SEI ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##75: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match SEI with [ SEI ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct76 : Πop2.ΠP:Prop.SHA = op2 → match op2 with [ SHA ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##76: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match SHA with [ SHA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct77 : Πop2.ΠP:Prop.SLA = op2 → match op2 with [ SLA ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##77: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match SLA with [ SLA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct78 : Πop2.ΠP:Prop.STA = op2 → match op2 with [ STA ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##78: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match STA with [ STA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct79 : Πop2.ΠP:Prop.STHX = op2 → match op2 with [ STHX ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##79: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match STHX with [ STHX ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct80 : Πop2.ΠP:Prop.STOP = op2 → match op2 with [ STOP ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##80: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match STOP with [ STOP ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct81 : Πop2.ΠP:Prop.STX = op2 → match op2 with [ STX ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##81: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match STX with [ STX ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct82 : Πop2.ΠP:Prop.SUB = op2 → match op2 with [ SUB ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##82: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match SUB with [ SUB ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct83 : Πop2.ΠP:Prop.SWI = op2 → match op2 with [ SWI ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##83: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match SWI with [ SWI ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct84 : Πop2.ΠP:Prop.TAP = op2 → match op2 with [ TAP ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##84: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match TAP with [ TAP ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct85 : Πop2.ΠP:Prop.TAX = op2 → match op2 with [ TAX ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##85: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match TAX with [ TAX ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct86 : Πop2.ΠP:Prop.TPA = op2 → match op2 with [ TPA ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##86: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match TPA with [ TPA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct87 : Πop2.ΠP:Prop.TST = op2 → match op2 with [ TST ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##87: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match TST with [ TST ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct88 : Πop2.ΠP:Prop.TSX = op2 → match op2 with [ TSX ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##88: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match TSX with [ TSX ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct89 : Πop2.ΠP:Prop.TXA = op2 → match op2 with [ TXA ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##89: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match TXA with [ TXA ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct90 : Πop2.ΠP:Prop.TXS = op2 → match op2 with [ TXS ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##90: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match TXS with [ TXS ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
ndefinition opcode_destruct91 : Πop2.ΠP:Prop.WAIT = op2 → match op2 with [ WAIT ⇒ P → P | _ ⇒ P ].
#op2; #P; ncases op2; nnormalize;
##[ ##91: #H; napply (λx:P.x)
- ##| ##*: #H; napply (False_ind (λ_.?) ?);
+ ##| ##*: #H; napply False_ind;
nchange with (match WAIT with [ WAIT ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
--- /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: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* *)
+(* ********************************************************************** *)
+
+include "freescale/bool.ma".
+
+(* ********** *)
+(* QUATERNARI *)
+(* ********** *)
+
+ninductive quatern : Type ≝
+ q0 : quatern
+| q1 : quatern
+| q2 : quatern
+| q3 : quatern.
+
+(* operatore = *)
+ndefinition eq_qu ≝
+λn1,n2:quatern.
+ match n1 with
+ [ q0 ⇒ match n2 with [ q0 ⇒ true | _ ⇒ false ]
+ | q1 ⇒ match n2 with [ q1 ⇒ true | _ ⇒ false ]
+ | q2 ⇒ match n2 with [ q2 ⇒ true | _ ⇒ false ]
+ | q3 ⇒ match n2 with [ q3 ⇒ true | _ ⇒ false ]
+ ].
+
+(* iteratore sui quaternari *)
+ndefinition forall_qu ≝ λP.
+ P q0 ⊗ P q1 ⊗ P q2 ⊗ P q3.
+
+(* operatore successorre *)
+ndefinition succ_qu ≝
+λn.match n with
+ [ q0 ⇒ q1 | q1 ⇒ q2 | q2 ⇒ q3 | q3 ⇒ q0 ].
+
+(* quaternari ricorsivi *)
+ninductive rec_quatern : quatern → Type ≝
+ qu_O : rec_quatern q0
+| qu_S : ∀n.rec_quatern n → rec_quatern (succ_qu n).
+
+(* quaternari → quaternari ricorsivi *)
+ndefinition qu_to_recqu ≝
+λn.match n return λx.rec_quatern x with
+ [ q0 ⇒ qu_O
+ | q1 ⇒ qu_S ? qu_O
+ | q2 ⇒ qu_S ? (qu_S ? qu_O)
+ | q3 ⇒ qu_S ? (qu_S ? (qu_S ? qu_O))
+ ].
--- /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: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* *)
+(* ********************************************************************** *)
+
+include "freescale/bool_lemmas.ma".
+include "freescale/quatern.ma".
+
+(* ********** *)
+(* QUATERNARI *)
+(* ********** *)
+
+ndefinition quatern_destruct_aux ≝
+Πn1,n2:quatern.ΠP:Prop.n1 = n2 →
+ match n1 with
+ [ q0 ⇒ match n2 with [ q0 ⇒ P → P | _ ⇒ P ]
+ | q1 ⇒ match n2 with [ q1 ⇒ P → P | _ ⇒ P ]
+ | q2 ⇒ match n2 with [ q2 ⇒ P → P | _ ⇒ P ]
+ | q3 ⇒ match n2 with [ q3 ⇒ P → P | _ ⇒ P ]
+ ].
+
+ndefinition quatern_destruct : quatern_destruct_aux.
+ #n1; #n2; #P;
+ nelim n1;
+ ##[ ##1: nelim n2; nnormalize; #H;
+ ##[ ##1: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match q0 with [ q0 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+ ##| ##2: nelim n2; nnormalize; #H;
+ ##[ ##2: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match q1 with [ q1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+ ##| ##3: nelim n2; nnormalize; #H;
+ ##[ ##3: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match q2 with [ q2 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+ ##| ##4: nelim n2; nnormalize; #H;
+ ##[ ##4: napply (λx:P.x)
+ ##| ##*: napply False_ind;
+ nchange with (match q3 with [ q3 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+ ##]
+nqed.
+
+nlemma symmetric_eqqu : symmetricT quatern bool eq_qu.
+ #n1; #n2;
+ nelim n1;
+ nelim n2;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma eqqu_to_eq : ∀n1,n2.eq_qu n1 n2 = true → n1 = n2.
+ #n1; #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,6,11,16: #H; napply refl_eq
+ ##| ##*: #H; napply (bool_destruct … H)
+ ##]
+nqed.
+
+nlemma eq_to_eqqu : ∀n1,n2.n1 = n2 → eq_qu n1 n2 = true.
+ #n1; #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,6,11,16: #H; napply refl_eq
+ ##| ##*: #H; napply (quatern_destruct … H)
+ ##]
+nqed.
nlemma proj1: ∀A,B:Prop.A ∧ B → A.
#A; #B; #H;
+ (* \ldots al posto di ??? *)
napply (And_ind A B … H);
#H1; #H2;
napply H1.
ex_intro2: ∀x:A.Q x → R x → ex2 A Q R.
ndefinition iff ≝
-λA,B.(A -> B) ∧ (B -> A).
+λA,B.(A → B) ∧ (B → A).
(* higher_order_defs/relations *)
ninductive list (A:Type) : Type ≝
nil: list A
-| cons: A -> list A -> list A.
+| cons: A → list A → list A.
nlet rec append A (l1: list A) l2 on l1 ≝
match l1 with
- [ nil => l2
- | (cons hd tl) => cons A hd (append A tl l2) ].
+ [ nil ⇒ l2
+ | (cons hd tl) ⇒ cons A hd (append A tl l2) ].
notation "hvbox(hd break :: tl)"
right associative with precedence 47
| false ⇒ mk_word16 wh' wl' ]]].
(* operatore rotazione destra n-volte *)
-nlet rec ror_w16_n (w:word16) (n:nat) on n ≝
- match n with
- [ O ⇒ w
- | S n' ⇒ ror_w16_n (ror_w16 w) n' ].
+nlet rec ror_w16_n (w:word16) (n:exadecim) (r:rec_exadecim n) on r ≝
+ match r with
+ [ ex_O ⇒ w
+ | ex_S t n' ⇒ ror_w16_n (ror_w16 w) t n' ].
(* operatore rotazione sinistra con carry *)
ndefinition rcl_w16 ≝
| false ⇒ mk_word16 wh' wl' ]]].
(* operatore rotazione sinistra n-volte *)
-nlet rec rol_w16_n (w:word16) (n:nat) on n ≝
- match n with
- [ O ⇒ w
- | S n' ⇒ rol_w16_n (rol_w16 w) n' ].
+nlet rec rol_w16_n (w:word16) (n:exadecim) (r:rec_exadecim n) on r ≝
+ match r with
+ [ ex_O ⇒ w
+ | ex_S t n' ⇒ rol_w16_n (rol_w16 w) t n' ].
(* operatore not/complemento a 1 *)
ndefinition not_w16 ≝
(* operatore Most Significant Bit *)
ndefinition MSB_w16 ≝ λw:word16.eq_ex x8 (and_ex x8 (b8h (w16h w))).
-(* word → naturali *)
-ndefinition nat_of_word16 ≝ λw:word16. 256 * (nat_of_byte8 (w16h w)) + (nat_of_byte8 (w16l w)).
-
(* operatore predecessore *)
ndefinition pred_w16 ≝
λw:word16.match eq_b8 (w16l w) (mk_byte8 x0 x0) with
]]]]]].
(* divisione senza segno (secondo la logica delle ALU): (quoziente resto) overflow *)
-nlet rec div_b8_aux (divd:word16) (divs:word16) (molt:byte8) (q:byte8) (c:nat) on c ≝
+nlet rec div_b8_aux (divd:word16) (divs:word16) (molt:byte8) (q:byte8) (c:oct) (rc:rec_oct c) on rc ≝
let w' ≝ plus_w16_d_d divd (compl_w16 divs) in
- match c with
- [ O ⇒ match le_w16 divs divd with
+ match rc with
+ [ oc_O ⇒ match le_w16 divs divd with
[ true ⇒ triple … (or_b8 molt q) (w16l w') (⊖ (eq_b8 (w16h w') 〈x0,x0〉))
| false ⇒ triple … q (w16l divd) (⊖ (eq_b8 (w16h divd) 〈x0,x0〉)) ]
- | S c' ⇒ match le_w16 divs divd with
- [ true ⇒ div_b8_aux w' (ror_w16 divs) (ror_b8 molt) (or_b8 molt q) c'
- | false ⇒ div_b8_aux divd (ror_w16 divs) (ror_b8 molt) q c' ]].
+ | oc_S t c' ⇒ match le_w16 divs divd with
+ [ true ⇒ div_b8_aux w' (ror_w16 divs) (ror_b8 molt) (or_b8 molt q) t c'
+ | false ⇒ div_b8_aux divd (ror_w16 divs) (ror_b8 molt) q t c' ]].
ndefinition div_b8 ≝
λw:word16.λb:byte8.match eq_b8 b 〈x0,x0〉 with
(* 3) ad ogni ciclo il divisore e il moltiplicatore vengono scalati di 1 a dx *)
(* 4) il moltiplicatore e' la quantita' aggiunta al quoziente se il divisore *)
(* puo' essere sottratto al dividendo *)
- | false ⇒ div_b8_aux w (rol_w16_n 〈〈x0,x0〉:b〉 7) 〈x8,x0〉 〈x0,x0〉 7 ]].
+ | false ⇒ div_b8_aux w (rol_w16_n 〈〈x0,x0〉:b〉 ? (ex_to_recex x7)) 〈x8,x0〉 〈x0,x0〉 ? (oct_to_recoct o7) ]].
(* operatore x in [inf,sup] *)
-ndefinition in_range ≝
+ndefinition inrange_w16 ≝
λx,inf,sup:word16.(le_w16 inf sup) ⊗ (ge_w16 x inf) ⊗ (le_w16 x sup).
(* iteratore sulle word *)
-ndefinition forall_word16 ≝
+ndefinition forall_w16 ≝
λP.
- forall_byte8 (λbh.
- forall_byte8 (λbl.
+ forall_b8 (λbh.
+ forall_b8 (λbl.
P (mk_word16 bh bl ))).
+
+(* word16 ricorsive *)
+ninductive rec_word16 : word16 → Type ≝
+ w16_O : rec_word16 〈〈x0,x0〉:〈x0,x0〉〉
+| w16_S : ∀n.rec_word16 n → rec_word16 (succ_w16 n).
+
+(* word16 → word16 ricorsive *)
+ndefinition w16_to_recw16_aux1_1 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈x1,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? recw
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1_2 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈x2,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_1 ? recw)
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1_3 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈x3,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_2 ? recw)
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1_4 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈x4,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_3 ? recw)
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1_5 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈x5,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_4 ? recw)
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1_6 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈x6,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_5 ? recw)
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1_7 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈x7,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_6 ? recw)
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1_8 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈x8,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_7 ? recw)
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1_9 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈x9,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_8 ? recw)
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1_10 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈xA,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_9 ? recw)
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1_11 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈xB,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_10 ? recw)
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1_12 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈xC,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_11 ? recw)
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1_13 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈xD,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_12 ? recw)
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1_14 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈xE,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_13 ? recw)
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1_15 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈n:〈xF,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_14 ? recw)
+ ))))))))))))))).
+
+ndefinition w16_to_recw16_aux1 : Πn.rec_word16 〈n:〈x0,x0〉〉 → rec_word16 〈(succ_b8 n):〈x0,x0〉〉 ≝
+λn.λrecw:rec_word16 〈n:〈x0,x0〉〉.
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (
+ w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_S ? (w16_to_recw16_aux1_15 ? recw)
+ ))))))))))))))).
+
+(* ... cifra byte superiore *)
+nlet rec w16_to_recw16_aux2 (n:byte8) (r:rec_byte8 n) on r ≝
+ match r return λx.λy:rec_byte8 x.rec_word16 〈x:〈x0,x0〉〉 with
+ [ b8_O ⇒ w16_O
+ | b8_S t n' ⇒ w16_to_recw16_aux1 ? (w16_to_recw16_aux2 t n')
+ ].
+
+(* ... cifra esadecimale n.2 *)
+ndefinition w16_to_recw16_aux3 ≝
+λb,n.λrecw:rec_word16 〈b:〈x0,x0〉〉.
+ match n return λx.rec_word16 〈b:〈x,x0〉〉 with
+ [ x0 ⇒ recw
+ | x1 ⇒ w16_to_recw16_aux1_1 ? recw
+ | x2 ⇒ w16_to_recw16_aux1_2 ? recw
+ | x3 ⇒ w16_to_recw16_aux1_3 ? recw
+ | x4 ⇒ w16_to_recw16_aux1_4 ? recw
+ | x5 ⇒ w16_to_recw16_aux1_5 ? recw
+ | x6 ⇒ w16_to_recw16_aux1_6 ? recw
+ | x7 ⇒ w16_to_recw16_aux1_7 ? recw
+ | x8 ⇒ w16_to_recw16_aux1_8 ? recw
+ | x9 ⇒ w16_to_recw16_aux1_9 ? recw
+ | xA ⇒ w16_to_recw16_aux1_10 ? recw
+ | xB ⇒ w16_to_recw16_aux1_11 ? recw
+ | xC ⇒ w16_to_recw16_aux1_12 ? recw
+ | xD ⇒ w16_to_recw16_aux1_13 ? recw
+ | xE ⇒ w16_to_recw16_aux1_14 ? recw
+ | xF ⇒ w16_to_recw16_aux1_15 ? recw
+ ].
+
+nlemma w16_to_recw16_aux4_1 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,x1〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? input).
+nqed.
+
+nlemma w16_to_recw16_aux4_2 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,x2〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? (w16_to_recw16_aux4_1 … input)).
+nqed.
+
+nlemma w16_to_recw16_aux4_3 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,x3〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? (w16_to_recw16_aux4_2 … input)).
+nqed.
+
+nlemma w16_to_recw16_aux4_4 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,x4〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? (w16_to_recw16_aux4_3 … input)).
+nqed.
+
+nlemma w16_to_recw16_aux4_5 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,x5〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? (w16_to_recw16_aux4_4 … input)).
+nqed.
+
+nlemma w16_to_recw16_aux4_6 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,x6〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? (w16_to_recw16_aux4_5 … input)).
+nqed.
+
+nlemma w16_to_recw16_aux4_7 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,x7〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? (w16_to_recw16_aux4_6 … input)).
+nqed.
+
+nlemma w16_to_recw16_aux4_8 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,x8〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? (w16_to_recw16_aux4_7 … input)).
+nqed.
+
+nlemma w16_to_recw16_aux4_9 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,x9〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? (w16_to_recw16_aux4_8 … input)).
+nqed.
+
+nlemma w16_to_recw16_aux4_10 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,xA〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? (w16_to_recw16_aux4_9 … input)).
+nqed.
+
+nlemma w16_to_recw16_aux4_11 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,xB〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? (w16_to_recw16_aux4_10 … input)).
+nqed.
+
+nlemma w16_to_recw16_aux4_12 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,xC〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? (w16_to_recw16_aux4_11 … input)).
+nqed.
+
+nlemma w16_to_recw16_aux4_13 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,xD〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? (w16_to_recw16_aux4_12 … input)).
+nqed.
+
+nlemma w16_to_recw16_aux4_14 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,xE〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? (w16_to_recw16_aux4_13 … input)).
+nqed.
+
+nlemma w16_to_recw16_aux4_15 : Πn,e.rec_word16 〈n:〈e,x0〉〉 → rec_word16 〈n:〈e,xF〉〉.
+ #n; #e; nelim e; #input; napply (w16_S ? (w16_to_recw16_aux4_14 … input)).
+nqed.
+
+(* ... cifra esadecimale n.1 *)
+ndefinition w16_to_recw16_aux4 ≝
+λb,e,n.λrecw:rec_word16 〈b:〈e,x0〉〉.
+ match n return λx.rec_word16 〈b:〈e,x〉〉 with
+ [ x0 ⇒ recw
+ | x1 ⇒ w16_to_recw16_aux4_1 … recw
+ | x2 ⇒ w16_to_recw16_aux4_2 … recw
+ | x3 ⇒ w16_to_recw16_aux4_3 … recw
+ | x4 ⇒ w16_to_recw16_aux4_4 … recw
+ | x5 ⇒ w16_to_recw16_aux4_5 … recw
+ | x6 ⇒ w16_to_recw16_aux4_6 … recw
+ | x7 ⇒ w16_to_recw16_aux4_7 … recw
+ | x8 ⇒ w16_to_recw16_aux4_8 … recw
+ | x9 ⇒ w16_to_recw16_aux4_9 … recw
+ | xA ⇒ w16_to_recw16_aux4_10 … recw
+ | xB ⇒ w16_to_recw16_aux4_11 … recw
+ | xC ⇒ w16_to_recw16_aux4_12 … recw
+ | xD ⇒ w16_to_recw16_aux4_13 … recw
+ | xE ⇒ w16_to_recw16_aux4_14 … recw
+ | xF ⇒ w16_to_recw16_aux4_15 … recw
+ ].
+
+nlemma w16_to_recw16_aux5 : ∀b.rec_byte8 (〈b8h b,b8l b〉) → rec_byte8 b.
+ #b; nelim b; #e1; #e2; nnormalize; #input; napply input. nqed.
+
+ndefinition w16_to_recw16 ≝
+λn.w16_to_recw16_aux4 (w16h n) (b8h (w16l n)) (b8l (w16l n))
+ (w16_to_recw16_aux3 (w16h n) (b8h (w16l n)) (w16_to_recw16_aux2 (w16h n) ?)).
+ nelim n; #b1; #b2;
+ nchange with (rec_byte8 b1);
+ napply (w16_to_recw16_aux5 b1);
+ napply (b8_to_recb8 b1).
+nqed.
| false ⇒ mk_word32 wh' wl' ]]].
(* operatore rotazione destra n-volte *)
-nlet rec ror_w32_n (dw:word32) (n:nat) on n ≝
- match n with
- [ O ⇒ dw
- | S n' ⇒ ror_w32_n (ror_w32 dw) n' ].
+nlet rec ror_w32_n (dw:word32) (n:bitrigesim) (r:rec_bitrigesim n) on r ≝
+ match r with
+ [ bi_O ⇒ dw
+ | bi_S t n' ⇒ ror_w32_n (ror_w32 dw) t n' ].
(* operatore rotazione sinistra con carry *)
ndefinition rcl_w32 ≝
| false ⇒ mk_word32 wh' wl' ]]].
(* operatore rotazione sinistra n-volte *)
-nlet rec rol_w32_n (dw:word32) (n:nat) on n ≝
- match n with
- [ O ⇒ dw
- | S n' ⇒ rol_w32_n (rol_w32 dw) n' ].
+nlet rec rol_w32_n (dw:word32) (n:bitrigesim) (r:rec_bitrigesim n) on r ≝
+ match r with
+ [ bi_O ⇒ dw
+ | bi_S t n' ⇒ rol_w32_n (rol_w32 dw) t n' ].
(* operatore not/complemento a 1 *)
ndefinition not_w32 ≝
(* operatore Most Significant Bit *)
ndefinition MSB_w32 ≝ λdw:word32.eq_ex x8 (and_ex x8 (b8h (w16h (w32h dw)))).
-(* word → naturali *)
-ndefinition nat_of_word32 ≝ λdw:word32. (256 * 256 * (nat_of_word16 (w32h dw))) + (nat_of_word16 (w32l dw)).
-
(* operatore predecessore *)
ndefinition pred_w32 ≝
λdw:word32.match eq_w16 (w32l dw) (mk_word16 (mk_byte8 x0 x0) (mk_byte8 x0 x0)) with
]]]]]].
(* divisione senza segno (secondo la logica delle ALU): (quoziente resto) overflow *)
-nlet rec div_w16_aux (divd:word32) (divs:word32) (molt:word16) (q:word16) (c:nat) on c ≝
+nlet rec div_w16_aux (divd:word32) (divs:word32) (molt:word16) (q:word16) (c:exadecim) (rc:rec_exadecim c) on rc ≝
let w' ≝ plus_w32_d_d divd (compl_w32 divs) in
- match c with
- [ O ⇒ match le_w32 divs divd with
+ match rc with
+ [ ex_O ⇒ match le_w32 divs divd with
[ true ⇒ triple … (or_w16 molt q) (w32l w') (⊖ (eq_w16 (w32h w') 〈〈x0,x0〉:〈x0,x0〉〉))
| false ⇒ triple … q (w32l divd) (⊖ (eq_w16 (w32h divd) 〈〈x0,x0〉:〈x0,x0〉〉)) ]
- | S c' ⇒ match le_w32 divs divd with
- [ true ⇒ div_w16_aux w' (ror_w32 divs) (ror_w16 molt) (or_w16 molt q) c'
- | false ⇒ div_w16_aux divd (ror_w32 divs) (ror_w16 molt) q c' ]].
+ | ex_S t c' ⇒ match le_w32 divs divd with
+ [ true ⇒ div_w16_aux w' (ror_w32 divs) (ror_w16 molt) (or_w16 molt q) t c'
+ | false ⇒ div_w16_aux divd (ror_w32 divs) (ror_w16 molt) q t c' ]].
ndefinition div_w16 ≝
λw:word32.λb:word16.match eq_w16 b 〈〈x0,x0〉:〈x0,x0〉〉 with
(* 3) ad ogni ciclo il divisore e il moltiplicatore vengono scalati di 1 a dx *)
(* 4) il moltiplicatore e' la quantita' aggiunta al quoziente se il divisore *)
(* puo' essere sottratto al dividendo *)
- | false ⇒ div_w16_aux w (rol_w32_n 〈〈〈x0,x0〉:〈x0,x0〉〉.b〉 15) 〈〈x8,x0〉:〈x0,x0〉〉 〈〈x0,x0〉:〈x0,x0〉〉 15 ]].
+ | false ⇒ div_w16_aux w (rol_w32_n 〈〈〈x0,x0〉:〈x0,x0〉〉.b〉 ? (bit_to_recbit t0F)) 〈〈x8,x0〉:〈x0,x0〉〉 〈〈x0,x0〉:〈x0,x0〉〉 ? (ex_to_recex xF) ]].
(* operatore x in [inf,sup] *)
-ndefinition in_range ≝
+ndefinition inrange_w32 ≝
λx,inf,sup:word32.(le_w32 inf sup) ⊗ (ge_w32 x inf) ⊗ (le_w32 x sup).
(* iteratore sulle word *)
-ndefinition forall_word32 ≝
+ndefinition forall_w32 ≝
λP.
- forall_word16 (λbh.
- forall_word16 (λbl.
+ forall_w16 (λbh.
+ forall_w16 (λbl.
P (mk_word32 bh bl ))).
include "utility/ascii.ma".
include "freescale/theory.ma".
-include "freescale/nat.ma".
include "utility/utility.ma".
(* ************************ *)
include "utility/string.ma".
include "utility/ascii_lemmas2.ma".
-include "freescale/nat_lemmas.ma".
include "utility/utility_lemmas.ma".
(* ************************ *)
(* ********************************************************************** *)
include "freescale/theory.ma".
-include "freescale/nat_lemmas.ma".
include "freescale/option.ma".
(* ************** *)
projects / helm.git / commitdiff