-freescale/option.ma freescale/bool.ma
-freescale/exadecim.ma freescale/bool.ma freescale/nat.ma freescale/prod.ma
-freescale/memory_struct.ma freescale/aux_bases.ma freescale/byte8.ma
-freescale/prod.ma freescale/bool.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
-freescale/prod_lemmas.ma freescale/bool_lemmas.ma freescale/prod.ma
-freescale/exadecim_lemmas.ma freescale/bool_lemmas.ma freescale/exadecim.ma
+freescale/byte8.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
-freescale/opcode.ma freescale/opcode_base.ma
-freescale/aux_bases_lemmas.ma freescale/aux_bases.ma freescale/bool_lemmas.ma
-freescale/memory_abs.ma freescale/memory_bits.ma freescale/memory_func.ma freescale/memory_trees.ma
-freescale/bool_lemmas.ma freescale/bool.ma freescale/theory.ma
-freescale/table_RS08.ma freescale/opcode.ma
-freescale/word32_lemmas.ma freescale/word16_lemmas.ma freescale/word32.ma
-freescale/opcode_base.ma freescale/aux_bases.ma freescale/theory.ma freescale/word16.ma
-freescale/nat_lemmas.ma freescale/bool_lemmas.ma freescale/nat.ma
-freescale/memory_trees.ma freescale/memory_struct.ma freescale/option.ma freescale/theory.ma freescale/word16.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 utility/ascii_lemmas2.ma utility/string.ma
+freescale/table_HCS08_tests.ma freescale/table_HCS08.ma
+freescale/multivm.ma freescale/load_write.ma freescale/nat_lemmas.ma
+freescale/opcode_base_lemmas.ma freescale/bool_lemmas.ma freescale/opcode_base.ma
freescale/table_HC05_tests.ma freescale/table_HC05.ma
-freescale/aux_bases.ma freescale/byte8.ma freescale/nat.ma
-freescale/word16_lemmas.ma freescale/byte8_lemmas.ma freescale/word16.ma
-freescale/table_HCS08.ma freescale/opcode.ma
-freescale/table_HC08_tests.ma freescale/table_HC08.ma
-freescale/opcode_base_lemmas_instrmode1.ma freescale/aux_bases_lemmas.ma freescale/exadecim_lemmas.ma freescale/opcode_base.ma
-freescale/table_RS08_tests.ma freescale/table_RS08.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/opcode_base_lemmas_instrmode2.ma freescale/opcode_base_lemmas_instrmode1.ma
-freescale/table_HCS08_tests.ma freescale/table_HCS08.ma
-freescale/opcode_base_lemmas_opcode2.ma freescale/opcode_base_lemmas_opcode1.ma
-freescale/status.ma freescale/memory_abs.ma freescale/opcode_base.ma freescale/prod.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/table_RS08.ma freescale/opcode.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
+test_errori.ma freescale/byte8_lemmas.ma utility/utility.ma
+freescale/memory_struct.ma freescale/aux_bases.ma freescale/byte8.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/opcode_base_lemmas.ma freescale/bool_lemmas.ma freescale/opcode_base.ma
+freescale/exadecim_lemmas.ma freescale/bool_lemmas.ma freescale/exadecim.ma
freescale/word16.ma freescale/byte8.ma
-freescale/model.ma freescale/status.ma
-freescale/multivm.ma freescale/load_write.ma
-freescale/bool.ma freescale/pts.ma
-freescale/nat.ma freescale/bool.ma freescale/pts.ma
-freescale/table_HC08.ma freescale/opcode.ma
-freescale/theory.ma freescale/pts.ma
-freescale/byte8_lemmas.ma freescale/byte8.ma freescale/exadecim_lemmas.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/load_write.ma freescale/model.ma freescale/translation.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/byte8.ma freescale/exadecim.ma
-freescale/translation.ma freescale/option.ma freescale/table_HC05.ma freescale/table_HC08.ma freescale/table_HCS08.ma freescale/table_RS08.ma
+freescale/table_HC08.ma freescale/opcode.ma
+freescale/prod.ma freescale/bool.ma
+utility/string.ma utility/ascii.ma utility/utility.ma
+freescale/table_HCS08.ma freescale/opcode.ma
freescale/word32.ma freescale/word16.ma
-freescale/memory_func.ma freescale/memory_struct.ma freescale/option.ma freescale/theory.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/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/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
+freescale/word16_lemmas.ma freescale/byte8_lemmas.ma freescale/word16.ma
+freescale/exadecim.ma freescale/bool.ma freescale/nat.ma freescale/prod.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
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/byte8.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/bool_lemmas.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/pts.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/theory.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/exadecim.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/exadecim_lemmas.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/bool.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/bool_lemmas.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/model.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/medium_tests_tools.ma".
+include "utility/utility.ma".
+
+(* ************************ *)
+(* HCS08GB60 String Reverse *)
+(* ************************ *)
+
+(* versione ridotta, in cui non si riazzerano gli elementi di counters *)
+ndefinition dTest_HCS08_sReverse_source : word16 → (list byte8) ≝
+λelems:word16.
+let m ≝ HCS08 in source_to_byte8 m (
+(* BEFORE: A=0x00 H:X=0x0D4B SP=0x0D4A PC=0x18E0 Z=true *)
+
+(* static unsigned char dati[3072]={...};
+
+ void swap(unsigned char *a, unsigned char *b)
+ { unsigned char tmp=*a; *a=*b; *b=tmp; return; } *)
+
+(* [0x18C8] allineamento *) (compile m ? NOP maINH I) @
+
+(* argomenti: HX e [0x0D49-A], passaggio ibrido reg, stack *)
+(* [0x18C9] PSHX *) (compile m ? PSHX maINH I) @
+(* [0x18CA] PSHH *) (compile m ? PSHH maINH I) @
+(* [0x18CB] LDHX 5,SP *) (compile m ? LDHX (maSP1 〈x0,x5〉) I) @
+(* [0x18CE] LDA ,X *) (compile m ? LDA maIX0 I) @
+(* [0x18CF] LDHX 1,SP *) (compile m ? LDHX (maSP1 〈x0,x1〉) I) @
+(* [0x18D2] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x18D3] LDA ,X *) (compile m ? LDA maIX0 I) @
+(* [0x18D4] LDHX 6,SP *) (compile m ? LDHX (maSP1 〈x0,x6〉) I) @
+(* [0x18D7] STA ,X *) (compile m ? STA maIX0 I) @
+(* [0x18D8] LDHX 2,SP *) (compile m ? LDHX (maSP1 〈x0,x2〉) I) @
+(* [0x18DB] PULA *) (compile m ? PULA maINH I) @
+(* [0x18DC] STA ,X *) (compile m ? STA maIX0 I) @
+(* [0x18DD] AIS #2 *) (compile m ? AIS (maIMM1 〈x0,x2〉) I) @
+(* [0x18DF] RTS *) (compile m ? RTS maINH I) @
+
+(* void main(void)
+ {
+ unsigned int pos=0,limit=0;
+
+ for(limit=3072;pos<(limit/2);pos++)
+ { swap(&dati[pos],&dati[limit-pos-1]); } *)
+
+(* [0x18E0] LDHX #elems *) (compile m ? LDHX (maIMM2 elems) I) @
+(* [0x18E3] STHX 4,SP *) (compile m ? STHX (maSP1 〈x0,x4〉) I) @
+(* [0x18E6] BRA *+52 ; 191A *) (compile m ? BRA (maIMM1 〈x3,x2〉) I) @
+(* [0x18E8] TSX *) (compile m ? TSX maINH I) @
+(* [0x18E9] LDA 2,X *) (compile m ? LDA (maIX1 〈x0,x2〉) I) @
+(* [0x18EB] ADD #0x00 *) (compile m ? ADD (maIMM1 〈x0,x0〉) I) @
+(* [0x18ED] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x18EE] LDA 1,X *) (compile m ? LDA (maIX1 〈x0,x1〉) I) @
+(* [0x18F0] ADC #0x01 *) (compile m ? ADC (maIMM1 〈x0,x1〉) I) @
+(* [0x18F2] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x18F3] LDA 4,X *) (compile m ? LDA (maIX1 〈x0,x4〉) I) @
+(* [0x18F5] SUB 2,X *) (compile m ? SUB (maIX1 〈x0,x2〉) I) @
+(* [0x18F7] STA ,X *) (compile m ? STA maIX0 I) @
+(* [0x18F8] LDA 3,X *) (compile m ? LDA (maIX1 〈x0,x3〉) I) @
+(* [0x18FA] SBC 1,X *) (compile m ? SBC (maIX1 〈x0,x1〉) I) @
+(* [0x18FC] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x18FD] LDX ,X *) (compile m ? LDX maIX0 I) @
+(* [0x18FE] PULH *) (compile m ? PULH maINH I) @
+(* [0x18FF] AIX #-1 *) (compile m ? AIX (maIMM1 〈xF,xF〉) I) @
+(* [0x1901] TXA *) (compile m ? TXA maINH I) @
+(* [0x1902] ADD #0x00 *) (compile m ? ADD (maIMM1 〈x0,x0〉) I) @
+(* [0x1904] PSHH *) (compile m ? PSHH maINH I) @
+(* [0x1905] TSX *) (compile m ? TSX maINH I) @
+(* [0x1906] STA 3,X *) (compile m ? STA (maIX1 〈x0,x3〉) I) @
+(* [0x1908] PULA *) (compile m ? PULA maINH I) @
+(* [0x1909] ADC #0x01 *) (compile m ? ADC (maIMM1 〈x0,x1〉) I) @
+(* [0x190B] LDX 3,X *) (compile m ? LDX (maIX1 〈x0,x3〉) I) @
+(* [0x190D] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x190E] PULH *) (compile m ? PULH maINH I) @
+(* [0x190F] BSR *-70 ; 18C9 *) (compile m ? BSR (maIMM1 〈xB,x8〉) I) @
+(* [0x1911] AIS #2 *) (compile m ? AIS (maIMM1 〈x0,x2〉) I) @
+(* [0x1913] TSX *) (compile m ? TSX maINH I) @
+(* [0x1914] INC 2,X *) (compile m ? INC (maIX1 〈x0,x2〉) I) @
+(* [0x1916] BNE *+4 ; 191A *) (compile m ? BNE (maIMM1 〈x0,x2〉) I) @
+(* [0x1918] INC 1,X *) (compile m ? INC (maIX1 〈x0,x1〉) I) @
+(* [0x191A] TSX *) (compile m ? TSX maINH I) @
+(* [0x191B] LDA 3,X *) (compile m ? LDA (maIX1 〈x0,x3〉) I) @
+(* [0x191D] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x191E] PULH *) (compile m ? PULH maINH I) @
+(* [0x191F] LSRA *) (compile m ? LSR maINHA I) @
+(* [0x1920] TSX *) (compile m ? TSX maINH I) @
+(* [0x1921] LDX 4,X *) (compile m ? LDX (maIX1 〈x0,x4〉) I) @
+(* [0x1923] RORX *) (compile m ? ROR maINHX I) @
+(* [0x1924] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x1925] PULH *) (compile m ? PULH maINH I) @
+(* [0x1926] CPHX 2,SP *) (compile m ? CPHX (maSP1 〈x0,x2〉) I) @
+(* [0x1929] BHI *-65 ; 18E8 *) (compile m ? BHI (maIMM1 〈xB,xD〉) I)
+
+(* [0x192B] !FINE!
+ attraverso simulazione in CodeWarrior si puo' enunciare che dopo
+ 42+79*n+5*(n>>9) ci sara' il reverse di n byte (PARI) e
+ H:X=n/2 *)
+ ).
+
+(* creazione del processore+caricamento+impostazione registri *)
+ndefinition dTest_HCS08_sReverse_status ≝
+λt:memory_impl.
+λA_op:byte8.
+λHX_op:word16.
+λelems:word16.
+λdata:list byte8.
+ set_acc_8_low_reg HCS08 t (* A<-A_op *)
+ (set_z_flag HCS08 t (* Z<-true *)
+ (setweak_sp_reg HCS08 t (* SP<-0x0D4A *)
+ (setweak_indX_16_reg HCS08 t (* H:X<-HX_op *)
+ (set_pc_reg HCS08 t (* PC<-0x18E0 *)
+ (start_of_mcu_version_HCS08 MC9S08GB60 t
+ (load_from_source_at t (* carica data in RAM:dTest_HCS08_RAM *)
+ (load_from_source_at t (zero_memory t) (* carica source in ROM:dTest_HCS08_prog *)
+ (dTest_HCS08_sReverse_source elems) dTest_HCS08_prog)
+ data dTest_HCS08_RAM)
+ (build_memory_type_of_mcu_version (FamilyHCS08 MC9S08GB60) t)
+ (mk_byte8 x0 x0) (mk_byte8 x0 x0) (* non deterministici tutti a 0 *)
+ false false false false false false) (* non deterministici tutti a 0 *)
+ (mk_word16 (mk_byte8 x1 x8) (mk_byte8 xE x0)))
+ HX_op)
+ (mk_word16 (mk_byte8 x0 xD) (mk_byte8 x4 xA)))
+ true)
+ A_op.
+
+(* parametrizzazione dell'enunciato del teorema *)
+(* primo sbozzo: confronto esecuzione con hexdump... *)
+nlemma dTest_HCS08_sReverse_dump_aux ≝
+λt:memory_impl.λstring:list byte8.
+ (* 1) la stringa deve avere una lunghezza ∈ [0,3072] *)
+ (byte8_bounded_strlen string 〈〈x0,xC〉:〈x0,x0〉〉) ∧
+ (* 2) la stringa deve avere lunghezza pari *)
+ ((and_b8 (w16l (byte8_strlen string)) 〈x0,x1〉) = 〈x0,x0〉) ∧
+ (* 3) match di esecuzione su tempo in forma di tempo esatto *)
+ (match execute HCS08 t
+ (* parametri IN: t,H:X,strlen(string),string *)
+ (TickOK ? (dTest_HCS08_sReverse_status t 〈x0,x0〉 〈〈x0,xD〉:〈x4,xB〉〉 (byte8_strlen string) string))
+ (* tempo di esecuzione 42+79*n+5*(n>>9) *)
+ (42+79*(nat_of_word16 (byte8_strlen string))+5*((nat_of_word16 (byte8_strlen string))/512)) with
+ [ TickERR s _ ⇒ None ?
+ (* azzeramento tutta RAM tranne dati *)
+ | TickSUSP s _ ⇒ None ?
+ | TickOK s ⇒ Some ? (byte8_hexdump t (get_mem_desc HCS08 t s) dTest_HCS08_RAM (nat_of_word16 (byte8_strlen string)))
+ ] =
+ Some ? (reverse_list ? string)).
+
+(* confronto esecuzione con hexdump... *)
+(*
+lemma dTest_HCS08_sReverse_dump :
+ dTest_HCS08_sReverse_dump_aux MEM_TREE dTest_random_32.
+ unfold dTest_HCS08_sReverse_dump_aux;
+ split;
+ [ split; [ normalize in ⊢ (%); autobatch ] reflexivity ]
+ reflexivity.
+qed.
+*)
+
+(*
+(* parametrizzazione dell'enunciato del teorema *)
+(* dimostrazione senza svolgimento degli stati *)
+lemma dTest_HCS08_sReverse_aux ≝
+λt:memory_impl.λstring:list byte8.
+ (* 1) la stringa deve avere una lunghezza ∈ [0,3072] *)
+ (byte8_bounded_strlen string 〈〈x0,xC〉:〈x0,x0〉〉) ∧
+ (* 2) la stringa deve avere lunghezza pari *)
+ ((and_b8 (w16l (byte8_strlen string)) 〈x0,x1〉) = 〈x0,x0〉) ∧
+ (* 3) match di esecuzione su tempo in forma di tempo esatto *)
+ (match execute HCS08 t
+ (* parametri IN: t,H:X,strlen(string),string *)
+ (TickOK ? (dTest_HCS08_sReverse_status t 〈x0,x0〉 〈〈x0,xD〉:〈x4,xB〉〉 (byte8_strlen string) string))
+ (* tempo di esecuzione 42+79*n+5*(n>>9) *)
+ (42+79*(nat_of_word16 (byte8_strlen string))+5*((nat_of_word16 (byte8_strlen string))/512)) with
+ [ TickERR s _ ⇒ None ?
+ (* azzeramento tutta RAM tranne dati *)
+ | TickSUSP s _ ⇒ None ?
+ | TickOK s ⇒ Some ? (set_mem_desc HCS08 t s (load_from_source_at t (get_mem_desc HCS08 t s) dTest_zeros 〈〈x0,xD〉:〈x0,x0〉〉))
+ ] =
+ Some ? (set_pc_reg HCS08 t
+ (dTest_HCS08_sReverse_status t (fst ?? (shr_b8 (w16h (byte8_strlen string)))) (fst ?? (shr_w16 (byte8_strlen string))) (byte8_strlen string) (reverse_list ? string))
+ (mk_word16 (mk_byte8 x1 x9) (mk_byte8 x2 xB)))).
+
+(*
+lemma dTest_HCS08_sReverse :
+ dTest_HCS08_sReverse_aux MEM_TREE dTest_random_32.
+ unfold dTest_HCS08_sReverse_aux;
+ split;
+ [ split; [ normalize in ⊢ (%); autobatch ] reflexivity ]
+
+ rewrite > (breakpoint HCS08 MEM_TREE (TickOK ? (dTest_HCS08_sReverse_status MEM_TREE 〈〈x0,xD〉:〈x4,xB〉〉 (byte8_strlen dTest_random_32) dTest_random_32)) 3 (39+79*byte8_strlen dTest_random_32+5*(byte8_strlen dTest_random_32/512))) in ⊢ (? ? match % in tick_result return ? with [TickERR⇒?|TickSUSP⇒?|TickOK⇒?] ?);
+ letin status0 ≝ (dTest_HCS08_sReverse_status MEM_TREE 〈〈x0,xD〉:〈x4,xB〉〉 (byte8_strlen dTest_random_32) dTest_random_32);
+ change in ⊢ (? ? match ? ? ? (? ? ? % ?) ? in tick_result return ? with [TickERR⇒?|TickSUSP⇒?|TickOK⇒?] ?) with
+ (TickOK ? status0);
+ rewrite > (execute_HCS08_LDHX_maIMM2 MEM_TREE status0 〈x0,x0〉 〈x2,x0〉) in ⊢ (? ? match ? ? ? % ? in tick_result return ? with [TickERR⇒?|TickSUSP⇒?|TickOK⇒?] ?);
+ [ 2,3,4,5: reflexivity; ]
+
+ letin status1 ≝ (set_pc_reg HCS08 MEM_TREE (setweak_v_flag HCS08 MEM_TREE (setweak_n_flag HCS08 MEM_TREE (set_z_flag HCS08 MEM_TREE (set_alu HCS08 MEM_TREE (dTest_HCS08_sReverse_status MEM_TREE 〈〈x0,xD〉:〈x4,xB〉〉 (byte8_strlen dTest_random_32) dTest_random_32) (set_indX_16_reg_HC08 (alu HCS08 MEM_TREE (dTest_HCS08_sReverse_status MEM_TREE 〈〈x0,xD〉:〈x4,xB〉〉 (byte8_strlen dTest_random_32) dTest_random_32)) 〈〈x0,x0〉:〈x2,x0〉〉)) (eq_w16 〈〈x0,x0〉:〈x2,x0〉〉 〈〈x0,x0〉:〈x0,x0〉〉)) (MSB_w16 〈〈x0,x0〉:〈x2,x0〉〉)) false) (filtered_plus_w16 HCS08 MEM_TREE (dTest_HCS08_sReverse_status MEM_TREE 〈〈x0,xD〉:〈x4,xB〉〉 (byte8_strlen dTest_random_32) dTest_random_32) (get_pc_reg HCS08 MEM_TREE (dTest_HCS08_sReverse_status MEM_TREE 〈〈x0,xD〉:〈x4,xB〉〉 (byte8_strlen dTest_random_32) dTest_random_32)) 3));
+ change in ⊢ (? ? match ? ? ? % ? in tick_result return ? with [TickERR⇒?|TickSUSP⇒?|TickOK⇒?] ?) with (TickOK ? status1);
+
+ rewrite > (breakpoint HCS08 MEM_TREE (TickOK ? status1) 5 (34+79*byte8_strlen dTest_random_32+5*(byte8_strlen dTest_random_32/512))) in ⊢ (? ? match % in tick_result return ? with [TickERR⇒?|TickSUSP⇒?|TickOK⇒?] ?);
+ change in ⊢ (? ? match ? ? ? (? ? ? % ?) ? in tick_result return ? with [TickERR⇒?|TickSUSP⇒?|TickOK⇒?] ?) with (TickOK ? status1);
+ rewrite > (execute_HCS08_STHX_maSP1 status1 〈x0,x4〉)
+ in ⊢ (? ? match ? ? ? % ? in tick_result return ? with [TickERR⇒?|TickSUSP⇒?|TickOK⇒?] ?);
+ [ 2,3,4,5,6,7: reflexivity; ]
+
+ elim daemon.
+
+qed.
+*)
+
+definition sReverseCalc ≝
+λstring:list byte8.
+ match execute HCS08 MEM_TREE
+ (TickOK ? (dTest_HCS08_sReverse_status MEM_TREE 〈x0,x0〉 〈〈x0,xD〉:〈x4,xB〉〉 (byte8_strlen string) string))
+ (42+79*(nat_of_word16 (byte8_strlen string))+5*((nat_of_word16 (byte8_strlen string))/512)) with
+ [ TickERR s _ ⇒ None ?
+ | TickSUSP s _ ⇒ None ?
+ | TickOK s ⇒ Some ? (set_mem_desc HCS08 MEM_TREE s (load_from_source_at MEM_TREE (get_mem_desc HCS08 MEM_TREE s) dTest_zeros 〈〈x0,xD〉:〈x0,x0〉〉))
+ ].
+
+definition sReverseNoCalc ≝
+λstring:list byte8.
+ Some ? (set_pc_reg HCS08 MEM_TREE
+ (dTest_HCS08_sReverse_status MEM_TREE (fst ?? (shr_b8 (w16h (byte8_strlen string))))
+ (fst ?? (shr_w16 (byte8_strlen string)))
+ (byte8_strlen string) (reverse_list ? string))
+ (mk_word16 (mk_byte8 x1 x9) (mk_byte8 x2 xB))).
+
+definition sReverseCalc32 ≝ sReverseCalc dTest_random_32.
+definition sReverseCalc64 ≝ sReverseCalc dTest_random_64.
+definition sReverseCalc128 ≝ sReverseCalc dTest_random_128.
+definition sReverseCalc256 ≝ sReverseCalc dTest_random_256.
+definition sReverseCalc512 ≝ sReverseCalc dTest_random_512.
+definition sReverseCalc1024 ≝ sReverseCalc dTest_random_1024.
+definition sReverseCalc2048 ≝ sReverseCalc dTest_random_2048.
+definition sReverseCalc3072 ≝ sReverseCalc dTest_random_3072.
+
+definition sReverseNoCalc32 ≝ sReverseNoCalc dTest_random_32.
+definition sReverseNoCalc64 ≝ sReverseNoCalc dTest_random_64.
+definition sReverseNoCalc128 ≝ sReverseNoCalc dTest_random_128.
+definition sReverseNoCalc256 ≝ sReverseNoCalc dTest_random_256.
+definition sReverseNoCalc512 ≝ sReverseNoCalc dTest_random_512.
+definition sReverseNoCalc1024 ≝ sReverseNoCalc dTest_random_1024.
+definition sReverseNoCalc2048 ≝ sReverseNoCalc dTest_random_2048.
+definition sReverseNoCalc3072 ≝ sReverseNoCalc dTest_random_3072.
+
+(* *********************** *)
+(* HCS08GB60 Counting Sort *)
+(* *********************** *)
+
+(* versione ridotta, in cui non si riazzerano gli elementi di counters *)
+definition dTest_HCS08_cSort_source : word16 → (list byte8) ≝
+λelems:word16.
+let m ≝ HCS08 in source_to_byte8 m (
+(* BEFORE: A=0x00 H:X=0x0F4C SP=0x0F4B PC=0x18C8 Z=true *)
+
+(* /* IPOTESI: INIT VARIABILI+ARRAY GIA' ESEGUITO */
+ static unsigned int counters[256]={ campitura di 0 };
+ static unsigned char dati[3072]={ dati random };
+
+ void CountingSort(void)
+ {
+ unsigned int index=0,position=0; *)
+
+(* /* TESI: CODICE DA ESEGUIRE
+
+ /* calcolo del # ripetizioni degli elementi byte */
+ for(;index<3072;index++)
+ { counters[dati[index]]++; } *)
+
+(* [0x18C8] BRA *+31;18E7 *) (compile m ? BRA (maIMM1 〈x1,xD〉) I) @
+(* [0x18CA] LDHX 1,SP *) (compile m ? LDHX (maSP1 〈x0,x1〉) I) @
+(* [0x18CD] LDA 256,X *) (compile m ? LDA (maIX2 〈〈x0,x1〉:〈x0,x0〉〉) I) @
+(* [0x18D0] LSLA *) (compile m ? ASL maINHA I) @
+(* [0x18D1] CLRX *) (compile m ? CLR maINHX I) @
+(* [0x18D2] ROLX *) (compile m ? ROL maINHX I) @
+(* [0x18D3] ADD #0x00 *) (compile m ? ADD (maIMM1 〈x0,x0〉) I) @
+(* [0x18D5] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x18D6] TXA *) (compile m ? TXA maINH I) @
+(* [0x18D7] ADC #0x0D *) (compile m ? ADC (maIMM1 〈x0,xD〉) I) @
+(* [0x18D9] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x18DA] PULH *) (compile m ? PULH maINH I) @
+(* [0x18DB] PULX *) (compile m ? PULX maINH I) @
+(* [0x18DC] INC 1,X *) (compile m ? INC (maIX1 〈x0,x1〉) I) @
+(* [0x18DE] BNE *+3 *) (compile m ? BNE (maIMM1 〈x0,x1〉) I) @
+(* [0x18E0] INC ,X *) (compile m ? INC maIX0 I) @
+(* [0x18E1] TSX *) (compile m ? TSX maINH I) @
+(* [0x18E2] INC 1,X *) (compile m ? INC (maIX1 〈x0,x1〉) I) @
+(* [0x18E4] BNE *+3 *) (compile m ? BNE (maIMM1 〈x0,x1〉) I) @
+(* [0x18E6] INC ,X *) (compile m ? INC maIX0 I) @
+(* [0x18E7] LDHX 1,SP *) (compile m ? LDHX (maSP1 〈x0,x1〉) I) @
+(* [0x18EA] CPHX #elems *) (compile m ? CPHX (maIMM2 elems) I) @ (* dimensione dei dati al massimo 0x0C00 *)
+(* [0x18ED] BCS *-35;18CA *) (compile m ? BCS (maIMM1 〈xD,xB〉) I) @
+
+(* /* sovrascrittura di dati per produrre la versione ordinata */
+ for(index=0;index<256;index++)
+ {
+ while(counters[index]--)
+ { dati[position++]=index; }
+ } *)
+
+(* [0x18EF] TSX *) (compile m ? TSX maINH I) @
+(* [0x18F0] CLR 1,X *) (compile m ? CLR (maIX1 〈x0,x1〉) I) @
+(* [0x18F2] CLR ,X *) (compile m ? CLR maIX0 I) @
+(* [0x18F3] BRA *+16 *) (compile m ? BRA (maIMM1 〈x0,xE〉) I) @
+(* [0x18F5] TSX *) (compile m ? TSX maINH I) @
+(* [0x18F6] LDA 1,X *) (compile m ? LDA (maIX1 〈x0,x1〉) I) @
+(* [0x18F8] LDHX 3,SP *) (compile m ? LDHX (maSP1 〈x0,x3〉) I) @
+(* [0x18FB] STA 256,X *) (compile m ? STA (maIX2 〈〈x0,x1〉:〈x0,x0〉〉) I) @
+(* [0x18FE] AIX #1 *) (compile m ? AIX (maIMM1 〈x0,x1〉) I) @
+(* [0x1900] STHX 3,SP *) (compile m ? STHX (maSP1 〈x0,x3〉) I) @
+(* [0x1903] TSX *) (compile m ? TSX maINH I) @
+(* [0x1904] LDX 1,X *) (compile m ? LDX (maIX1 〈x0,x1〉) I) @
+(* [0x1906] LSLX *) (compile m ? ASL maINHX I) @
+(* [0x1907] LDA 1,SP *) (compile m ? LDA (maSP1 〈x0,x1〉) I) @
+(* [0x190A] ROLA *) (compile m ? ROL maINHA I) @
+(* [0x190B] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x190C] PULH *) (compile m ? PULH maINH I) @
+(* [0x190D] PSHX *) (compile m ? PSHX maINH I) @
+(* [0x190E] LDHX 3328,X *) (compile m ? LDHX (maIX2 〈〈x0,xD〉:〈x0,x0〉〉) I) @
+(* [0x1912] PSHX *) (compile m ? PSHX maINH I) @
+(* [0x1913] PSHH *) (compile m ? PSHH maINH I) @
+(* [0x1914] AIX #-1 *) (compile m ? AIX (maIMM1 〈xF,xF〉) I) @
+(* [0x1916] PSHH *) (compile m ? PSHH maINH I) @
+(* [0x1917] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x1918] PULH *) (compile m ? PULH maINH I) @
+(* [0x1919] PSHX *) (compile m ? PSHX maINH I) @
+(* [0x191A] LDX 5,SP *) (compile m ? LDX (maSP1 〈x0,x5〉) I) @
+(* [0x191D] PULA *) (compile m ? PULA maINH I) @
+(* [0x191E] STA 3329,X *) (compile m ? STA (maIX2 〈〈x0,xD〉:〈x0,x1〉〉) I) @
+(* [0x1921] PULA *) (compile m ? PULA maINH I) @
+(* [0x1922] STA 3328,X *) (compile m ? STA (maIX2 〈〈x0,xD〉:〈x0,x0〉〉) I) @
+(* [0x1925] PULH *) (compile m ? PULH maINH I) @
+(* [0x1926] PULX *) (compile m ? PULX maINH I) @
+(* [0x1927] CPHX #0x0000 *) (compile m ? CPHX (maIMM2 〈〈x0,x0〉:〈x0,x0〉〉) I) @
+(* [0x192A] PULH *) (compile m ? PULH maINH I) @
+(* [0x192B] BNE *-54 *) (compile m ? BNE (maIMM1 〈xC,x8〉) I) @
+(* [0x192D] TSX *) (compile m ? TSX maINH I) @
+(* [0x192E] INC 1,X *) (compile m ? INC (maIX1 〈x0,x1〉) I) @
+(* [0x1930] BNE *+3 *) (compile m ? BNE (maIMM1 〈x0,x1〉) I) @
+(* [0x1932] INC ,X *) (compile m ? INC maIX0 I) @
+(* [0x1933] LDHX 1,SP *) (compile m ? LDHX (maSP1 〈x0,x1〉) I) @
+(* [0x1936] CPHX #0x0100 *) (compile m ? CPHX (maIMM2 〈〈x0,x1〉:〈x0,x0〉〉) I) @
+(* [0x1939] BNE *-54 *) (compile m ? BNE (maIMM1 〈xC,x8〉) I) @
+(* [0x193B] STOP *) (compile m ? STOP maINH I)
+
+(* [0x193C] !FINE!
+ attraverso simulazione in CodeWarrior si puo' enunciare che dopo
+ 25700+150n si sara' entrati in stato STOP corrispondente con ordinamento
+ di n byte, A=0xFF H:X=0x0100 *)
+ ).
+
+(* creazione del processore+caricamento+impostazione registri *)
+definition dTest_HCS08_cSort_status ≝
+λt:memory_impl.
+λI_op:bool.
+λA_op:byte8.
+λHX_op:word16.
+λelems:word16.
+λdata:list byte8.
+ setweak_i_flag HCS08 t (* I<-I_op *)
+ (set_acc_8_low_reg HCS08 t (* A<-A_op *)
+ (set_z_flag HCS08 t (* Z<-true *)
+ (setweak_sp_reg HCS08 t (* SP<-0x0F4B *)
+ (setweak_indX_16_reg HCS08 t (* H:X<-HX_op *)
+ (set_pc_reg HCS08 t (* PC<-dTest_HCS08_prog *)
+ (start_of_mcu_version_HCS08
+ MC9S08GB60 t
+ (load_from_source_at t (* carica data in RAM:dTest_HCS08_RAM *)
+ (load_from_source_at t (zero_memory t) (* carica source in ROM:dTest_HCS08_prog *)
+ (dTest_HCS08_cSort_source elems) dTest_HCS08_prog)
+ data dTest_HCS08_RAM)
+ (build_memory_type_of_mcu_version (FamilyHCS08 MC9S08GB60) t)
+ (mk_byte8 x0 x0) (mk_byte8 x0 x0) (* non deterministici tutti a 0 *)
+ false false false false false false) (* non deterministici tutti a 0 *)
+ dTest_HCS08_prog)
+ HX_op)
+ (mk_word16 (mk_byte8 x0 xF) (mk_byte8 x4 xB)))
+ true)
+ A_op)
+ I_op.
+
+(* parametrizzazione dell'enunciato del teorema parziale *)
+lemma dTest_HCS08_cSort_aux ≝
+λt:memory_impl.λstring:list byte8.
+ (* 1) la stringa deve avere una lunghezza ∈ [0,3072] *)
+ (byte8_bounded_strlen string 〈〈x0,xC〉:〈x0,x0〉〉) ∧
+ (* 2) match di esecuzione su tempo in forma di upperbound *)
+ (match execute HCS08 t
+ (* parametri IN: t,A,H:X,strlen(string),string *)
+ (TickOK ? (dTest_HCS08_cSort_status t true 〈x0,x0〉 〈〈x0,xF〉:〈x4,xC〉〉 (byte8_strlen string) string))
+ (* tempo di esecuzione 25700+150*n *)
+ ((nat_of_word16 〈〈x6,x4〉:〈x6,x4〉〉)+(nat_of_byte8 〈x9,x6〉)*(nat_of_word16 (byte8_strlen string))) with
+ [ TickERR s _ ⇒ None ?
+ (* azzeramento tutta RAM tranne dati *)
+ | TickSUSP s _ ⇒ Some ? (set_mem_desc HCS08 t s (load_from_source_at t (get_mem_desc HCS08 t s) dTest_zeros 〈〈x0,xD〉:〈x0,x0〉〉))
+ | TickOK s ⇒ None ?
+ ] =
+ Some ? (set_pc_reg HCS08 t
+ (dTest_HCS08_cSort_status t false 〈xF,xF〉 〈〈x0,x1〉:〈x0,x0〉〉 (byte8_strlen string) (byte8_list_ordering string))
+ (mk_word16 (mk_byte8 x1 x9) (mk_byte8 x3 xC)))).
+
+(* dimostrazione senza svolgimento degli stati *)
+(*
+lemma dTest_HCS08_cSort :
+ dTest_HCS08_cSort_aux MEM_TREE dTest_random_32.
+ unfold dTest_HCS08_cSort_aux;
+ split;
+ [ normalize in ⊢ (%); autobatch ]
+ reflexivity.
+qed.
+*)
+
+definition cSortCalc ≝
+λstring:list byte8.
+ match execute HCS08 MEM_TREE
+ (TickOK ? (dTest_HCS08_cSort_status MEM_TREE true 〈x0,x0〉 〈〈x0,xF〉:〈x4,xC〉〉 (byte8_strlen string) string))
+ ((nat_of_word16 〈〈x6,x4〉:〈x6,x4〉〉)+(nat_of_byte8 〈x9,x6〉)*(nat_of_word16 (byte8_strlen string))) with
+ [ TickERR s _ ⇒ None ?
+ | TickSUSP s _ ⇒ Some ? (set_mem_desc HCS08 MEM_TREE s (load_from_source_at MEM_TREE (get_mem_desc HCS08 MEM_TREE s) dTest_zeros 〈〈x0,xD〉:〈x0,x0〉〉))
+ | TickOK s ⇒ None ?
+ ].
+
+definition cSortNoCalc ≝
+λstring:list byte8.
+ Some ? (set_pc_reg HCS08 MEM_TREE
+ (dTest_HCS08_cSort_status MEM_TREE false 〈xF,xF〉 〈〈x0,x1〉:〈x0,x0〉〉 (byte8_strlen string) (byte8_list_ordering string))
+ (mk_word16 (mk_byte8 x1 x9) (mk_byte8 x3 xC))).
+
+definition cSortCalc32 ≝ cSortCalc dTest_random_32.
+definition cSortCalc64 ≝ cSortCalc dTest_random_64.
+definition cSortCalc128 ≝ cSortCalc dTest_random_128.
+definition cSortCalc256 ≝ cSortCalc dTest_random_256.
+definition cSortCalc512 ≝ cSortCalc dTest_random_512.
+definition cSortCalc1024 ≝ cSortCalc dTest_random_1024.
+definition cSortCalc2048 ≝ cSortCalc dTest_random_2048.
+definition cSortCalc3072 ≝ cSortCalc dTest_random_3072.
+
+definition cSortNoCalc32 ≝ cSortNoCalc dTest_random_32.
+definition cSortNoCalc64 ≝ cSortNoCalc dTest_random_64.
+definition cSortNoCalc128 ≝ cSortNoCalc dTest_random_128.
+definition cSortNoCalc256 ≝ cSortNoCalc dTest_random_256.
+definition cSortNoCalc512 ≝ cSortNoCalc dTest_random_512.
+definition cSortNoCalc1024 ≝ cSortNoCalc dTest_random_1024.
+definition cSortNoCalc2048 ≝ cSortNoCalc dTest_random_2048.
+definition cSortNoCalc3072 ≝ cSortNoCalc dTest_random_3072.
+
+(* ********************** *)
+(* HCS08GB60 numeri aurei *)
+(* ********************** *)
+
+(* versione ridotta, in cui non si riazzerano gli elementi di counters *)
+definition dTest_HCS08_gNum_source : word16 → (list byte8) ≝
+λelems:word16.
+let m ≝ HCS08 in source_to_byte8 m (
+(* BEFORE: A=0x00 HX=0x1A00 PC=0x18BE SP=0x016F Z=1 (I=1) *)
+
+(*
+static unsigned int result[16]={ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 };
+word result[16] = 0x0100
+
+void goldenNumbers(void)
+{
+unsigned int res_pos=0,tested_num=0,divisor=0;
+unsigned long int acc=0;
+*)
+
+(* [0x18BE] AIS #-10 *) (compile m ? AIS (maIMM1 〈xF,x6〉) I) @
+(* [0x18C0] TSX *) (compile m ? TSX maINH I) @
+(* [0x18C1] CLR 9,x *) (compile m ? CLR (maIX1 〈x0,x9〉) I) @
+(* [0x18C3] CLR 8,X *) (compile m ? CLR (maIX1 〈x0,x8〉) I) @
+(* [0x18C5] CLR 1,X *) (compile m ? CLR (maIX1 〈x0,x1〉) I) @
+(* [0x18C7] CLR ,X *) (compile m ? CLR maIX0 I) @
+(* [0x18C8] CLR 3,X *) (compile m ? CLR (maIX1 〈x0,x3〉) I) @
+(* [0x18CA] CLR 2,X *) (compile m ? CLR (maIX1 〈x0,x2〉) I) @
+(* [0x18CC] JSR 0x1951 *) (compile m ? JSR (maIMM2 〈〈x1,x9〉:〈x5,x1〉〉) I) @
+
+(*
+for(tested_num=1;tested_num<2;tested_num++)
+ {
+*)
+
+(* [0x18CF] STHX 1,SP *) (compile m ? STHX (maSP1 〈x0,x1〉) I) @
+(* [0x18D2] BRA *+116 ; 0x1946 *) (compile m ? BRA (maIMM1 〈x7,x2〉) I) @
+(* [0x18D4] BSR *+125 ; 0x1951 *) (compile m ? BSR (maIMM1 〈x7,xB〉) I) @
+(* [0x18D6] STHX 3,SP *) (compile m ? STHX (maSP1 〈x0,x3〉) I) @
+
+(*
+ for(acc=0,divisor=1;divisor<tested_num;divisor++)
+ {
+ if(!(tested_num%divisor))
+ { acc+=divisor; }
+ }
+*)
+
+(* [0x18D9] BRA *+61 ; 0x1916 *) (compile m ? BRA (maIMM1 〈x3,xB〉) I) @
+(* [0x18DB] LDHX 1,SP *) (compile m ? LDHX (maSP1 〈x0,x1〉) I) @
+(* [0x18DE] PSHX *) (compile m ? PSHX maINH I) @
+(* [0x18DF] PSHH *) (compile m ? PSHH maINH I) @
+(* [0x18E0] LDHX 5,SP *) (compile m ? LDHX (maSP1 〈x0,x5〉) I) @
+(* [0x18E3] JSR 0x1A1A *) (compile m ? JSR (maIMM2 〈〈x1,xA〉:〈x1,xA〉〉) I) @
+(* [0x18E6] AIS #2 *) (compile m ? AIS (maIMM1 〈x0,x2〉) I) @
+(* [0x18E8] CPHX #0x0000 *) (compile m ? CPHX (maIMM2 〈〈x0,x0〉:〈x0,x0〉〉) I) @
+(* [0x18EB] BNE *+33 ; 0x190C *) (compile m ? BNE (maIMM1 〈x1,xF〉) I) @
+(* [0x18ED] TSX *) (compile m ? TSX maINH I) @
+(* [0x18EE] LDA 3,X *) (compile m ? LDA (maIX1 〈x0,x3〉) I) @
+(* [0x18F0] LDX 2,X *) (compile m ? LDX (maIX1 〈x0,x2〉) I) @
+(* [0x18F2] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x18F3] PSHX *) (compile m ? PSHX maINH I) @
+(* [0x18F4] CLRA *) (compile m ? CLR maINHA I) @
+(* [0x18F5] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x18F6] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x18F7] TSX *) (compile m ? TSX maINH I) @
+(* [0x18F8] PSHX *) (compile m ? PSHX maINH I) @
+(* [0x19F9] PSHH *) (compile m ? PSHH maINH I) @
+(* [0x18FA] AIX #8 *) (compile m ? AIX (maIMM1 〈x0,x8〉) I) @
+(* [0x18FC] PSHX *) (compile m ? PSHX maINH I) @
+(* [0x18FD] PSHH *) (compile m ? PSHH maINH I) @
+(* [0x18FE] LDHX 3,SP *) (compile m ? LDHX (maSP1 〈x0,x3〉) I) @
+(* [0x1901] JSR 0x1A2A *) (compile m ? JSR (maIMM2 〈〈x1,xA〉:〈x2,xA〉〉) I) @
+(* [0x1904] TSX *) (compile m ? TSX maINH I) @
+(* [0x1905] AIX #14 *) (compile m ? AIX (maIMM1 〈x0,xE〉) I) @
+(* [0x1907] JSR 0x1A30 *) (compile m ? JSR (maIMM2 〈〈x1,xA〉:〈x3,x0〉〉) I) @
+(* [0x190A] AIS #6 *) (compile m ? AIS (maIMM1 〈x0,x6〉) I) @
+(* [0x190C] STA 0x1800 !COP! *) (compile m ? STA (maDIR2 〈〈x0,xC〉:〈x0,x0〉〉) I) @
+(* [0x190F] TSX *) (compile m ? TSX maINH I) @
+(* [0x1910] INC 3,X *) (compile m ? INC (maIX1 〈x0,x3〉) I) @
+(* [0x1912] BNE *+4 ; 0x1916 *) (compile m ? BNE (maIMM1 〈x0,x2〉) I) @
+(* [0x1914] INC 2,X *) (compile m ? INC (maIX1 〈x0,x2〉) I) @
+(* [0x1916] LDHX 1,SP *) (compile m ? LDHX (maSP1 〈x0,x1〉) I) @
+(* [0x1919] CPHX 3,SP *) (compile m ? CPHX (maSP1 〈x0,x3〉) I) @
+(* [0x191C] BHI *-65 ; 0x18DB *) (compile m ? BHI (maIMM1 〈xB,xD〉) I) @
+
+(*
+ if(acc==tested_num)
+ { result[res_pos++]=tested_num; }
+ }
+}
+*)
+
+(* [0x191E] CPHX 7,SP *) (compile m ? CPHX (maSP1 〈x0,x7〉) I) @
+(* [0x1921] BNE *+31 ; 0x1940 *) (compile m ? BNE (maIMM1 〈x1,xD〉) I) @
+(* [0x1923] LDHX 5,SP *) (compile m ? LDHX (maSP1 〈x0,x5〉) I) @
+(* [0x1926] BNE *+26 ; 0x1940 *) (compile m ? BNE (maIMM1 〈x1,x8〉) I) @
+(* [0x1928] LDHX 9,SP *) (compile m ? LDHX (maSP1 〈x0,x9〉) I) @
+(* [0x192B] PSHX *) (compile m ? PSHX maINH I) @
+(* [0x192C] AIX #1 *) (compile m ? AIX (maIMM1 〈x0,x1〉) I) @
+(* [0x192E] STHX 10,SP *) (compile m ? STHX (maSP1 〈x0,xA〉) I) @
+(* [0x1931] PULX *) (compile m ? PULX maINH I) @
+(* [0x1932] LSLX *) (compile m ? ASL maINHX I) @
+(* [0x1933] LDA 2,SP *) (compile m ? LDA (maSP1 〈x0,x2〉) I) @
+(* [0x1936] CLRH *) (compile m ? CLR maINHH I) @
+(* [0x1937] STA 257,X *) (compile m ? STA (maIX2 〈〈x0,x1〉:〈x0,x1〉〉) I) @
+(* [0x193A] LDA 1,SP *) (compile m ? LDA (maSP1 〈x0,x1〉) I) @
+(* [0x193D] STA 256,X *) (compile m ? STA (maIX2 〈〈x0,x1〉:〈x0,x0〉〉) I) @
+(* [0x1940] TSX *) (compile m ? TSX maINH I) @
+(* [0x1941] INC 1,X *) (compile m ? INC (maIX1 〈x0,x1〉) I) @
+(* [0x1943] BNE *+3 ; 0x1946 *) (compile m ? BNE (maIMM1 〈x0,x1〉) I) @
+(* [0x1945] INC ,X *) (compile m ? INC maIX0 I) @
+(* [0x1946] LDHX 1,SP *) (compile m ? LDHX (maSP1 〈x0,x1〉) I) @
+(* [0x1949] CPHX #elems *) (compile m ? CPHX (maIMM2 elems) I) @
+(* [0x194C] BCS *-120 ; 0x18D4 *) (compile m ? BCS (maIMM1 〈x8,x6〉) I) @
+(* [0x194E] AIS #10 *) (compile m ? AIS (maIMM1 〈x0,xA〉) I) @
+(* [0x1950] STOP ->1951 !FINE! *) (compile m ? STOP maINH I) @
+(* [0x1951] CLRX *) (compile m ? CLR maINHX I) @
+(* [0x1952] CLRH *) (compile m ? CLR maINHH I) @
+(* [0x1953] STHX 9,SP *) (compile m ? STHX (maSP1 〈x0,x9〉) I) @
+(* [0x1956] CLRH *) (compile m ? CLR maINHH I) @
+(* [0x1957] STHX 7,SP *) (compile m ? STHX (maSP1 〈x0,x7〉) I) @
+(* [0x195A] INCX *) (compile m ? INC maINHX I) @
+(* [0x195B] RTS *) (compile m ? RTS maINH I) @
+
+(*
+static void _PUSH_ARGS_L(void) { ... }
+*)
+
+(* [0x195C] LDA 3,X *) (compile m ? LDA (maIX1 〈x0,x3〉) I) @
+(* [0x195E] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x195F] LDA 2,X *) (compile m ? LDA (maIX1 〈x0,x2〉) I) @
+(* [0x1961] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x1962] LDHX ,X *) (compile m ? LDHX maIX0 I) @
+(* [0x1964] PSHX *) (compile m ? PSHX maINH I) @
+(* [0x1965] PSHH *) (compile m ? PSHH maINH I) @
+(* [0x1966] LDHX 7,SP *) (compile m ? LDHX (maSP1 〈x0,x7〉) I) @
+(* [0x1969] LDA 3,X *) (compile m ? LDA (maIX1 〈x0,x3〉) I) @
+(* [0x196B] STA 17,SP *) (compile m ? STA (maSP1 〈x1,x1〉) I) @
+(* [0x196E] LDA 2,X *) (compile m ? LDA (maIX1 〈x0,x2〉) I) @
+(* [0x1970] STA 16,SP *) (compile m ? STA (maSP1 〈x1,x0〉) I) @
+(* [0x1973] LDHX ,X *) (compile m ? LDHX maIX0 I) @
+(* [0x1975] STHX 14,SP *) (compile m ? STHX (maSP1 〈x0,xE〉) I) @
+(* [0x1978] LDHX 5,SP *) (compile m ? LDHX (maSP1 〈x0,x5〉) I) @
+(* [0x197B] JMP ,X *) (compile m ? JMP maINHX0ADD I) @
+
+(*
+static void _ENTER_BINARY_L(void) { ... }
+*)
+
+(* [0x197C] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x197D] PSHX *) (compile m ? PSHX maINH I) @
+(* [0x197E] PSHH *) (compile m ? PSHH maINH I) @
+(* [0x197F] PSHX *) (compile m ? PSHX maINH I) @
+(* [0x1980] PSHH *) (compile m ? PSHH maINH I) @
+(* [0x1981] LDHX 6,SP *) (compile m ? LDHX (maSP1 〈x0,x6〉) I) @
+(* [0x1984] PSHX *) (compile m ? PSHX maINH I) @
+(* [0x1985] PSHH *) (compile m ? PSHH maINH I) @
+(* [0x1986] LDHX 10,SP *) (compile m ? LDHX (maSP1 〈x0,xA〉) I) @
+(* [0x1989] STHX 8,SP *) (compile m ? STHX (maSP1 〈x0,x8〉) I) @
+(* [0x198C] LDHX 12,SP *) (compile m ? LDHX (maSP1 〈x0,xC〉) I) @
+(* [0x198F] JMP 0x195C *) (compile m ? JMP (maIMM2 〈〈x1,x9〉:〈x5,xC〉〉) I) @
+
+(*
+static void _IDIVMOD (char dummy_sgn, int j, int dummy, int i, ...) { ... }
+*)
+
+(* [0x1992] TST 4,SP *) (compile m ? TST (maSP1 〈x0,x4〉) I) @
+(* [0x1995] BNE *+28 ; 0x19B1 *) (compile m ? BNE (maIMM1 〈x1,xA〉) I) @
+(* [0x1997] TSX *) (compile m ? TSX maINH I) @
+(* [0x1998] LDA 7,X *) (compile m ? LDA (maIX1 〈x0,x7〉) I) @
+(* [0x199A] LDX 4,X *) (compile m ? LDX (maIX1 〈x0,x4〉) I) @
+(* [0x199C] CLRH *) (compile m ? CLR maINHH I) @
+(* [0x199D] DIV *) (compile m ? DIV maINH I) @
+(* [0x199E] STA 4,SP *) (compile m ? STA (maSP1 〈x0,x4〉) I) @
+(* [0x19A1] LDA 9,SP *) (compile m ? LDA (maSP1 〈x0,x9〉) I) @
+(* [0x19A4] DIV *) (compile m ? DIV maINH I) @
+(* [0x19A5] STA 5,SP *) (compile m ? STA (maSP1 〈x0,x5〉) I) @
+(* [0x19A8] CLR 8,SP *) (compile m ? CLR (maSP1 〈x0,x8〉) I) @
+(* [0x19AB] PSHH *) (compile m ? PSHH maINH I) @
+(* [0x19AC] PULA *) (compile m ? PULA maINH I) @
+(* [0x19AD] STA 9,SP *) (compile m ? STA (maSP1 〈x0,x9〉) I) @
+(* [0x19B0] RTS *) (compile m ? RTS maINH I) @
+(* [0x19B1] CLRA *) (compile m ? CLR maINHA I) @
+(* [0x19B2] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x19B3] LDX #0x08 *) (compile m ? LDX (maIMM1 〈x0,x8〉) I) @
+(* [0x19B5] CLC *) (compile m ? CLC maINH I) @
+(* [0x19B6] ROL 10,SP *) (compile m ? ROL (maSP1 〈x0,xA〉) I) @
+(* [0x19B9] ROL 9,SP *) (compile m ? ROL (maSP1 〈x0,x9〉) I) @
+(* [0x19BC] ROL 1,SP *) (compile m ? ROL (maSP1 〈x0,x1〉) I) @
+(* [0x19BF] LDA 5,SP *) (compile m ? LDA (maSP1 〈x0,x5〉) I) @
+(* [0x19C2] CMP 1,SP *) (compile m ? CMP (maSP1 〈x0,x1〉) I) @
+(* [0x19C5] BHI *+31 ; 0x19E4 *) (compile m ? BHI (maIMM1 〈x1,xD〉) I) @
+(* [0x19C7] BNE *+10 ; 0x19D1 *) (compile m ? BNE (maIMM1 〈x0,x8〉) I) @
+(* [0x19C9] LDA 6,SP *) (compile m ? LDA (maSP1 〈x0,x6〉) I) @
+(* [0x19CC] CMP 9,SP *) (compile m ? CMP (maSP1 〈x0,x9〉) I) @
+(* [0x19CF] BHI *+21 ; 0x19E4 *) (compile m ? BHI (maIMM1 〈x1,x3〉) I) @
+(* [0x19D1] LDA 9,SP *) (compile m ? LDA (maSP1 〈x0,x9〉) I) @
+(* [0x19D4] SUB 6,SP *) (compile m ? SUB (maSP1 〈x0,x6〉) I) @
+(* [0x19D7] STA 9,SP *) (compile m ? STA (maSP1 〈x0,x9〉) I) @
+(* [0x19DA] LDA 1,SP *) (compile m ? LDA (maSP1 〈x0,x1〉) I) @
+(* [0x19DD] SBC 5,SP *) (compile m ? SBC (maSP1 〈x0,x5〉) I) @
+(* [0x19E0] STA 1,SP *) (compile m ? STA (maSP1 〈x0,x1〉) I) @
+(* [0x19E3] SEC *) (compile m ? SEC maINH I) @
+(* [0x19E4] DBNZX *-46 ; 0x19B6 *) (compile m ? DBNZ (maINHX_and_IMM1 〈xD,x0〉) I) @
+(* [0x19E6] LDA 10,SP *) (compile m ? LDA (maSP1 〈x0,xA〉) I) @
+(* [0x19E9] ROLA *) (compile m ? ROL maINHA I) @
+(* [0x19EA] STA 6,SP *) (compile m ? STA (maSP1 〈x0,x6〉) I) @
+(* [0x19ED] LDA 9,SP *) (compile m ? LDA (maSP1 〈x0,x9〉) I) @
+(* [0x19F0] STA 10,SP *) (compile m ? STA (maSP1 〈x0,xA〉) I) @
+(* [0x19F3] PULA *) (compile m ? PULA maINH I) @
+(* [0x19F4] STA 8,SP *) (compile m ? STA (maSP1 〈x0,x8〉) I) @
+(* [0x19F7] CLR 4,SP *) (compile m ? CLR (maSP1 〈x0,x4〉) I) @
+(* [0x19FA] RTS *) (compile m ? RTS maINH I) @
+
+(*
+static void _LADD_k_is_k_plus_j(_PARAM_BINARY_L) { ... }
+*)
+
+(* [0x19FB] TSX *) (compile m ? TSX maINH I) @
+(* [0x19FC] LDA 18,X *) (compile m ? LDA (maIX1 〈x1,x2〉) I) @
+(* [0x19FE] ADD 5,X *) (compile m ? ADD (maIX1 〈x0,x5〉) I) @
+(* [0x1A00] STA 18,X *) (compile m ? STA (maIX1 〈x1,x2〉) I) @
+(* [0x1A02] LDA 17,X *) (compile m ? LDA (maIX1 〈x1,x1〉) I) @
+(* [0x1A04] ADC 4,X *) (compile m ? ADC (maIX1 〈x0,x4〉) I) @
+(* [0x1A06] STA 17,X *) (compile m ? STA (maIX1 〈x1,x1〉) I) @
+(* [0x1A08] LDA 16,X *) (compile m ? LDA (maIX1 〈x1,x0〉) I) @
+(* [0x1A0A] ADC 3,X *) (compile m ? ADC (maIX1 〈x0,x3〉) I) @
+(* [0x1A0C] STA 16,X *) (compile m ? STA (maIX1 〈x1,x0〉) I) @
+(* [0x1A0E] LDA 15,X *) (compile m ? LDA (maIX1 〈x0,xF〉) I) @
+(* [0x1A10] ADC 2,X *) (compile m ? ADC (maIX1 〈x0,x2〉) I) @
+(* [0x1A12] STA 15,X *) (compile m ? STA (maIX1 〈x0,xF〉) I) @
+(* [0x1A14] AIS #10 *) (compile m ? AIS (maIMM1 〈x0,xA〉) I) @
+(* [0x1A16] PULH *) (compile m ? PULH maINH I) @
+(* [0x1A17] PULX *) (compile m ? PULX maINH I) @
+(* [0x1A18] PULA *) (compile m ? PULA maINH I) @
+(* [0x1A19] RTS *) (compile m ? RTS maINH I) @
+
+(*
+void _IMODU_STAR08(int i, ...) { ... }
+*)
+
+(* [0x1A1A] AIS #-2 *) (compile m ? AIS (maIMM1 〈xF,xE〉) I) @
+(* [0x1A1C] STHX 1,SP *) (compile m ? STHX (maSP1 〈x0,x1〉) I) @
+(* [0x1A1F] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x1A20] JSR 0x1992 *) (compile m ? JSR (maIMM2 〈〈x1,x9〉:〈x9,x2〉〉) I) @
+(* [0x1A23] PULA *) (compile m ? PULA maINH I) @
+(* [0x1A24] AIS #2 *) (compile m ? AIS (maIMM1 〈x0,x2〉) I) @
+(* [0x1A26] LDHX 3,SP *) (compile m ? LDHX (maSP1 〈x0,x3〉) I) @
+(* [0x1A29] RTS *) (compile m ? RTS maINH I) @
+
+(*
+void _LADD(void) { ... }
+*)
+
+(* [0x1A2A] JSR 0x197C *) (compile m ? JSR (maIMM2 〈〈x1,x9〉:〈x7,xC〉〉) I) @
+(* [0x1A2D] JSR 0x19FB *) (compile m ? JSR (maIMM2 〈〈x1,x9〉:〈xF,xB〉〉) I) @
+
+(*
+void _POP32(void) { ... }
+*)
+
+(* [0x1A30] PSHA *) (compile m ? PSHA maINH I) @
+(* [0x1A31] LDA 4,SP *) (compile m ? LDA (maSP1 〈x0,x4〉) I) @
+(* [0x1A34] STA ,X *) (compile m ? STA maIX0 I) @
+(* [0x1A35] LDA 5,SP *) (compile m ? LDA (maSP1 〈x0,x5〉) I) @
+(* [0x1A38] STA 1,X *) (compile m ? STA (maIX1 〈x0,x1〉) I) @
+(* [0x1A3A] LDA 6,SP *) (compile m ? LDA (maSP1 〈x0,x6〉) I) @
+(* [0x1A3D] STA 2,X *) (compile m ? STA (maIX1 〈x0,x2〉) I) @
+(* [0x1A3F] LDA 7,SP *) (compile m ? LDA (maSP1 〈x0,x7〉) I) @
+(* [0x1A42] STA 3,X *) (compile m ? STA (maIX1 〈x0,x3〉) I) @
+(* [0x1A44] PULA *) (compile m ? PULA maINH I) @
+(* [0x1A45] PULH *) (compile m ? PULH maINH I) @
+(* [0x1A46] PULX *) (compile m ? PULX maINH I) @
+(* [0x1A47] AIS #4 *) (compile m ? AIS (maIMM1 〈x0,x4〉) I) @
+(* [0x1A49] JMP ,X *) (compile m ? JMP maINHX0ADD I)
+
+(* attraverso simulazione in CodeWarrior si puo' enunciare che dopo
+ 80+(65*n*(n+1)*(n+2))/6 si sara' entrati in stato STOP corrispondente
+ AFTER: HX=num PC=0x1951 I=0 *)
+ ).
+
+(* creazione del processore+caricamento+impostazione registri *)
+definition dTest_HCS08_gNum_status ≝
+λt:memory_impl.
+λI_op:bool.
+λA_op:byte8.
+λHX_op:word16.
+λPC_op:word16.
+λaddr:word16.
+λelems:word16.
+λdata:list byte8.
+ setweak_i_flag HCS08 t (* I<-I_op *)
+ (set_acc_8_low_reg HCS08 t (* A<-A_op *)
+ (set_z_flag HCS08 t (* Z<-true *)
+ (setweak_sp_reg HCS08 t (* SP<-0x016F *)
+ (setweak_indX_16_reg HCS08 t (* H:X<-HX_op *)
+ (set_pc_reg HCS08 t (* PC<-PC_op *)
+ (start_of_mcu_version_HCS08
+ MC9S08GB60 t
+ (load_from_source_at t (* carica data in RAM:dTest_HCS08_RAM *)
+ (load_from_source_at t (zero_memory t) (* carica source in ROM:addr *)
+ (dTest_HCS08_cSort_source elems) addr)
+ data dTest_HCS08_RAM)
+ (build_memory_type_of_mcu_version (FamilyHCS08 MC9S08GB60) t)
+ (mk_byte8 x0 x0) (mk_byte8 x0 x0) (* non deterministici tutti a 0 *)
+ false false false false false false) (* non deterministici tutti a 0 *)
+ PC_op)
+ HX_op)
+ (mk_word16 (mk_byte8 x0 x1) (mk_byte8 x6 xF)))
+ true)
+ A_op)
+ I_op.
+
+(* NUMERI AUREI: Somma divisori(x)=x, fino a 0xFFFF sono 6/28/496/8128 *)
+definition dTest_HCS08_gNum_aurei ≝
+λnum:word16.match gt_w16 num 〈〈x1,xF〉:〈xC,x0〉〉 with
+ [ true ⇒ [ 〈x0,x0〉 ; 〈x0,x6〉 ; 〈x0,x0〉 ; 〈x1,xC〉 ; 〈x0,x1〉 ; 〈xF,x0〉 ; 〈x1,xF〉 ; 〈xC,x0〉 ]
+ | false ⇒ match gt_w16 num 〈〈x0,x1〉:〈xF,x0〉〉 with
+ [ true ⇒ [ 〈x0,x0〉 ; 〈x0,x6〉 ; 〈x0,x0〉 ; 〈x1,xC〉 ; 〈x0,x1〉 ; 〈xF,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ]
+ | false ⇒ match gt_w16 num 〈〈x0,x0〉:〈x1,xC〉〉 with
+ [ true ⇒ [ 〈x0,x0〉 ; 〈x0,x6〉 ; 〈x0,x0〉 ; 〈x1,xC〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ]
+ | false ⇒ match gt_w16 num 〈〈x0,x0〉:〈x0,x6〉〉 with
+ [ true ⇒ [ 〈x0,x0〉 ; 〈x0,x6〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ]
+ | false ⇒ [ 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ]
+ ]
+ ]
+ ]
+ ] @ [ 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉
+ ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉
+ ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ; 〈x0,x0〉 ].
+
+(* esecuzione execute k*(n+2) *)
+let rec dTest_HCS08_gNum_execute1 (m:mcu_type) (t:memory_impl) (s:tick_result (any_status m t)) (n,ntot:nat) on n ≝
+ match s with
+ [ TickERR s' error ⇒ TickERR ? s' error
+ | TickSUSP s' susp ⇒ TickSUSP ? s' susp
+ | TickOK s' ⇒ match n with
+ [ O ⇒ TickOK ? s'
+ | S n' ⇒ dTest_HCS08_gNum_execute1 m t (execute m t (TickOK ? s') (ntot+2)) n' ntot ]
+ ].
+
+(* esecuzione execute k*(n+1)*(n+2) *)
+let rec dTest_HCS08_gNum_execute2 (m:mcu_type) (t:memory_impl) (s:tick_result (any_status m t)) (n,ntot:nat) on n ≝
+ match s with
+ [ TickERR s' error ⇒ TickERR ? s' error
+ | TickSUSP s' susp ⇒ TickSUSP ? s' susp
+ | TickOK s' ⇒ match n with
+ [ O ⇒ TickOK ? s'
+ | S n' ⇒ dTest_HCS08_gNum_execute2 m t (dTest_HCS08_gNum_execute1 m t (TickOK ? s') (ntot+1) ntot) n' ntot ]
+ ].
+
+(* esecuzione execute k*n*(n+1)*(n+2) *)
+let rec dTest_HCS08_gNum_execute3 (m:mcu_type) (t:memory_impl) (s:tick_result (any_status m t)) (n,ntot:nat) on n ≝
+ match s with
+ [ TickERR s' error ⇒ TickERR ? s' error
+ | TickSUSP s' susp ⇒ TickSUSP ? s' susp
+ | TickOK s' ⇒ match n with
+ [ O ⇒ TickOK ? s'
+ | S n' ⇒ dTest_HCS08_gNum_execute3 m t (dTest_HCS08_gNum_execute2 m t (TickOK ? s') ntot ntot) n' ntot ]
+ ].
+
+(* esecuzione execute 80+11*n*(n+1)*(n+2) *)
+definition dTest_HCS08_gNum_execute4 ≝
+λm:mcu_type.λt:memory_impl.λs:tick_result (any_status m t).λntot:nat.
+ match s with
+ [ TickERR s' error ⇒ TickERR ? s' error
+ | TickSUSP s' susp ⇒ TickSUSP ? s' susp
+ | TickOK s' ⇒ execute m t (dTest_HCS08_gNum_execute3 m t (TickOK ? s') 11 ntot) 80
+ ].
+
+(* parametrizzazione dell'enunciato del teorema parziale *)
+lemma dTest_HCS08_gNum_aux ≝
+λt:memory_impl.λnum:word16.
+ (* 2) match di esecuzione su tempo in forma di upperbound *)
+ match dTest_HCS08_gNum_execute4 HCS08 t
+ (TickOK ? (dTest_HCS08_gNum_status t true 〈x0,x0〉 〈〈x1,xA〉:〈x0,x0〉〉 〈〈x1,x8〉:〈xB,xE〉〉 〈〈x1,x8〉:〈xB,xE〉〉 num dTest_zeros))
+ (* tempo di esecuzione 80+11*n*(n+1)*(n+2) *)
+ (nat_of_word16 num) with
+ [ TickERR s _ ⇒ None ?
+ (* azzeramento tutta RAM tranne dati *)
+ | TickSUSP s _ ⇒ Some ? (set_mem_desc HCS08 t s (load_from_source_at t (get_mem_desc HCS08 t s) dTest_zeros3K 〈〈x0,x1〉:〈x2,x0〉〉))
+ | TickOK s ⇒ None ?
+ ] =
+ Some ? (dTest_HCS08_gNum_status t false 〈x0,x0〉 num 〈〈x1,x9〉:〈x5,x1〉〉 〈〈x1,x8〉:〈xB,xE〉〉 num (dTest_HCS08_gNum_aurei num)).
+
+definition gNumCalc ≝
+λnum:word16.
+ match dTest_HCS08_gNum_execute4 HCS08 MEM_TREE
+ (TickOK ? (dTest_HCS08_gNum_status MEM_TREE true 〈x0,x0〉 〈〈x1,xA〉:〈x0,x0〉〉 〈〈x1,x8〉:〈xB,xE〉〉 〈〈x1,x8〉:〈xB,xE〉〉 num dTest_zeros))
+ (nat_of_word16 num) with
+ [ TickERR s _ ⇒ None ?
+ | TickSUSP s _ ⇒ Some ? (set_mem_desc HCS08 MEM_TREE s (load_from_source_at MEM_TREE (get_mem_desc HCS08 MEM_TREE s) dTest_zeros3K 〈〈x0,x1〉:〈x2,x0〉〉))
+ | TickOK s ⇒ None ?
+ ].
+
+definition gNumNoCalc ≝
+λnum:word16.
+ Some ? (dTest_HCS08_gNum_status MEM_TREE false 〈x0,x0〉 num 〈〈x1,x9〉:〈x5,x1〉〉 〈〈x1,x8〉:〈xB,xE〉〉 num (dTest_HCS08_gNum_aurei num)).
+
+definition gNumCalc1 ≝ gNumCalc 〈〈x0,x0〉:〈x0,x1〉〉.
+definition gNumCalc2 ≝ gNumCalc 〈〈x0,x0〉:〈x0,x2〉〉.
+definition gNumCalc5 ≝ gNumCalc 〈〈x0,x0〉:〈x0,x5〉〉.
+definition gNumCalc10 ≝ gNumCalc 〈〈x0,x0〉:〈x0,xA〉〉.
+definition gNumCalc20 ≝ gNumCalc 〈〈x0,x0〉:〈x1,x4〉〉.
+definition gNumCalc50 ≝ gNumCalc 〈〈x0,x0〉:〈x3,x2〉〉.
+definition gNumCalc100 ≝ gNumCalc 〈〈x0,x0〉:〈x6,x4〉〉.
+definition gNumCalc250 ≝ gNumCalc 〈〈x0,x0〉:〈xF,xA〉〉.
+definition gNumCalc500 ≝ gNumCalc 〈〈x0,x1〉:〈xF,x4〉〉.
+definition gNumCalc1000 ≝ gNumCalc 〈〈x0,x3〉:〈xE,x8〉〉.
+
+definition gNumNoCalc1 ≝ gNumNoCalc 〈〈x0,x0〉:〈x0,x1〉〉.
+definition gNumNoCalc2 ≝ gNumNoCalc 〈〈x0,x0〉:〈x0,x2〉〉.
+definition gNumNoCalc5 ≝ gNumNoCalc 〈〈x0,x0〉:〈x0,x5〉〉.
+definition gNumNoCalc10 ≝ gNumNoCalc 〈〈x0,x0〉:〈x0,xA〉〉.
+definition gNumNoCalc20 ≝ gNumNoCalc 〈〈x0,x0〉:〈x1,x4〉〉.
+definition gNumNoCalc50 ≝ gNumNoCalc 〈〈x0,x0〉:〈x3,x2〉〉.
+definition gNumNoCalc100 ≝ gNumNoCalc 〈〈x0,x0〉:〈x6,x4〉〉.
+definition gNumNoCalc250 ≝ gNumNoCalc 〈〈x0,x0〉:〈xF,xA〉〉.
+definition gNumNoCalc500 ≝ gNumNoCalc 〈〈x0,x1〉:〈xF,x4〉〉.
+definition gNumNoCalc1000 ≝ gNumNoCalc 〈〈x0,x3〉:〈xE,x8〉〉.
+*)
+
--- /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/multivm.ma".
+
+(* ********* *)
+(* INDIRIZZI *)
+(* ********* *)
+
+(* specifico per MC9S08GB60 in modo da caricare codice compilato da CodeWarrior *)
+(* l'obbiettivo e' dimostrare una routine scritta in C *)
+(* passo 1 e' formalizzare l'uso di 3Kb dei 4Kb di RAM [0x0100-0x0CFF] *)
+ndefinition dTest_HCS08_RAM ≝ 〈〈x0,x1〉:〈x0,x0〉〉.
+ndefinition dTest_HCS08_prog ≝ 〈〈x1,x8〉:〈xC,x8〉〉.
+
+(* ***** *)
+(* TOOLS *)
+(* ***** *)
+
+(* visita di un albero da 256B di elementi: ln16(256)=2 passaggi *)
+ndefinition dTest_visit ≝
+λdata:Array16T (Array16T (list byte8)).λaddr:byte8.
+ getn_array16T (b8l addr) ?
+ (getn_array16T (b8h addr) ? data).
+
+(* scrittura di un elemento in un albero da 256B *)
+ndefinition dTest_update ≝
+λdata:Array16T (Array16T (list byte8)).λaddr:byte8.λv:list byte8.
+ let lev2 ≝ getn_array16T (b8h addr) ? data in
+ setn_array16T (b8h addr) ? data
+ (setn_array16T (b8l addr) ? lev2 v) .
+
+(* array a 0 *)
+ndefinition dTest_zero_array ≝
+let elem ≝ nil byte8 in
+let lev2 ≝ array_16T ?
+ elem elem elem elem elem elem elem elem
+ elem elem elem elem elem elem elem elem
+ in
+let lev1 ≝ array_16T ?
+ lev2 lev2 lev2 lev2 lev2 lev2 lev2 lev2
+ lev2 lev2 lev2 lev2 lev2 lev2 lev2 lev2
+ in
+lev1.
+
+(* incrementa n-simo elemento *)
+ndefinition dTest_inc ≝
+λdata:Array16T (Array16T (list byte8)).λaddr:byte8.
+ dTest_update data addr ((dTest_visit data addr)@[ addr ]).
+
+(* costruisce una lista a partire dai conteggi per elemento *)
+ndefinition dTest_build_list_from_count ≝
+λdata:Array16T (Array16T (list byte8)).
+ let aux1 ≝ λparam1:Array16T (list byte8).
+ match param1 with
+ [ array_16T e00 e01 e02 e03 e04 e05 e06 e07 e08 e09 e10 e11 e12 e13 e14 e15 ⇒
+ e00@e01@e02@e03@e04@e05@e06@e07@e08@e09@e10@e11@e12@e13@e14@e15 ] in
+ let aux2 ≝ λparam2:Array16T (Array16T (list byte8)).
+ match param2 with
+ [ array_16T e00 e01 e02 e03 e04 e05 e06 e07 e08 e09 e10 e11 e12 e13 e14 e15 ⇒
+ (aux1 e00)@(aux1 e01)@(aux1 e02)@(aux1 e03)@(aux1 e04)@(aux1 e05)@(aux1 e06)@(aux1 e07)@
+ (aux1 e08)@(aux1 e09)@(aux1 e10)@(aux1 e11)@(aux1 e12)@(aux1 e13)@(aux1 e14)@(aux1 e15) ] in
+ aux2 data.
+
+(* ci sono ora tutti gli elementi per definire l'ordinamento *)
+(* di una lista di byte8 secondo il counting sort *)
+nlet rec byte8_list_ordering_aux (source:list byte8) (count:Array16T (Array16T (list byte8))) on source ≝
+ match source with
+ [ nil ⇒ dTest_build_list_from_count count
+ | cons hd tl ⇒ byte8_list_ordering_aux tl (dTest_inc count hd)
+ ].
+
+ndefinition byte8_list_ordering ≝
+λsource:list byte8.byte8_list_ordering_aux source dTest_zero_array.
+
+(* strlen esadecimale limitato, considerando overflow! *)
+nlet rec byte8_bounded_strlen_aux (source:list byte8) (count,limit:word16) on source ≝
+ match source with
+ [ nil ⇒ True
+ | cons _ tl ⇒ match eq_w16 count 〈〈xF,xF〉:〈xF,xF〉〉 with
+ [ true ⇒ False
+ | false ⇒ match le_w16 (succ_w16 count) limit with
+ [ true ⇒ byte8_bounded_strlen_aux tl (succ_w16 count) limit
+ | false ⇒ False
+ ]
+ ]
+ ].
+
+ndefinition byte8_bounded_strlen ≝
+λsource:list byte8.λlimit:word16.
+ byte8_bounded_strlen_aux source 〈〈x0,x0〉:〈x0,x0〉〉 limit.
+
+(* strlen esadecimale normale *)
+nlet rec byte8_strlen_aux (source:list byte8) (count:word16) on source ≝
+ match source with
+ [ nil ⇒ count
+ | cons _ tl ⇒ byte8_strlen_aux tl (succ_w16 count)
+ ].
+
+ndefinition byte8_strlen ≝
+λsource:list byte8.
+ byte8_strlen_aux source 〈〈x0,x0〉:〈x0,x0〉〉.
+
+(* hex dump: memory -> list byte8 *)
+nlet rec byte8_hexdump_aux (t:memory_impl) (mem:aux_mem_type t) (inf:word16) (count:nat) (out:list byte8) on count ≝
+ match count with
+ [ O ⇒ out
+ | S n ⇒ byte8_hexdump_aux t mem (succ_w16 inf) n (out@[ mem_read_abs t mem inf ])
+ ].
+
+ndefinition byte8_hexdump ≝
+λt:memory_impl.λmem:aux_mem_type t.λinf:word16.λcount:nat.
+ byte8_hexdump_aux t mem inf count [].
+
+(* ************* *)
+(* TEST PATTERNS *)
+(* ************* *)
+
+(* lista di 3072 numeri random generati da Mathematica, in blocchi da 32 *)
+ndefinition dTest_random_ex00 ≝
+[〈x8,x1〉;〈x5,xE〉;〈x7,x6〉;〈xD,x1〉;〈x7,x5〉;〈x1,x0〉;〈x8,x5〉;〈x9,x0〉;〈x1,xF〉;〈x1,x2〉;〈xE,x2〉;〈x3,xC〉;〈x1,xD〉;〈x0,x6〉;〈x3,xC〉;〈xD,x1〉
+;〈x8,x3〉;〈xE,xB〉;〈x7,x2〉;〈x1,xF〉;〈x9,x0〉;〈xF,x0〉;〈x4,x7〉;〈xA,x3〉;〈xD,x0〉;〈x4,x6〉;〈xC,x5〉;〈x3,x2〉;〈xC,x9〉;〈x0,xB〉;〈x1,xB〉;〈x7,x3〉 ].
+
+ndefinition dTest_random_ex01 ≝
+[〈x1,x1〉;〈xA,xF〉;〈xD,x2〉;〈xB,xF〉;〈x0,xB〉;〈xB,xC〉;〈x0,x8〉;〈xE,x5〉;〈xF,xE〉;〈xA,xC〉;〈xF,xC〉;〈x9,x4〉;〈x3,x4〉;〈x8,x8〉;〈x2,x8〉;〈xD,xB〉
+;〈xD,x3〉;〈x3,xD〉;〈x3,x8〉;〈x6,xA〉;〈x4,xD〉;〈x7,x4〉;〈x4,x9〉;〈x7,xE〉;〈x6,xF〉;〈x4,xD〉;〈x3,xD〉;〈x3,xA〉;〈xC,x2〉;〈xD,x3〉;〈x3,x6〉;〈x7,x0〉 ].
+
+ndefinition dTest_random_ex02 ≝
+[〈x8,x0〉;〈xC,x9〉;〈x3,xB〉;〈x5,x2〉;〈x8,xF〉;〈x1,xE〉;〈x8,x4〉;〈x5,x2〉;〈x2,xD〉;〈xA,xF〉;〈x1,xB〉;〈x0,x1〉;〈x3,x5〉;〈x7,x2〉;〈x1,x0〉;〈x0,x7〉
+;〈x5,xD〉;〈xA,xB〉;〈xE,x0〉;〈x7,x6〉;〈xB,xD〉;〈x3,xC〉;〈x0,xD〉;〈xC,xE〉;〈xB,x7〉;〈x9,xD〉;〈xA,x9〉;〈xF,x3〉;〈xC,x1〉;〈x9,x3〉;〈x8,xC〉;〈x4,xE〉 ].
+
+ndefinition dTest_random_ex03 ≝
+[〈xF,x8〉;〈xC,x3〉;〈x1,x3〉;〈x3,xA〉;〈xA,x2〉;〈xB,xD〉;〈x1,x0〉;〈x9,xB〉;〈x5,xC〉;〈xC,x8〉;〈xE,x5〉;〈xC,x8〉;〈xA,x6〉;〈xF,xB〉;〈x1,x3〉;〈xC,x8〉
+;〈x6,x4〉;〈x0,x9〉;〈xD,x6〉;〈xD,x7〉;〈x3,x9〉;〈xF,x9〉;〈xE,x4〉;〈x0,x3〉;〈x4,x9〉;〈xC,xE〉;〈x7,x1〉;〈x5,x7〉;〈x3,x4〉;〈x2,xE〉;〈xA,x3〉;〈x5,x3〉 ].
+
+ndefinition dTest_random_ex04 ≝
+[〈xF,x9〉;〈x2,xA〉;〈xF,x0〉;〈xE,x1〉;〈x6,x6〉;〈x8,x9〉;〈x2,xE〉;〈x8,x6〉;〈xC,x7〉;〈x2,xD〉;〈x1,x2〉;〈xD,x5〉;〈x4,xA〉;〈x7,x9〉;〈x6,xD〉;〈x1,xB〉
+;〈x4,x1〉;〈x9,x4〉;〈x6,xC〉;〈x6,xD〉;〈xF,x4〉;〈x5,xD〉;〈x8,xB〉;〈xB,xE〉;〈xC,x8〉;〈xE,x5〉;〈xA,x4〉;〈xB,xA〉;〈xB,x1〉;〈x2,x1〉;〈x5,x0〉;〈x6,xB〉 ].
+
+ndefinition dTest_random_ex05 ≝
+[〈x9,x5〉;〈x0,x6〉;〈x4,x5〉;〈xE,x0〉;〈x0,xF〉;〈x5,xA〉;〈xC,xE〉;〈xC,x8〉;〈x8,x2〉;〈x4,xF〉;〈xC,x2〉;〈xF,x5〉;〈xF,x8〉;〈x1,x3〉;〈xD,xA〉;〈x2,xB〉
+;〈x7,x9〉;〈xB,xF〉;〈xA,x4〉;〈x5,xA〉;〈xD,x2〉;〈x7,x6〉;〈x8,xD〉;〈x1,xF〉;〈x1,x5〉;〈x5,xA〉;〈xD,xE〉;〈x2,x3〉;〈x9,xD〉;〈x7,xE〉;〈x6,x7〉;〈x6,x3〉 ].
+
+ndefinition dTest_random_ex06 ≝
+[〈x1,x1〉;〈xF,x5〉;〈x2,x4〉;〈xD,x6〉;〈x6,xA〉;〈x0,xC〉;〈x7,xF〉;〈x1,x2〉;〈xD,x6〉;〈xE,xE〉;〈xB,xA〉;〈x4,x4〉;〈x3,x9〉;〈x9,x2〉;〈x6,x6〉;〈xE,xA〉
+;〈x2,x3〉;〈x4,x4〉;〈xC,xF〉;〈x7,x4〉;〈x6,xB〉;〈x8,x3〉;〈x7,x7〉;〈x0,x4〉;〈x6,x4〉;〈xB,x3〉;〈x3,xC〉;〈x2,x6〉;〈xF,xC〉;〈xD,x5〉;〈x4,x1〉;〈xB,x7〉 ].
+
+ndefinition dTest_random_ex07 ≝
+[〈x2,x4〉;〈xE,x0〉;〈xB,x4〉;〈x1,x3〉;〈x3,x2〉;〈x4,x5〉;〈x1,x8〉;〈xD,xB〉;〈x0,x0〉;〈xB,x6〉;〈x5,xF〉;〈x3,xA〉;〈xB,x7〉;〈x4,xF〉;〈xB,x4〉;〈xD,xF〉
+;〈xF,x4〉;〈x1,xA〉;〈x1,x0〉;〈xE,x9〉;〈xC,x5〉;〈x2,xC〉;〈xB,xC〉;〈x5,xB〉;〈x0,x5〉;〈x4,xA〉;〈x5,x2〉;〈xC,x0〉;〈x1,xF〉;〈x5,x9〉;〈xF,x2〉;〈xE,x5〉 ].
+
+ndefinition dTest_random_ex08 ≝
+[〈x9,x7〉;〈x5,x1〉;〈xF,x7〉;〈x3,xC〉;〈x7,x7〉;〈x8,x1〉;〈x7,xC〉;〈xB,x0〉;〈x1,xD〉;〈x1,xA〉;〈x7,xB〉;〈x4,x7〉;〈x7,x9〉;〈xC,x2〉;〈x3,xF〉;〈xD,x3〉
+;〈xB,x6〉;〈xD,x7〉;〈xC,x9〉;〈x9,x2〉;〈x0,xD〉;〈x7,xF〉;〈x0,xB〉;〈x7,x5〉;〈x0,xE〉;〈x5,x1〉;〈x9,xF〉;〈x4,xC〉;〈xE,x5〉;〈xD,x0〉;〈xC,x1〉;〈x3,x9〉 ].
+
+ndefinition dTest_random_ex09 ≝
+[〈x7,xF〉;〈xE,xA〉;〈x4,x1〉;〈x0,x5〉;〈x0,x8〉;〈x7,xE〉;〈x7,x6〉;〈x2,xF〉;〈x6,x2〉;〈x7,x1〉;〈xF,x8〉;〈x3,x8〉;〈xB,x6〉;〈x7,x0〉;〈xD,xD〉;〈xD,x0〉
+;〈xA,xD〉;〈x7,x8〉;〈x3,xD〉;〈x7,xB〉;〈xC,xC〉;〈x6,xD〉;〈x3,xF〉;〈xA,xC〉;〈xC,x7〉;〈x6,xE〉;〈xF,xF〉;〈x4,x5〉;〈xC,x1〉;〈x7,x4〉;〈xB,xF〉;〈x2,x9〉 ].
+
+ndefinition dTest_random_ex0A ≝
+[〈x4,x9〉;〈xC,x5〉;〈x7,xC〉;〈x2,xD〉;〈xF,x2〉;〈xC,xC〉;〈xF,xA〉;〈x5,x8〉;〈xA,xC〉;〈x5,x8〉;〈x5,x1〉;〈x0,xE〉;〈x4,x8〉;〈x7,x0〉;〈x4,x1〉;〈xE,xD〉
+;〈x9,x5〉;〈xB,x4〉;〈x4,x7〉;〈xF,x1〉;〈x8,x1〉;〈xE,x4〉;〈x4,x0〉;〈x5,x4〉;〈x7,xB〉;〈xA,x1〉;〈xD,x2〉;〈x0,x2〉;〈xC,x5〉;〈x7,xD〉;〈x7,xA〉;〈xF,x1〉 ].
+
+ndefinition dTest_random_ex0B ≝
+[〈x0,x0〉;〈x8,xD〉;〈x6,x6〉;〈xB,x0〉;〈xA,x9〉;〈x7,xA〉;〈x2,xB〉;〈x2,xC〉;〈x6,xF〉;〈x5,xF〉;〈x6,xF〉;〈x4,xE〉;〈x2,xB〉;〈x1,x1〉;〈xF,xF〉;〈x4,x7〉
+;〈x7,xF〉;〈xC,xF〉;〈xD,x3〉;〈x8,x5〉;〈xB,x8〉;〈x4,xD〉;〈x9,x9〉;〈x8,x3〉;〈x7,x6〉;〈xE,x8〉;〈x3,x0〉;〈xF,x8〉;〈xD,x0〉;〈x5,x9〉;〈xB,x8〉;〈x7,x1〉 ].
+
+ndefinition dTest_random_ex0C ≝
+[〈x5,x7〉;〈xA,xF〉;〈xB,x5〉;〈xD,x5〉;〈xF,xC〉;〈x8,x2〉;〈x1,x6〉;〈x1,x0〉;〈xB,x3〉;〈xC,x1〉;〈x1,xA〉;〈x0,x1〉;〈x1,x1〉;〈xF,xF〉;〈x5,x9〉;〈x2,x4〉
+;〈xC,x5〉;〈x7,x2〉;〈xD,x8〉;〈xD,x0〉;〈xA,xD〉;〈xF,xE〉;〈xD,x7〉;〈x1,x1〉;〈xC,xE〉;〈xF,x9〉;〈xB,x8〉;〈x7,x7〉;〈x3,xA〉;〈x1,xF〉;〈x6,x1〉;〈x1,xB〉 ].
+
+ndefinition dTest_random_ex0D ≝
+[〈xB,xB〉;〈x5,x5〉;〈x8,x0〉;〈x7,xC〉;〈x2,x5〉;〈x3,x4〉;〈x8,x9〉;〈xF,x2〉;〈xC,x9〉;〈xD,xF〉;〈x3,x5〉;〈xC,x5〉;〈x1,x2〉;〈xF,x0〉;〈x0,x5〉;〈xD,xE〉
+;〈x2,x6〉;〈x4,x9〉;〈xB,x7〉;〈x3,x9〉;〈x0,x5〉;〈xC,x2〉;〈xD,xB〉;〈xF,xC〉;〈x9,xF〉;〈xA,x9〉;〈x6,x6〉;〈xA,xD〉;〈x4,xA〉;〈x3,xF〉;〈xB,xF〉;〈x6,xD〉 ].
+
+ndefinition dTest_random_ex0E ≝
+[〈x8,x7〉;〈x6,xA〉;〈xB,x1〉;〈x3,xE〉;〈xB,x6〉;〈x0,xE〉;〈x7,xA〉;〈x3,xB〉;〈x4,x5〉;〈xE,x9〉;〈xC,xE〉;〈x6,xA〉;〈x6,xA〉;〈x7,x0〉;〈x6,x0〉;〈x6,xA〉
+;〈x2,xC〉;〈xD,x2〉;〈xB,x8〉;〈x3,x6〉;〈x2,x1〉;〈x0,x0〉;〈x5,x4〉;〈x3,x1〉;〈x6,x0〉;〈x1,xB〉;〈x4,xC〉;〈xC,xA〉;〈xB,xE〉;〈x5,xF〉;〈x8,x1〉;〈xB,x7〉 ].
+
+ndefinition dTest_random_ex0F ≝
+[〈x9,xB〉;〈x2,x6〉;〈x9,x4〉;〈x2,xB〉;〈x4,x1〉;〈x2,xB〉;〈x9,x8〉;〈x6,x3〉;〈x6,x6〉;〈x6,x5〉;〈x4,x6〉;〈x2,x3〉;〈xE,x5〉;〈x0,x7〉;〈x9,xE〉;〈x1,xC〉
+;〈x3,x8〉;〈x5,xC〉;〈x9,x7〉;〈x6,x3〉;〈x5,x3〉;〈x6,x6〉;〈x0,x8〉;〈x5,xD〉;〈x0,x8〉;〈xD,xB〉;〈x6,xE〉;〈x5,x6〉;〈x7,x0〉;〈x3,x2〉;〈x4,x5〉;〈x0,x2〉 ].
+
+ndefinition dTest_random_ex10 ≝
+[〈x6,x3〉;〈x7,x2〉;〈x9,xC〉;〈xD,x9〉;〈x5,x0〉;〈x0,x6〉;〈x5,x9〉;〈x1,x7〉;〈x6,x8〉;〈xD,x2〉;〈xD,x7〉;〈x8,xE〉;〈x6,x9〉;〈x5,xF〉;〈x8,x1〉;〈x8,x4〉
+;〈x8,x7〉;〈xD,xC〉;〈x9,x8〉;〈xE,x5〉;〈xB,x5〉;〈xC,x3〉;〈x2,x5〉;〈x6,xC〉;〈x9,x2〉;〈xD,xD〉;〈x2,xA〉;〈xD,x1〉;〈x1,x4〉;〈x7,xE〉;〈x1,x7〉;〈xB,x2〉 ].
+
+ndefinition dTest_random_ex11 ≝
+[〈x9,x8〉;〈x5,x5〉;〈xF,xC〉;〈x3,xD〉;〈x8,xD〉;〈xE,xF〉;〈x8,x1〉;〈xB,x8〉;〈xB,xB〉;〈x5,x1〉;〈x0,x0〉;〈xB,x4〉;〈x2,xE〉;〈x3,x0〉;〈x6,x0〉;〈x7,xE〉
+;〈x9,x0〉;〈xE,x3〉;〈xF,x4〉;〈x7,x2〉;〈x1,xC〉;〈xB,x3〉;〈x7,x8〉;〈x1,xB〉;〈x9,xF〉;〈x1,xB〉;〈x0,x3〉;〈xA,x3〉;〈x0,x5〉;〈xD,xE〉;〈x3,x8〉;〈xB,xA〉 ].
+
+ndefinition dTest_random_ex12 ≝
+[〈x0,xE〉;〈xE,xD〉;〈xE,xC〉;〈x1,xF〉;〈x3,x8〉;〈xE,x3〉;〈xF,x7〉;〈xA,xA〉;〈xE,x9〉;〈x3,xD〉;〈xF,xF〉;〈xF,x3〉;〈x1,x4〉;〈x2,xC〉;〈x8,x8〉;〈x6,x1〉
+;〈x3,x0〉;〈xA,xB〉;〈x1,x8〉;〈xD,xC〉;〈xF,xE〉;〈x6,xA〉;〈x2,x9〉;〈xF,x1〉;〈xC,xB〉;〈x9,x0〉;〈x7,x8〉;〈x9,x9〉;〈x1,xF〉;〈x2,x8〉;〈xF,x9〉;〈xC,xB〉 ].
+
+ndefinition dTest_random_ex13 ≝
+[〈x1,x4〉;〈x8,x4〉;〈xF,x3〉;〈xD,x6〉;〈x7,xE〉;〈xE,xC〉;〈x5,x6〉;〈xC,xE〉;〈xD,xA〉;〈x5,xE〉;〈x6,x1〉;〈xF,x1〉;〈x6,x6〉;〈x6,x9〉;〈x9,x3〉;〈x5,x9〉
+;〈x3,xC〉;〈x1,xD〉;〈x6,xB〉;〈xF,x4〉;〈x5,x9〉;〈x4,xD〉;〈x3,x8〉;〈xA,x9〉;〈x3,xB〉;〈x7,xF〉;〈xB,x2〉;〈xE,xC〉;〈xA,xE〉;〈xF,x6〉;〈xB,x2〉;〈x2,x2〉 ].
+
+ndefinition dTest_random_ex14 ≝
+[〈x6,x4〉;〈x2,x7〉;〈x6,xC〉;〈x2,x0〉;〈xE,xE〉;〈x5,x1〉;〈x3,xE〉;〈x8,x8〉;〈xD,xD〉;〈xC,x1〉;〈xD,xC〉;〈xC,x1〉;〈x6,x6〉;〈x6,x1〉;〈x4,x2〉;〈x7,x7〉
+;〈x3,x6〉;〈x0,x8〉;〈x2,x9〉;〈x6,x0〉;〈xA,x9〉;〈xF,xC〉;〈x7,xC〉;〈xA,x7〉;〈xB,x4〉;〈xF,xC〉;〈x8,x7〉;〈x1,xD〉;〈x6,xC〉;〈xA,x2〉;〈x3,xF〉;〈x1,xD〉 ].
+
+ndefinition dTest_random_ex15 ≝
+[〈x1,x7〉;〈x0,xF〉;〈x0,x2〉;〈x2,x6〉;〈xA,x2〉;〈x6,xA〉;〈x5,xC〉;〈xE,xD〉;〈x2,x7〉;〈xC,x5〉;〈x7,xB〉;〈xF,x5〉;〈x9,xC〉;〈x8,x5〉;〈x6,x3〉;〈x5,x6〉
+;〈xC,x3〉;〈x4,xB〉;〈x1,xB〉;〈xA,x0〉;〈x1,xB〉;〈x8,x9〉;〈x3,x5〉;〈xD,x6〉;〈xD,x9〉;〈xD,xD〉;〈x2,xE〉;〈x6,x2〉;〈x7,x5〉;〈xE,x7〉;〈x1,x8〉;〈x4,xD〉 ].
+
+ndefinition dTest_random_ex16 ≝
+[〈xD,x7〉;〈x5,x8〉;〈xA,x7〉;〈x5,xF〉;〈x9,x4〉;〈x8,x7〉;〈xA,x8〉;〈xE,x7〉;〈x2,xB〉;〈xF,x2〉;〈xE,x7〉;〈xB,x9〉;〈x0,x6〉;〈xA,xF〉;〈xD,xA〉;〈xD,xC〉
+;〈xC,x6〉;〈x3,xF〉;〈x8,xD〉;〈x7,x9〉;〈x9,x5〉;〈xD,xA〉;〈x5,xB〉;〈x9,x2〉;〈xE,xE〉;〈x3,xC〉;〈xF,xE〉;〈x4,x9〉;〈x5,xA〉;〈x1,x0〉;〈x4,xD〉;〈x8,x9〉 ].
+
+ndefinition dTest_random_ex17 ≝
+[〈x8,x3〉;〈x2,x6〉;〈xE,xC〉;〈x8,xD〉;〈xC,x9〉;〈x7,x7〉;〈xE,xE〉;〈xF,x1〉;〈x4,x0〉;〈x6,xD〉;〈x4,x9〉;〈x5,x7〉;〈x9,xB〉;〈xC,x4〉;〈x1,xF〉;〈x8,x0〉
+;〈x9,x5〉;〈xB,xC〉;〈xE,x8〉;〈xF,x9〉;〈xD,x7〉;〈x1,x4〉;〈x3,xE〉;〈xC,x3〉;〈x6,xF〉;〈x8,xF〉;〈x7,x2〉;〈xD,x5〉;〈xB,xE〉;〈x8,xA〉;〈xA,x3〉;〈xF,x7〉 ].
+
+ndefinition dTest_random_ex18 ≝
+[〈x6,x0〉;〈x3,xA〉;〈x7,x4〉;〈xF,xB〉;〈xB,xD〉;〈x7,x4〉;〈x8,x3〉;〈xE,x3〉;〈x9,xD〉;〈xD,x9〉;〈xB,x8〉;〈x1,x3〉;〈x5,x0〉;〈x4,x0〉;〈x8,xA〉;〈x9,x6〉
+;〈x3,xA〉;〈xA,x6〉;〈xE,xC〉;〈x7,xC〉;〈x1,x5〉;〈x8,x7〉;〈x4,xD〉;〈x6,xA〉;〈xA,xA〉;〈xE,x0〉;〈xB,xA〉;〈xF,xF〉;〈x3,xB〉;〈xE,x2〉;〈x5,x1〉;〈x2,x2〉 ].
+
+ndefinition dTest_random_ex19 ≝
+[〈x2,x2〉;〈x1,xF〉;〈xA,x1〉;〈x2,x1〉;〈xA,xF〉;〈x3,x7〉;〈x8,xA〉;〈xD,xF〉;〈xE,x3〉;〈x6,x9〉;〈xE,xE〉;〈xC,x4〉;〈xE,x7〉;〈x7,x1〉;〈x9,x6〉;〈x1,x1〉
+;〈xE,x4〉;〈x3,x9〉;〈xE,x5〉;〈xA,xF〉;〈xF,x5〉;〈x5,x7〉;〈xE,xB〉;〈x5,x5〉;〈x6,x5〉;〈x8,xB〉;〈x3,xE〉;〈x8,xD〉;〈x4,x6〉;〈x5,x3〉;〈xB,x2〉;〈x1,x9〉 ].
+
+ndefinition dTest_random_ex1A ≝
+[〈x3,x4〉;〈xE,x9〉;〈x4,xA〉;〈x4,xB〉;〈x5,x2〉;〈x3,x0〉;〈x3,xF〉;〈xA,x7〉;〈x4,xF〉;〈x1,xA〉;〈xB,x8〉;〈x6,x4〉;〈x5,xB〉;〈xD,x9〉;〈x6,xD〉;〈x6,x1〉
+;〈xA,x5〉;〈xC,xF〉;〈x8,xC〉;〈xD,xD〉;〈xE,x6〉;〈xD,x5〉;〈x3,x6〉;〈x0,xC〉;〈x8,xD〉;〈xF,x7〉;〈x4,xE〉;〈x9,xC〉;〈xB,xF〉;〈x2,xB〉;〈x4,x4〉;〈xD,x1〉 ].
+
+ndefinition dTest_random_ex1B ≝
+[〈xC,x0〉;〈x8,x0〉;〈x0,x8〉;〈xA,xD〉;〈xC,xE〉;〈xB,xD〉;〈x4,xC〉;〈x5,x3〉;〈x6,x5〉;〈xB,x6〉;〈x4,x8〉;〈xF,x6〉;〈x6,x4〉;〈x7,xC〉;〈x9,x8〉;〈x1,x0〉
+;〈x9,xD〉;〈xF,xD〉;〈x4,x9〉;〈xC,x4〉;〈xD,xD〉;〈x1,x4〉;〈xB,x6〉;〈x6,xF〉;〈x3,xB〉;〈x4,x6〉;〈xD,x7〉;〈x1,xA〉;〈x4,x4〉;〈xA,x4〉;〈x8,x1〉;〈x3,x1〉 ].
+
+ndefinition dTest_random_ex1C ≝
+[〈xA,x2〉;〈x4,x0〉;〈x7,x0〉;〈x3,x9〉;〈x9,xA〉;〈x4,xC〉;〈x4,xF〉;〈x9,x3〉;〈x9,xD〉;〈xD,x4〉;〈x9,x7〉;〈x3,x9〉;〈xA,x8〉;〈xA,x8〉;〈xF,x9〉;〈xB,x3〉
+;〈xE,x7〉;〈xD,x8〉;〈x4,xD〉;〈x6,xD〉;〈x8,x8〉;〈x6,xB〉;〈x5,x4〉;〈x5,x5〉;〈x9,x2〉;〈x1,x9〉;〈xE,x4〉;〈xB,x1〉;〈xE,x3〉;〈x4,x6〉;〈xD,x5〉;〈x6,xC〉 ].
+
+ndefinition dTest_random_ex1D ≝
+[〈xF,x9〉;〈x3,x3〉;〈xE,x5〉;〈xD,x2〉;〈x7,x7〉;〈x1,x8〉;〈x8,x6〉;〈x1,x4〉;〈x7,xE〉;〈x1,xE〉;〈xC,x8〉;〈xB,x4〉;〈xC,xE〉;〈xC,x7〉;〈x5,x7〉;〈x2,xD〉
+;〈x5,x2〉;〈xE,x7〉;〈x5,x7〉;〈x9,xB〉;〈x1,xA〉;〈x4,x9〉;〈x0,x9〉;〈x4,xB〉;〈xF,x6〉;〈xB,x5〉;〈x0,xA〉;〈x2,xC〉;〈xB,xA〉;〈x1,xF〉;〈x2,x6〉;〈x3,x8〉 ].
+
+ndefinition dTest_random_ex1E ≝
+[〈x6,x0〉;〈x3,x4〉;〈xC,x4〉;〈x8,x9〉;〈xB,xF〉;〈x0,x4〉;〈x5,xF〉;〈xF,x4〉;〈x1,x1〉;〈xF,x3〉;〈x4,xA〉;〈xE,x2〉;〈xD,x8〉;〈x3,x6〉;〈xF,xA〉;〈x4,x3〉
+;〈x0,xC〉;〈x6,x0〉;〈x5,x1〉;〈x2,xD〉;〈x0,x3〉;〈xF,xC〉;〈x9,x2〉;〈x2,x1〉;〈xC,xA〉;〈x7,x5〉;〈x6,x6〉;〈xD,xC〉;〈x8,x4〉;〈xC,x4〉;〈x6,xF〉;〈xF,x0〉 ].
+
+ndefinition dTest_random_ex1F ≝
+[〈x0,x4〉;〈x5,x2〉;〈xA,xB〉;〈x9,xA〉;〈xC,xE〉;〈xA,xA〉;〈x2,xF〉;〈x3,x6〉;〈xF,x3〉;〈xA,x7〉;〈x4,x2〉;〈x0,x7〉;〈x5,xE〉;〈xB,x6〉;〈x5,xB〉;〈x9,x8〉
+;〈x7,x9〉;〈x4,x3〉;〈x8,x8〉;〈x9,xA〉;〈x0,xA〉;〈x5,x5〉;〈xE,x3〉;〈x9,x8〉;〈x7,x5〉;〈xA,x2〉;〈xE,xA〉;〈xB,x9〉;〈x3,x2〉;〈x4,x1〉;〈x0,x7〉;〈x3,x8〉 ].
+
+ndefinition dTest_random_ex20 ≝
+[〈xB,x1〉;〈x0,x3〉;〈x4,xE〉;〈x6,xF〉;〈x9,x7〉;〈x3,xC〉;〈x5,x4〉;〈xB,xB〉;〈xB,xC〉;〈x0,xB〉;〈x0,xC〉;〈xA,xB〉;〈x3,xB〉;〈x2,x8〉;〈xA,xA〉;〈x0,x4〉
+;〈x5,x0〉;〈xA,x3〉;〈x6,xB〉;〈xF,xA〉;〈xF,x0〉;〈xE,x6〉;〈x1,x8〉;〈xD,x8〉;〈x7,xA〉;〈x5,xF〉;〈x0,x3〉;〈x8,x2〉;〈x9,x6〉;〈x9,xA〉;〈xB,xF〉;〈x1,x5〉 ].
+
+ndefinition dTest_random_ex21 ≝
+[〈x8,x5〉;〈xE,xF〉;〈xB,x3〉;〈x7,xB〉;〈xE,xE〉;〈xE,xF〉;〈x1,x0〉;〈x6,x9〉;〈xC,x2〉;〈xF,x9〉;〈x2,xD〉;〈x8,x1〉;〈xF,x3〉;〈x0,xE〉;〈xC,x3〉;〈x7,xF〉
+;〈xD,xD〉;〈x2,xE〉;〈x2,xA〉;〈xB,xD〉;〈xE,xA〉;〈x9,x2〉;〈xF,xF〉;〈xF,xA〉;〈x7,xB〉;〈xD,x3〉;〈x3,x0〉;〈x7,x5〉;〈x6,x7〉;〈xA,x8〉;〈x0,xF〉;〈x2,x1〉 ].
+
+ndefinition dTest_random_ex22 ≝
+[〈xD,xC〉;〈xE,x5〉;〈xE,x2〉;〈x8,x9〉;〈x2,x9〉;〈xC,x5〉;〈xA,x3〉;〈xA,x2〉;〈x4,x2〉;〈x3,xF〉;〈xA,x3〉;〈x5,x8〉;〈xE,x0〉;〈x7,xC〉;〈x0,x3〉;〈xF,xF〉
+;〈x2,x8〉;〈x8,xB〉;〈x8,xB〉;〈x1,x2〉;〈xD,x8〉;〈xA,x8〉;〈x7,x6〉;〈xB,x9〉;〈xE,x2〉;〈xF,xE〉;〈x2,x1〉;〈x3,xF〉;〈xA,xC〉;〈x4,x6〉;〈xB,xC〉;〈xF,x8〉 ].
+
+ndefinition dTest_random_ex23 ≝
+[〈xD,x3〉;〈xE,xB〉;〈xF,xC〉;〈x9,xF〉;〈xE,x7〉;〈x6,x1〉;〈xC,xB〉;〈xB,xF〉;〈x4,xE〉;〈xC,x4〉;〈x9,x7〉;〈x1,xE〉;〈x0,xD〉;〈x7,x9〉;〈x8,x3〉;〈xA,xB〉
+;〈x4,xC〉;〈x2,x6〉;〈x6,x3〉;〈x6,xF〉;〈xE,xE〉;〈x5,x9〉;〈x8,x1〉;〈x0,x2〉;〈x2,xC〉;〈xE,xD〉;〈x6,xF〉;〈x0,x4〉;〈x1,x0〉;〈xE,x0〉;〈xD,xA〉;〈xB,xE〉 ].
+
+ndefinition dTest_random_ex24 ≝
+[〈xE,xE〉;〈x5,x7〉;〈xB,x0〉;〈x3,x1〉;〈x4,x1〉;〈xD,xC〉;〈x3,xC〉;〈xC,xC〉;〈x5,x8〉;〈x2,x8〉;〈x2,xC〉;〈x1,xB〉;〈x8,x6〉;〈xD,x6〉;〈xF,x9〉;〈xD,x5〉
+;〈x4,xA〉;〈xE,xA〉;〈x0,xB〉;〈x2,x0〉;〈x2,xC〉;〈x4,x2〉;〈xC,xE〉;〈x4,x5〉;〈x2,xB〉;〈x0,x1〉;〈xA,xA〉;〈xB,x1〉;〈x6,xE〉;〈xB,x7〉;〈xB,x7〉;〈x2,x8〉 ].
+
+ndefinition dTest_random_ex25 ≝
+[〈x9,x5〉;〈x1,x9〉;〈xA,x7〉;〈x5,xC〉;〈x4,xE〉;〈x7,xB〉;〈x3,xE〉;〈xD,x3〉;〈x9,x0〉;〈x8,x6〉;〈x7,x1〉;〈x1,x4〉;〈xD,x2〉;〈xD,x4〉;〈xB,x4〉;〈xF,x2〉
+;〈x3,x1〉;〈x2,x8〉;〈x4,x5〉;〈xF,xD〉;〈x7,x8〉;〈x5,xD〉;〈xF,xA〉;〈xF,x3〉;〈x9,x5〉;〈x4,xD〉;〈x3,x1〉;〈xB,x8〉;〈xC,xC〉;〈x2,x1〉;〈x1,x9〉;〈x4,x2〉 ].
+
+ndefinition dTest_random_ex26 ≝
+[〈x2,xA〉;〈xF,x2〉;〈xB,xA〉;〈x0,x4〉;〈x9,xF〉;〈x4,x3〉;〈x4,x5〉;〈x1,xC〉;〈x7,x4〉;〈xB,xB〉;〈x7,x0〉;〈x5,xE〉;〈x0,x1〉;〈xA,xC〉;〈x6,xD〉;〈xD,x7〉
+;〈x9,xC〉;〈x9,xD〉;〈x1,xA〉;〈x9,x8〉;〈xB,x1〉;〈xF,xC〉;〈x6,x1〉;〈xA,x3〉;〈x4,x1〉;〈x4,x1〉;〈xA,xF〉;〈x1,xD〉;〈xE,x1〉;〈x3,x2〉;〈x1,x9〉;〈x6,x0〉 ].
+
+ndefinition dTest_random_ex27 ≝
+[〈x2,x9〉;〈x9,x7〉;〈x8,x5〉;〈x5,x3〉;〈x5,x3〉;〈x9,x1〉;〈xB,x3〉;〈x9,x4〉;〈xD,x5〉;〈x9,xD〉;〈x4,xC〉;〈x3,x6〉;〈x0,xE〉;〈x8,x4〉;〈xA,x1〉;〈x4,x6〉
+;〈x6,xA〉;〈x1,xF〉;〈xF,x3〉;〈x6,xB〉;〈xB,xE〉;〈x4,xA〉;〈x1,x9〉;〈x7,x5〉;〈xF,xC〉;〈xC,x6〉;〈xE,xA〉;〈x7,xE〉;〈xD,x1〉;〈x3,x3〉;〈x6,x7〉;〈xB,x7〉 ].
+
+ndefinition dTest_random_ex28 ≝
+[〈xE,xE〉;〈x5,x9〉;〈xE,x2〉;〈xD,xD〉;〈x2,x2〉;〈x8,xC〉;〈x9,xB〉;〈x3,xE〉;〈x9,x8〉;〈xF,xC〉;〈x1,x3〉;〈xE,x2〉;〈x0,xC〉;〈x4,xE〉;〈x3,x1〉;〈x8,x7〉
+;〈x6,x7〉;〈x6,xA〉;〈x4,xC〉;〈x4,xC〉;〈x7,x2〉;〈x0,x0〉;〈x0,x5〉;〈x1,xF〉;〈xF,x6〉;〈x3,x0〉;〈xE,xE〉;〈xD,xE〉;〈xB,x1〉;〈x4,xC〉;〈xF,x7〉;〈xE,xC〉 ].
+
+ndefinition dTest_random_ex29 ≝
+[〈x2,xC〉;〈x4,x0〉;〈x6,xB〉;〈x6,x8〉;〈x9,x0〉;〈x8,x8〉;〈x6,xF〉;〈xB,x3〉;〈x4,x7〉;〈x6,x2〉;〈x9,x2〉;〈x9,xB〉;〈x2,xB〉;〈x3,x2〉;〈x4,x0〉;〈xA,x7〉
+;〈x8,x9〉;〈x4,x0〉;〈x2,x3〉;〈x5,xC〉;〈xF,x9〉;〈x2,x9〉;〈x6,x2〉;〈xA,xE〉;〈x5,xB〉;〈xC,x9〉;〈x2,xC〉;〈x9,x2〉;〈x6,xF〉;〈xF,x5〉;〈xA,x0〉;〈x0,xE〉 ].
+
+ndefinition dTest_random_ex2A ≝
+[〈xD,xE〉;〈xF,x9〉;〈x0,x9〉;〈x1,x0〉;〈x3,x9〉;〈x4,x6〉;〈xC,x5〉;〈xE,x2〉;〈x8,x3〉;〈xD,x5〉;〈x8,xE〉;〈x4,x6〉;〈x4,xC〉;〈xA,xC〉;〈x7,xF〉;〈x4,xF〉
+;〈xC,x1〉;〈x4,xF〉;〈x1,xA〉;〈x6,x1〉;〈x9,x6〉;〈x0,xB〉;〈x0,x0〉;〈x6,xF〉;〈x2,x6〉;〈x8,xC〉;〈xE,xE〉;〈x9,x3〉;〈x1,xB〉;〈x9,xE〉;〈xA,x5〉;〈x9,x6〉 ].
+
+ndefinition dTest_random_ex2B ≝
+[〈x2,xA〉;〈xE,xB〉;〈x4,x6〉;〈x5,xF〉;〈x3,xC〉;〈xD,x6〉;〈x2,xD〉;〈x9,x4〉;〈x6,xB〉;〈xF,x4〉;〈xD,xA〉;〈x6,x9〉;〈x5,x9〉;〈xA,xC〉;〈xB,xD〉;〈x9,xE〉
+;〈x4,x8〉;〈x0,x2〉;〈xD,xC〉;〈x5,xC〉;〈x6,x0〉;〈x2,xA〉;〈x6,xE〉;〈xC,xA〉;〈x6,xE〉;〈x1,xF〉;〈xD,x4〉;〈x3,xA〉;〈xB,x0〉;〈x9,xE〉;〈x8,xF〉;〈xA,xB〉 ].
+
+ndefinition dTest_random_ex2C ≝
+[〈xB,x2〉;〈x0,x2〉;〈x4,x7〉;〈x7,xD〉;〈xA,xB〉;〈xD,xB〉;〈xB,x5〉;〈x6,xD〉;〈xE,x2〉;〈x8,x9〉;〈x4,xD〉;〈x0,x4〉;〈xB,xE〉;〈xF,xA〉;〈x2,x2〉;〈x1,x4〉
+;〈x7,x1〉;〈x1,x2〉;〈x1,xB〉;〈x0,xD〉;〈xB,xA〉;〈x5,xA〉;〈x6,xC〉;〈x1,xE〉;〈x3,xA〉;〈x0,xF〉;〈x6,xE〉;〈x4,x4〉;〈xC,x8〉;〈xB,x5〉;〈x8,xC〉;〈x0,x3〉 ].
+
+ndefinition dTest_random_ex2D ≝
+[〈x0,x6〉;〈x6,x4〉;〈x8,x5〉;〈x2,x8〉;〈x6,x4〉;〈x2,x2〉;〈x8,x1〉;〈x7,x6〉;〈xF,xE〉;〈xF,xA〉;〈x6,x2〉;〈x9,x1〉;〈xB,xE〉;〈xB,xC〉;〈x6,x1〉;〈x4,xB〉
+;〈x7,xE〉;〈x5,x0〉;〈xB,xC〉;〈xE,xE〉;〈x6,x3〉;〈xC,xF〉;〈x1,xD〉;〈xF,xD〉;〈x6,x2〉;〈x5,xC〉;〈x8,x5〉;〈x9,xE〉;〈xA,x5〉;〈x2,x6〉;〈xE,x7〉;〈x4,x6〉 ].
+
+ndefinition dTest_random_ex2E ≝
+[〈x3,xB〉;〈xE,xA〉;〈xB,xE〉;〈x0,x4〉;〈x8,x8〉;〈xF,x2〉;〈x9,x2〉;〈x0,xB〉;〈xD,x9〉;〈xE,x9〉;〈x2,x9〉;〈x3,x8〉;〈x8,x8〉;〈x8,xA〉;〈x6,x9〉;〈x1,x7〉
+;〈x4,xB〉;〈xB,xF〉;〈x0,xC〉;〈xF,x2〉;〈xF,xD〉;〈x7,x3〉;〈x5,x9〉;〈xB,xE〉;〈x5,x4〉;〈x1,xC〉;〈xD,x3〉;〈x3,x1〉;〈x6,x2〉;〈x1,xB〉;〈xB,x7〉;〈x3,x2〉 ].
+
+ndefinition dTest_random_ex2F ≝
+[〈xA,x4〉;〈xF,x1〉;〈x7,x0〉;〈x9,xA〉;〈x4,x6〉;〈xA,x1〉;〈x1,xC〉;〈x0,x4〉;〈x6,xC〉;〈xF,x2〉;〈xE,x6〉;〈xC,x1〉;〈xA,x4〉;〈xF,x2〉;〈x2,xA〉;〈x4,xB〉
+;〈x3,x5〉;〈x9,xB〉;〈x9,x9〉;〈xF,xF〉;〈x0,x1〉;〈x1,x3〉;〈xF,x9〉;〈x5,xC〉;〈x3,xC〉;〈x5,x1〉;〈x8,xA〉;〈xA,x5〉;〈x5,xF〉;〈x9,xE〉;〈x5,xE〉;〈xC,x6〉 ].
+
+ndefinition dTest_random_ex30 ≝
+[〈x2,x1〉;〈x3,x7〉;〈xD,x2〉;〈xB,x9〉;〈x9,x8〉;〈xA,x1〉;〈x6,x0〉;〈xE,x9〉;〈x4,x5〉;〈xC,xA〉;〈xD,x7〉;〈xB,xD〉;〈xC,xF〉;〈x0,xF〉;〈x2,x4〉;〈xE,x5〉
+;〈x7,x9〉;〈x4,xB〉;〈x1,xC〉;〈x5,x7〉;〈x3,xA〉;〈x2,x4〉;〈x2,x2〉;〈x0,x8〉;〈x3,x3〉;〈xE,x2〉;〈xA,x2〉;〈x5,x8〉;〈x2,x5〉;〈x5,x4〉;〈x7,x1〉;〈x2,xB〉 ].
+
+ndefinition dTest_random_ex31 ≝
+[〈xF,xF〉;〈xE,xD〉;〈x4,x8〉;〈xF,x6〉;〈x2,x3〉;〈x3,x1〉;〈xB,xA〉;〈x5,x1〉;〈x9,xF〉;〈xA,xA〉;〈xC,xC〉;〈x0,x3〉;〈x1,x5〉;〈xC,x7〉;〈x2,xD〉;〈xD,x3〉
+;〈xE,xB〉;〈x8,xF〉;〈x8,x4〉;〈x4,x0〉;〈x5,x3〉;〈xA,xD〉;〈x6,x7〉;〈xE,xC〉;〈xA,xF〉;〈xD,xC〉;〈x1,xC〉;〈x7,x4〉;〈x6,xB〉;〈xA,xD〉;〈xC,xD〉;〈xA,x7〉 ].
+
+ndefinition dTest_random_ex32 ≝
+[〈x1,x1〉;〈x1,x0〉;〈xC,xF〉;〈xB,xE〉;〈xA,x1〉;〈x0,x1〉;〈x3,xF〉;〈xC,x0〉;〈x8,x5〉;〈x2,x8〉;〈x6,xB〉;〈xC,x3〉;〈x6,xD〉;〈xD,x8〉;〈x7,x5〉;〈x5,xA〉
+;〈xF,x0〉;〈x2,x2〉;〈x4,xB〉;〈x9,xC〉;〈x3,x1〉;〈xE,x4〉;〈xE,x7〉;〈xC,x6〉;〈xF,xC〉;〈x3,x0〉;〈xD,x5〉;〈xF,x9〉;〈x1,xA〉;〈x4,x0〉;〈x1,xF〉;〈x6,xD〉 ].
+
+ndefinition dTest_random_ex33 ≝
+[〈xD,x5〉;〈x7,x8〉;〈xB,x5〉;〈x7,x6〉;〈xC,x9〉;〈xE,x1〉;〈xD,xF〉;〈x1,x2〉;〈x6,x1〉;〈xD,xF〉;〈x9,xF〉;〈x5,x7〉;〈x7,xD〉;〈x0,xB〉;〈xA,xD〉;〈x5,xA〉
+;〈xA,x1〉;〈x8,x4〉;〈xE,x5〉;〈xF,x7〉;〈xB,xC〉;〈xD,x3〉;〈xA,x5〉;〈xB,x4〉;〈x8,x5〉;〈x6,x7〉;〈x3,x6〉;〈xF,xC〉;〈xB,x1〉;〈xB,x3〉;〈xC,xB〉;〈x1,xE〉 ].
+
+ndefinition dTest_random_ex34 ≝
+[〈xE,xC〉;〈x6,xE〉;〈xE,x1〉;〈x1,xC〉;〈xA,x5〉;〈x5,x3〉;〈x9,x8〉;〈xF,x6〉;〈xD,xF〉;〈x4,x1〉;〈x1,x3〉;〈x2,xE〉;〈x7,xF〉;〈x0,xE〉;〈x3,x8〉;〈x3,xC〉
+;〈xD,x4〉;〈x8,xC〉;〈x2,xA〉;〈x2,x8〉;〈x4,xE〉;〈x7,xE〉;〈x0,xE〉;〈xF,x7〉;〈xC,xA〉;〈x3,xE〉;〈xE,x4〉;〈xB,x4〉;〈x0,x5〉;〈x5,x8〉;〈xD,xC〉;〈x7,x8〉 ].
+
+ndefinition dTest_random_ex35 ≝
+[〈xD,x9〉;〈xF,x9〉;〈x7,x9〉;〈x8,x4〉;〈x0,x2〉;〈x3,xF〉;〈xC,xF〉;〈x3,x8〉;〈xD,x7〉;〈x2,x6〉;〈x1,xD〉;〈x1,x8〉;〈x4,xD〉;〈xE,xA〉;〈x7,xA〉;〈xD,x4〉
+;〈x2,x4〉;〈x0,xD〉;〈x4,xD〉;〈x9,x0〉;〈x1,x7〉;〈x1,xE〉;〈x6,xE〉;〈xB,x6〉;〈xC,xC〉;〈xC,x0〉;〈xB,x0〉;〈x5,xE〉;〈x9,x9〉;〈x6,xD〉;〈xC,xF〉;〈xE,xE〉 ].
+
+ndefinition dTest_random_ex36 ≝
+[〈x2,x9〉;〈xC,xF〉;〈xA,x2〉;〈x0,xC〉;〈xA,xB〉;〈x7,x4〉;〈x2,x9〉;〈x4,xE〉;〈x8,x2〉;〈x9,x3〉;〈x6,x9〉;〈x7,xB〉;〈xE,xC〉;〈xC,x7〉;〈x8,x9〉;〈xC,xA〉
+;〈xD,xD〉;〈xA,xC〉;〈x6,x5〉;〈x8,x0〉;〈x1,x4〉;〈x0,x9〉;〈x5,x5〉;〈x0,xE〉;〈x8,x4〉;〈x5,xE〉;〈x6,xF〉;〈x3,x4〉;〈x1,x8〉;〈xC,x9〉;〈x8,xB〉;〈xE,x4〉 ].
+
+ndefinition dTest_random_ex37 ≝
+[〈x3,xE〉;〈xC,x4〉;〈x1,x6〉;〈xA,x4〉;〈x1,x9〉;〈x3,x4〉;〈x0,xE〉;〈x5,xE〉;〈xF,x9〉;〈x0,x3〉;〈x1,x3〉;〈x7,x2〉;〈x2,x7〉;〈x2,x8〉;〈xA,x7〉;〈x6,xD〉
+;〈xC,x1〉;〈x1,xD〉;〈xF,x0〉;〈x2,x8〉;〈xF,xB〉;〈xF,x6〉;〈x3,x8〉;〈x0,x1〉;〈xF,x9〉;〈xB,xC〉;〈x6,x6〉;〈xF,x8〉;〈x6,xE〉;〈xD,x1〉;〈xB,x5〉;〈x3,x8〉 ].
+
+ndefinition dTest_random_ex38 ≝
+[〈x4,x3〉;〈xB,x6〉;〈x6,x8〉;〈xA,xC〉;〈x0,x9〉;〈xF,xD〉;〈x0,x9〉;〈x6,x8〉;〈xE,x0〉;〈x2,x2〉;〈xA,xF〉;〈x4,x0〉;〈x2,x6〉;〈x0,xC〉;〈x5,x2〉;〈xA,x7〉
+;〈xA,xD〉;〈xC,x3〉;〈x8,x2〉;〈xD,xC〉;〈x3,xC〉;〈x6,x5〉;〈xF,x2〉;〈xE,x8〉;〈xC,x0〉;〈x0,x6〉;〈x6,x4〉;〈xB,x1〉;〈x2,x0〉;〈x9,x5〉;〈x2,x2〉;〈xD,xD〉 ].
+
+ndefinition dTest_random_ex39 ≝
+[〈xA,xD〉;〈xF,xF〉;〈x1,xB〉;〈x8,xB〉;〈xB,x6〉;〈x4,xA〉;〈xB,xB〉;〈x9,x8〉;〈x1,xA〉;〈xE,xC〉;〈x7,xB〉;〈xA,x6〉;〈x2,xC〉;〈xE,x1〉;〈xC,x7〉;〈xD,xC〉
+;〈x1,x9〉;〈x0,x6〉;〈x0,xA〉;〈x9,xF〉;〈x5,x2〉;〈x2,xB〉;〈xC,xA〉;〈x2,xF〉;〈x4,x0〉;〈xF,x8〉;〈xE,xA〉;〈x8,x7〉;〈x8,x9〉;〈xF,xD〉;〈x5,xD〉;〈x0,x0〉 ].
+
+ndefinition dTest_random_ex3A ≝
+[〈x6,xE〉;〈x0,x0〉;〈x0,xD〉;〈x3,x0〉;〈x4,x3〉;〈x5,xA〉;〈x8,xF〉;〈x8,xA〉;〈xA,x4〉;〈x5,x0〉;〈x8,xF〉;〈x0,xC〉;〈x7,x7〉;〈xF,x2〉;〈x6,x5〉;〈xE,x4〉
+;〈x2,xD〉;〈xE,x5〉;〈xA,x8〉;〈x7,xF〉;〈x7,x8〉;〈xE,x3〉;〈x9,x5〉;〈xD,xA〉;〈x0,x7〉;〈x2,x9〉;〈x5,x1〉;〈x9,x4〉;〈xE,x4〉;〈x0,x1〉;〈xB,xF〉;〈x6,xE〉 ].
+
+ndefinition dTest_random_ex3B ≝
+[〈x9,x8〉;〈x9,xC〉;〈x9,x0〉;〈xA,x8〉;〈x0,xA〉;〈x3,xD〉;〈x3,xC〉;〈x5,x0〉;〈xE,xB〉;〈x1,x2〉;〈xC,x4〉;〈x5,xF〉;〈x4,x7〉;〈x7,xB〉;〈x2,xC〉;〈xD,xF〉
+;〈x7,x8〉;〈x1,x3〉;〈x7,x4〉;〈xE,x0〉;〈x7,xB〉;〈x7,x1〉;〈x4,x7〉;〈x4,x8〉;〈x1,xB〉;〈xE,x3〉;〈x6,xB〉;〈x0,xB〉;〈x4,xB〉;〈x5,x9〉;〈x9,x3〉;〈xD,xF〉 ].
+
+ndefinition dTest_random_ex3C ≝
+[〈xE,x1〉;〈x1,xB〉;〈xD,x0〉;〈xE,xD〉;〈x4,x7〉;〈x4,xD〉;〈xC,x2〉;〈xD,xE〉;〈x5,xC〉;〈xD,xA〉;〈x9,x5〉;〈xC,x8〉;〈x1,x0〉;〈x7,x7〉;〈x7,xF〉;〈xC,x0〉
+;〈xA,x7〉;〈xD,x3〉;〈xD,x3〉;〈xD,x8〉;〈x3,x4〉;〈xA,x1〉;〈x1,x5〉;〈xE,x0〉;〈x0,x4〉;〈x1,xE〉;〈x8,x2〉;〈xC,xA〉;〈xD,x9〉;〈x1,x1〉;〈xB,x1〉;〈xC,x9〉 ].
+
+ndefinition dTest_random_ex3D ≝
+[〈x4,xC〉;〈x4,xB〉;〈x0,x9〉;〈x4,x8〉;〈xF,xC〉;〈xD,xD〉;〈x6,xE〉;〈xC,xA〉;〈x7,x6〉;〈xA,xE〉;〈x8,xE〉;〈x3,xB〉;〈xF,xB〉;〈x6,x5〉;〈x8,x3〉;〈x1,xD〉
+;〈xD,xB〉;〈xA,xE〉;〈x4,xF〉;〈xC,x6〉;〈x1,xE〉;〈xC,x5〉;〈xC,xC〉;〈x7,xC〉;〈x2,x8〉;〈xF,x9〉;〈xD,x2〉;〈x8,x6〉;〈x1,x5〉;〈xF,xA〉;〈x4,x1〉;〈x4,x5〉 ].
+
+ndefinition dTest_random_ex3E ≝
+[〈x2,xE〉;〈x9,x5〉;〈xB,xF〉;〈x0,xD〉;〈x8,xB〉;〈x8,xD〉;〈x1,x1〉;〈x9,xC〉;〈xB,x8〉;〈xF,xB〉;〈x2,x6〉;〈xD,x6〉;〈x9,x1〉;〈x0,xD〉;〈xC,xD〉;〈x0,x7〉
+;〈x5,x0〉;〈xF,xA〉;〈x2,x9〉;〈x3,xF〉;〈x0,xC〉;〈x2,xB〉;〈xF,xE〉;〈x9,x7〉;〈x5,x5〉;〈x5,xA〉;〈x6,xD〉;〈x9,x6〉;〈x0,x5〉;〈x0,x9〉;〈x4,x5〉;〈xE,xF〉 ].
+
+ndefinition dTest_random_ex3F ≝
+[〈x0,xF〉;〈x7,x4〉;〈x9,x3〉;〈x6,xC〉;〈x8,x2〉;〈x3,x7〉;〈xE,xB〉;〈x5,x0〉;〈xF,x5〉;〈xC,x4〉;〈x0,xB〉;〈x3,x8〉;〈x2,xD〉;〈x8,xA〉;〈x9,x3〉;〈x6,xD〉
+;〈x1,xD〉;〈xE,x5〉;〈xF,x7〉;〈xE,x7〉;〈xD,x7〉;〈x5,xC〉;〈xB,x4〉;〈x5,x0〉;〈x7,x5〉;〈x0,xD〉;〈xF,x3〉;〈xC,xE〉;〈x3,x1〉;〈xF,x1〉;〈x8,xE〉;〈x8,xF〉 ].
+
+ndefinition dTest_random_ex40 ≝
+[〈xD,xB〉;〈x1,x4〉;〈xF,x6〉;〈x0,x3〉;〈xA,xB〉;〈xA,xE〉;〈xB,xC〉;〈xE,xB〉;〈xC,x8〉;〈x6,x7〉;〈xC,xC〉;〈xF,xF〉;〈x4,xF〉;〈xC,x6〉;〈x2,x9〉;〈x9,x5〉
+;〈xB,xC〉;〈x6,x5〉;〈x5,x2〉;〈xF,x2〉;〈x3,x5〉;〈xC,x4〉;〈xF,x4〉;〈x9,xB〉;〈x4,x5〉;〈x1,xC〉;〈xD,xB〉;〈x6,x1〉;〈xF,xE〉;〈x3,xF〉;〈xB,x9〉;〈xD,x8〉 ].
+
+ndefinition dTest_random_ex41 ≝
+[〈xF,x1〉;〈xA,xC〉;〈x0,x7〉;〈xA,x4〉;〈xB,x8〉;〈x8,x8〉;〈x9,x5〉;〈xB,x8〉;〈x5,x6〉;〈x3,x2〉;〈x5,xA〉;〈x3,xE〉;〈x2,x2〉;〈x0,xB〉;〈x9,x6〉;〈xE,xE〉
+;〈x6,xF〉;〈x1,xE〉;〈x3,x2〉;〈x4,x9〉;〈x4,xF〉;〈xC,xC〉;〈xD,xB〉;〈x5,x1〉;〈x4,xD〉;〈xD,x1〉;〈x4,xF〉;〈x0,x9〉;〈x5,xA〉;〈xA,xC〉;〈xE,x7〉;〈x8,x6〉 ].
+
+ndefinition dTest_random_ex42 ≝
+[〈x5,x8〉;〈xA,x5〉;〈xA,x7〉;〈x5,xE〉;〈x3,x6〉;〈x1,x1〉;〈x3,xA〉;〈x8,x9〉;〈x8,x2〉;〈xD,xC〉;〈x6,x2〉;〈x0,xE〉;〈xA,xB〉;〈x2,xB〉;〈x2,x5〉;〈xF,x9〉
+;〈x7,x7〉;〈x8,x6〉;〈x1,xD〉;〈x7,x9〉;〈x5,x1〉;〈xB,xD〉;〈x9,x8〉;〈xB,x7〉;〈xB,xB〉;〈xF,x6〉;〈xD,x9〉;〈x6,x6〉;〈x0,x1〉;〈x1,x2〉;〈xE,xB〉;〈x0,xA〉 ].
+
+ndefinition dTest_random_ex43 ≝
+[〈xC,xD〉;〈x1,xA〉;〈xA,xA〉;〈xC,xC〉;〈x6,x5〉;〈x4,x2〉;〈x8,xF〉;〈x2,xA〉;〈x4,x8〉;〈xC,x6〉;〈xB,xA〉;〈xD,x8〉;〈x2,xD〉;〈x2,x9〉;〈xE,x8〉;〈x5,x7〉
+;〈x7,x7〉;〈x7,xA〉;〈xB,x4〉;〈x4,x9〉;〈x6,x5〉;〈x4,x3〉;〈x5,x7〉;〈xF,xE〉;〈xC,x6〉;〈xC,x7〉;〈x6,x2〉;〈x6,x7〉;〈x5,x8〉;〈xD,x6〉;〈x9,xA〉;〈xC,x8〉 ].
+
+ndefinition dTest_random_ex44 ≝
+[〈xE,x8〉;〈x3,x0〉;〈x6,x0〉;〈x7,x3〉;〈x8,x9〉;〈x2,x3〉;〈x0,x8〉;〈x7,xA〉;〈xA,xC〉;〈x5,xD〉;〈x6,xD〉;〈xC,xE〉;〈x0,xC〉;〈x1,xB〉;〈x1,x7〉;〈xC,x1〉
+;〈x4,x2〉;〈x5,x3〉;〈x1,x5〉;〈x7,xC〉;〈x7,x4〉;〈x2,xB〉;〈x2,x5〉;〈x5,x6〉;〈x6,x1〉;〈xE,xC〉;〈x0,xB〉;〈x4,x2〉;〈x0,x4〉;〈xC,xA〉;〈x0,x9〉;〈xA,xB〉 ].
+
+ndefinition dTest_random_ex45 ≝
+[〈x1,xB〉;〈xD,x0〉;〈x9,xF〉;〈x6,xA〉;〈x7,xF〉;〈x4,x1〉;〈xF,x8〉;〈xE,xA〉;〈x8,x2〉;〈x8,x1〉;〈x4,x1〉;〈xC,xE〉;〈xC,xE〉;〈x0,xD〉;〈x2,xB〉;〈x3,x3〉
+;〈xA,x3〉;〈x6,x4〉;〈xF,xA〉;〈xA,x6〉;〈x3,x9〉;〈x7,xF〉;〈xF,x6〉;〈xB,x2〉;〈x5,x5〉;〈x6,xB〉;〈xA,xC〉;〈x3,x3〉;〈x9,x3〉;〈xE,x7〉;〈xB,xE〉;〈x3,x4〉 ].
+
+ndefinition dTest_random_ex46 ≝
+[〈xC,xF〉;〈xE,xF〉;〈xA,x2〉;〈xE,xE〉;〈xE,xD〉;〈xC,xB〉;〈xB,x0〉;〈x8,x9〉;〈xD,xA〉;〈x3,xB〉;〈xB,xE〉;〈x3,xE〉;〈x3,x3〉;〈x5,x1〉;〈xA,x5〉;〈x3,xC〉
+;〈xC,xC〉;〈xA,x0〉;〈xF,xD〉;〈x3,x9〉;〈xC,xB〉;〈xF,xC〉;〈x1,xF〉;〈x8,xD〉;〈x6,x8〉;〈xD,x4〉;〈x8,xC〉;〈xA,xA〉;〈x8,xE〉;〈x3,xA〉;〈x9,x7〉;〈x2,x6〉 ].
+
+ndefinition dTest_random_ex47 ≝
+[〈x6,xB〉;〈xA,xC〉;〈x8,xA〉;〈x4,xB〉;〈x7,x4〉;〈x3,xF〉;〈xB,x7〉;〈xB,xF〉;〈x0,xC〉;〈xE,x6〉;〈xC,xD〉;〈x4,x2〉;〈xF,xA〉;〈xE,xE〉;〈xF,x9〉;〈x0,xC〉
+;〈x2,xC〉;〈x7,x9〉;〈x7,xE〉;〈xD,x8〉;〈x4,x0〉;〈x7,xC〉;〈x3,x8〉;〈x4,x9〉;〈x7,x1〉;〈x7,x5〉;〈xB,x7〉;〈x3,x6〉;〈x0,x7〉;〈x1,xA〉;〈x2,xC〉;〈x1,xE〉 ].
+
+ndefinition dTest_random_ex48 ≝
+[〈x3,xC〉;〈x7,xA〉;〈x3,x8〉;〈x4,xA〉;〈x3,x4〉;〈x2,x0〉;〈x9,x5〉;〈x6,x0〉;〈xF,x7〉;〈xC,x3〉;〈xB,x1〉;〈x6,xE〉;〈xB,x1〉;〈x7,x0〉;〈x7,x4〉;〈x3,xB〉
+;〈x0,xD〉;〈x6,xD〉;〈xF,xB〉;〈xE,x5〉;〈xE,x2〉;〈x6,x6〉;〈x6,x8〉;〈x0,x8〉;〈xF,xB〉;〈x3,xC〉;〈x8,xC〉;〈xD,xD〉;〈x0,x2〉;〈x2,xE〉;〈x6,xE〉;〈xF,x1〉 ].
+
+ndefinition dTest_random_ex49 ≝
+[〈xA,xF〉;〈x7,x9〉;〈x6,x7〉;〈xE,x2〉;〈x4,xC〉;〈xA,x5〉;〈x7,x9〉;〈xC,x6〉;〈xB,x5〉;〈xA,xF〉;〈x1,x5〉;〈xF,xE〉;〈xE,x2〉;〈x2,xB〉;〈xC,xA〉;〈xE,x6〉
+;〈x3,xE〉;〈x2,xC〉;〈x5,x8〉;〈x7,x2〉;〈xC,xE〉;〈x7,x1〉;〈x8,xC〉;〈xB,xE〉;〈x2,x0〉;〈x6,x6〉;〈x0,x7〉;〈x6,xF〉;〈xD,x1〉;〈x8,x2〉;〈x3,x1〉;〈xF,x3〉 ].
+
+ndefinition dTest_random_ex4A ≝
+[〈x9,x5〉;〈x9,x1〉;〈x1,x2〉;〈xF,x3〉;〈x4,xF〉;〈x6,xC〉;〈xA,x6〉;〈x8,xE〉;〈xB,x2〉;〈x7,x8〉;〈xD,xE〉;〈x7,x9〉;〈xC,x5〉;〈x2,x2〉;〈xF,x3〉;〈x0,x7〉
+;〈xE,x7〉;〈x9,xE〉;〈x9,x2〉;〈x7,x3〉;〈x3,xC〉;〈xA,x1〉;〈xD,xA〉;〈x2,x1〉;〈x2,x3〉;〈x4,x5〉;〈xE,x5〉;〈x7,x4〉;〈x8,x4〉;〈xC,x2〉;〈x6,x8〉;〈x3,x5〉 ].
+
+ndefinition dTest_random_ex4B ≝
+[〈x9,xA〉;〈xC,x8〉;〈x2,xE〉;〈x1,xD〉;〈xD,x1〉;〈xA,x6〉;〈xD,xF〉;〈x0,x6〉;〈x7,xF〉;〈x8,xC〉;〈x2,x8〉;〈xF,x6〉;〈xC,x3〉;〈xF,x8〉;〈x6,x2〉;〈xF,x9〉
+;〈x5,x7〉;〈x2,x7〉;〈xD,x1〉;〈xD,x3〉;〈x0,xB〉;〈xA,x3〉;〈x8,x7〉;〈x8,x3〉;〈xC,x9〉;〈x1,x4〉;〈xB,x4〉;〈xC,x5〉;〈xE,xD〉;〈x5,x4〉;〈xE,x1〉;〈xB,x9〉 ].
+
+ndefinition dTest_random_ex4C ≝
+[〈x2,x9〉;〈x6,xF〉;〈xE,x3〉;〈x0,xD〉;〈xC,xC〉;〈xF,x6〉;〈x0,xD〉;〈x2,x4〉;〈x4,x5〉;〈x6,xE〉;〈xE,x4〉;〈xD,xB〉;〈xF,x9〉;〈xC,x1〉;〈xD,x4〉;〈xB,x4〉
+;〈xB,x5〉;〈x6,x6〉;〈x1,xC〉;〈x6,xE〉;〈xA,xF〉;〈x4,x0〉;〈xE,x6〉;〈x4,x9〉;〈x7,xE〉;〈x4,x1〉;〈x1,x8〉;〈x8,x7〉;〈xD,xF〉;〈xB,xB〉;〈x6,x0〉;〈x0,x5〉 ].
+
+ndefinition dTest_random_ex4D ≝
+[〈xF,x4〉;〈x5,xD〉;〈xA,x1〉;〈xD,x6〉;〈x6,x7〉;〈x2,xA〉;〈xC,x8〉;〈x7,x7〉;〈xF,x9〉;〈x8,xA〉;〈xF,x9〉;〈x2,x6〉;〈xE,xF〉;〈x7,x4〉;〈x5,x8〉;〈x6,xA〉
+;〈xC,x8〉;〈x3,x5〉;〈x1,x0〉;〈xC,x5〉;〈x1,xE〉;〈x0,xB〉;〈x8,x3〉;〈x6,xA〉;〈x4,x4〉;〈x8,xD〉;〈x5,xC〉;〈xF,xB〉;〈xF,xE〉;〈x9,x2〉;〈x0,x3〉;〈x4,x3〉 ].
+
+ndefinition dTest_random_ex4E ≝
+[〈x0,x5〉;〈xA,xF〉;〈xC,x0〉;〈xF,x3〉;〈x0,x4〉;〈x2,x8〉;〈x9,xD〉;〈x0,x9〉;〈x3,x5〉;〈xE,x3〉;〈x5,xF〉;〈x4,x5〉;〈xA,xB〉;〈xC,xD〉;〈x8,xC〉;〈xF,xD〉
+;〈x2,xC〉;〈x9,xD〉;〈xA,xF〉;〈x6,x4〉;〈x4,x3〉;〈x8,x0〉;〈x8,x2〉;〈xE,x5〉;〈x8,xE〉;〈x3,xD〉;〈x2,xD〉;〈xD,xB〉;〈xD,xF〉;〈xA,xB〉;〈x0,x8〉;〈x1,x6〉 ].
+
+ndefinition dTest_random_ex4F ≝
+[〈xE,xC〉;〈x7,xE〉;〈xA,x7〉;〈xC,xB〉;〈xD,x8〉;〈x5,xC〉;〈x2,xC〉;〈x8,x8〉;〈x9,x8〉;〈xC,x2〉;〈xA,xD〉;〈x1,xD〉;〈xB,x0〉;〈xB,x1〉;〈xC,xE〉;〈x9,x3〉
+;〈xE,x2〉;〈xF,x4〉;〈xD,xB〉;〈xA,x5〉;〈xB,x6〉;〈x4,x9〉;〈x8,x7〉;〈x1,xD〉;〈xA,x2〉;〈x7,x9〉;〈x3,x5〉;〈xB,xE〉;〈x5,x5〉;〈xC,xD〉;〈x6,x3〉;〈x2,xC〉 ].
+
+ndefinition dTest_random_ex50 ≝
+[〈x1,x0〉;〈x1,xF〉;〈xE,xC〉;〈x3,xB〉;〈x8,xA〉;〈x3,xF〉;〈x3,x8〉;〈x8,x0〉;〈x1,xC〉;〈x2,xD〉;〈x9,x2〉;〈x5,xF〉;〈xE,x1〉;〈xB,x5〉;〈xB,xC〉;〈x8,x3〉
+;〈xB,x6〉;〈x1,xB〉;〈xE,xD〉;〈x4,xF〉;〈x3,xA〉;〈xC,x4〉;〈xF,xE〉;〈xF,xF〉;〈xC,xB〉;〈x8,x1〉;〈x6,x7〉;〈xC,x2〉;〈x5,x9〉;〈xD,xA〉;〈x0,xA〉;〈x9,xC〉 ].
+
+ndefinition dTest_random_ex51 ≝
+[〈x2,x2〉;〈xE,xB〉;〈x9,x3〉;〈xE,x2〉;〈x7,xF〉;〈xA,xC〉;〈x4,xA〉;〈x8,x2〉;〈x8,x1〉;〈x3,xF〉;〈xE,xB〉;〈x8,xB〉;〈x0,xF〉;〈x9,xC〉;〈x4,x1〉;〈x8,x2〉
+;〈x9,xB〉;〈x7,xC〉;〈x5,x1〉;〈xA,x7〉;〈xA,xB〉;〈xA,xD〉;〈x9,x2〉;〈x1,x9〉;〈xF,x0〉;〈xF,xD〉;〈x9,x3〉;〈xF,x6〉;〈xA,xD〉;〈x2,x4〉;〈xC,xB〉;〈xD,xE〉 ].
+
+ndefinition dTest_random_ex52 ≝
+[〈xB,x5〉;〈xA,xB〉;〈x8,x1〉;〈x5,x4〉;〈xA,xE〉;〈x2,x4〉;〈x6,x4〉;〈xD,x2〉;〈xD,x0〉;〈xF,xE〉;〈x3,x3〉;〈x2,xA〉;〈x7,x5〉;〈x0,x7〉;〈x8,xF〉;〈x3,xA〉
+;〈x1,x2〉;〈x9,xF〉;〈xB,xE〉;〈x1,xB〉;〈x1,xB〉;〈x1,xF〉;〈xC,x7〉;〈xF,x1〉;〈x7,xC〉;〈x9,x1〉;〈x5,xD〉;〈x3,x2〉;〈xD,x9〉;〈xD,x6〉;〈xE,xA〉;〈x0,x6〉 ].
+
+ndefinition dTest_random_ex53 ≝
+[〈x5,xB〉;〈x6,x9〉;〈x6,xB〉;〈xA,xC〉;〈x0,x9〉;〈x1,x6〉;〈xA,x3〉;〈xC,xA〉;〈x8,xE〉;〈x8,x3〉;〈x3,x4〉;〈xB,x7〉;〈x4,x1〉;〈x2,x7〉;〈xB,x3〉;〈x0,x1〉
+;〈xE,x6〉;〈x0,x6〉;〈x8,xC〉;〈x0,x4〉;〈x3,xD〉;〈xB,xE〉;〈x2,xC〉;〈x6,x6〉;〈xB,x5〉;〈x8,x6〉;〈x1,x1〉;〈x1,x3〉;〈x6,xD〉;〈xD,x0〉;〈xB,xE〉;〈x8,xD〉 ].
+
+ndefinition dTest_random_ex54 ≝
+[〈xC,x7〉;〈x5,x5〉;〈x0,x2〉;〈xC,x1〉;〈x7,x6〉;〈x5,xF〉;〈x2,x0〉;〈x5,xE〉;〈xE,x4〉;〈x3,xE〉;〈x7,x7〉;〈xE,x1〉;〈x3,xF〉;〈xE,x8〉;〈x6,xC〉;〈x4,xA〉
+;〈xA,x0〉;〈xF,xE〉;〈xC,xE〉;〈x3,xF〉;〈x6,x7〉;〈x9,x4〉;〈x3,xF〉;〈xE,xF〉;〈xE,xF〉;〈x8,x6〉;〈xD,x9〉;〈x4,xA〉;〈x0,x8〉;〈x8,xB〉;〈xC,x8〉;〈x1,xC〉 ].
+
+ndefinition dTest_random_ex55 ≝
+[〈xA,xD〉;〈x2,x0〉;〈xA,x7〉;〈x8,xC〉;〈x0,x6〉;〈x6,x7〉;〈xA,xF〉;〈x7,x3〉;〈xC,xD〉;〈x1,x6〉;〈x8,x4〉;〈x3,x2〉;〈xD,x0〉;〈xF,x3〉;〈xD,xC〉;〈xD,xB〉
+;〈xB,x7〉;〈x2,x4〉;〈x6,xA〉;〈x6,x3〉;〈x1,xC〉;〈xA,x1〉;〈xD,xE〉;〈xB,xC〉;〈x9,x2〉;〈xF,x1〉;〈x5,xC〉;〈xE,x7〉;〈xE,x0〉;〈xD,x5〉;〈xA,x4〉;〈x4,xA〉 ].
+
+ndefinition dTest_random_ex56 ≝
+[〈x0,x0〉;〈xD,x6〉;〈x2,x2〉;〈x9,xC〉;〈x5,x2〉;〈x8,xF〉;〈xE,x8〉;〈x2,x2〉;〈xA,x2〉;〈xF,x0〉;〈x9,x8〉;〈x3,x8〉;〈x0,xD〉;〈xF,x6〉;〈x4,x3〉;〈x7,x9〉
+;〈x8,x2〉;〈xA,xF〉;〈xD,x5〉;〈xC,x1〉;〈x8,x2〉;〈x5,x2〉;〈xD,xB〉;〈x8,xF〉;〈x7,xE〉;〈xD,x1〉;〈x9,xD〉;〈xA,x6〉;〈x8,xE〉;〈x9,xE〉;〈xA,x9〉;〈x8,xE〉 ].
+
+ndefinition dTest_random_ex57 ≝
+[〈xD,x1〉;〈xF,x6〉;〈xB,x0〉;〈xE,xA〉;〈x8,x3〉;〈xE,x9〉;〈xF,x7〉;〈x3,xB〉;〈x4,xA〉;〈x0,x9〉;〈x1,xE〉;〈x3,x2〉;〈xD,x2〉;〈x5,xD〉;〈xD,x7〉;〈xA,xB〉
+;〈x4,xD〉;〈x6,xF〉;〈x5,x9〉;〈xF,xC〉;〈x4,x3〉;〈x4,x1〉;〈x0,x0〉;〈x3,xC〉;〈x9,x4〉;〈x5,x2〉;〈x5,x9〉;〈x6,xC〉;〈x6,xE〉;〈xE,x8〉;〈x6,x6〉;〈xF,x5〉 ].
+
+ndefinition dTest_random_ex58 ≝
+[〈x9,xC〉;〈x5,x7〉;〈x6,xC〉;〈xE,x2〉;〈x3,xB〉;〈xA,x2〉;〈x2,x1〉;〈xE,xE〉;〈xF,x6〉;〈x4,xF〉;〈xF,x3〉;〈x6,x2〉;〈xD,xB〉;〈x8,xF〉;〈x6,x4〉;〈xD,x3〉
+;〈x8,x0〉;〈x6,x9〉;〈x9,x7〉;〈x4,x7〉;〈x8,xB〉;〈xB,x6〉;〈x3,x8〉;〈x4,x5〉;〈xB,xE〉;〈x0,xD〉;〈x6,x1〉;〈xC,xF〉;〈x7,x8〉;〈xC,xF〉;〈x4,x1〉;〈x7,xF〉 ].
+
+ndefinition dTest_random_ex59 ≝
+[〈xF,x4〉;〈x5,xA〉;〈x8,xB〉;〈x7,x2〉;〈xE,x6〉;〈x7,xD〉;〈x4,xC〉;〈x1,x8〉;〈xE,xE〉;〈x3,xA〉;〈x1,x2〉;〈x9,x4〉;〈x3,x4〉;〈x3,x0〉;〈x3,x9〉;〈x0,x0〉
+;〈x9,x5〉;〈x6,x0〉;〈xF,xA〉;〈x7,xF〉;〈xA,x6〉;〈xC,x7〉;〈xB,x1〉;〈x7,xE〉;〈x0,xD〉;〈x2,x4〉;〈xF,xF〉;〈x4,x3〉;〈x7,x8〉;〈x8,x8〉;〈x6,xC〉;〈x0,x7〉 ].
+
+ndefinition dTest_random_ex5A ≝
+[〈x7,x3〉;〈x9,x2〉;〈xC,x8〉;〈x0,xB〉;〈x5,x0〉;〈x9,x7〉;〈xF,x4〉;〈x1,xB〉;〈xD,xB〉;〈x4,x5〉;〈x6,x2〉;〈x9,x1〉;〈x8,x7〉;〈x5,xD〉;〈xF,x5〉;〈x6,x1〉
+;〈x3,x8〉;〈xF,x3〉;〈x8,xA〉;〈x4,xF〉;〈xD,xB〉;〈x3,xD〉;〈x4,x3〉;〈x2,xF〉;〈xB,xA〉;〈xA,x9〉;〈xB,x4〉;〈xA,x9〉;〈x2,x6〉;〈x7,xE〉;〈x8,xC〉;〈x1,x6〉 ].
+
+ndefinition dTest_random_ex5B ≝
+[〈xF,xC〉;〈x1,xC〉;〈xA,x7〉;〈x9,xD〉;〈x7,xC〉;〈x8,x5〉;〈xA,x7〉;〈x3,x5〉;〈x8,x6〉;〈x4,xF〉;〈xC,x8〉;〈x9,xA〉;〈x0,xD〉;〈x2,x4〉;〈x0,x4〉;〈x5,x8〉
+;〈x4,x2〉;〈x3,x0〉;〈x7,x5〉;〈x8,xD〉;〈xB,xC〉;〈x7,x2〉;〈x3,x4〉;〈xF,x9〉;〈x4,x6〉;〈x5,xE〉;〈xF,x4〉;〈x5,xC〉;〈x6,x7〉;〈x0,x4〉;〈x8,x8〉;〈x2,x8〉 ].
+
+ndefinition dTest_random_ex5C ≝
+[〈xA,x9〉;〈xE,xC〉;〈xE,xC〉;〈x7,xC〉;〈x4,x6〉;〈x6,xE〉;〈x1,xC〉;〈xD,x9〉;〈xC,x0〉;〈x6,x1〉;〈x5,x8〉;〈x5,xE〉;〈x3,x7〉;〈xB,x0〉;〈x9,x9〉;〈x9,x7〉
+;〈xA,x0〉;〈x9,xB〉;〈x7,x7〉;〈x4,xA〉;〈xD,x0〉;〈xB,x5〉;〈x1,xD〉;〈xA,x6〉;〈x4,xA〉;〈xC,x5〉;〈x3,xA〉;〈x9,x4〉;〈xB,x4〉;〈x5,x0〉;〈x0,x6〉;〈xC,x0〉 ].
+
+ndefinition dTest_random_ex5D ≝
+[〈xA,x8〉;〈x0,x2〉;〈x5,xF〉;〈x0,xE〉;〈x2,x1〉;〈x0,x3〉;〈xB,x1〉;〈x9,x6〉;〈x0,x2〉;〈x9,x7〉;〈x8,x0〉;〈x1,xA〉;〈x0,xB〉;〈x3,xD〉;〈x2,x1〉;〈x7,xF〉
+;〈x0,x3〉;〈x2,x9〉;〈x3,x2〉;〈x6,x6〉;〈xB,xF〉;〈x3,xB〉;〈x5,x7〉;〈x5,x3〉;〈xE,x7〉;〈xD,x5〉;〈xE,x5〉;〈x4,x5〉;〈xA,x3〉;〈x1,xA〉;〈x1,xB〉;〈xF,x8〉 ].
+
+ndefinition dTest_random_ex5E ≝
+[〈xC,xF〉;〈xB,x3〉;〈x9,x5〉;〈x5,x9〉;〈x4,xE〉;〈x6,x4〉;〈x4,x3〉;〈xF,x4〉;〈x2,x5〉;〈xC,xC〉;〈x6,x1〉;〈x3,x5〉;〈xD,xF〉;〈x3,x6〉;〈x5,x5〉;〈xC,xF〉
+;〈x9,xA〉;〈x1,x1〉;〈xF,x6〉;〈xD,x4〉;〈x4,xF〉;〈x9,xB〉;〈xA,xF〉;〈xF,x2〉;〈x0,x3〉;〈x1,x9〉;〈x9,xB〉;〈xA,xB〉;〈xC,x4〉;〈x1,x9〉;〈xA,x1〉;〈xE,xA〉 ].
+
+ndefinition dTest_random_ex5F ≝
+[〈x1,xB〉;〈x2,x5〉;〈xA,xD〉;〈xA,xA〉;〈x0,x0〉;〈x5,xB〉;〈x9,xD〉;〈x6,xF〉;〈x8,x8〉;〈x6,xF〉;〈x3,x0〉;〈x8,x5〉;〈xC,x6〉;〈x1,x7〉;〈x5,x7〉;〈x1,x1〉
+;〈xA,xB〉;〈x0,x2〉;〈xD,xD〉;〈x9,x2〉;〈x4,xD〉;〈x8,x2〉;〈x0,x2〉;〈x3,x5〉;〈xC,xB〉;〈x4,x4〉;〈xA,x4〉;〈x4,x1〉;〈xD,x5〉;〈x1,x2〉;〈xE,x7〉;〈x4,xD〉 ].
+
+ndefinition dTest_random_32 ≝
+ dTest_random_ex00.
+
+ndefinition dTest_random_64 ≝
+ dTest_random_32@dTest_random_ex01.
+
+ndefinition dTest_random_128 ≝
+ dTest_random_64@dTest_random_ex02@dTest_random_ex03.
+
+ndefinition dTest_random_256 ≝
+ dTest_random_128@
+ dTest_random_ex04@dTest_random_ex05@dTest_random_ex06@dTest_random_ex07.
+
+ndefinition dTest_random_512 ≝
+ dTest_random_256@
+ dTest_random_ex08@dTest_random_ex09@dTest_random_ex0A@dTest_random_ex0B@
+ dTest_random_ex0C@dTest_random_ex0D@dTest_random_ex0E@dTest_random_ex0F.
+
+ndefinition dTest_random_1024 ≝
+ dTest_random_512@
+ dTest_random_ex10@dTest_random_ex11@dTest_random_ex12@dTest_random_ex13@
+ dTest_random_ex14@dTest_random_ex15@dTest_random_ex16@dTest_random_ex17@
+ dTest_random_ex18@dTest_random_ex19@dTest_random_ex1A@dTest_random_ex1B@
+ dTest_random_ex1C@dTest_random_ex1D@dTest_random_ex1E@dTest_random_ex1F.
+
+ndefinition dTest_random_2048 ≝
+ dTest_random_1024@
+ dTest_random_ex20@dTest_random_ex21@dTest_random_ex22@dTest_random_ex23@
+ dTest_random_ex24@dTest_random_ex25@dTest_random_ex26@dTest_random_ex27@
+ dTest_random_ex28@dTest_random_ex29@dTest_random_ex2A@dTest_random_ex2B@
+ dTest_random_ex2C@dTest_random_ex2D@dTest_random_ex2E@dTest_random_ex2F@
+ dTest_random_ex30@dTest_random_ex31@dTest_random_ex32@dTest_random_ex33@
+ dTest_random_ex34@dTest_random_ex35@dTest_random_ex36@dTest_random_ex37@
+ dTest_random_ex38@dTest_random_ex39@dTest_random_ex3A@dTest_random_ex3B@
+ dTest_random_ex3C@dTest_random_ex3D@dTest_random_ex3E@dTest_random_ex3F.
+
+ndefinition dTest_random_3072 ≝
+ dTest_random_2048@
+ dTest_random_ex40@dTest_random_ex41@dTest_random_ex42@dTest_random_ex43@
+ dTest_random_ex44@dTest_random_ex45@dTest_random_ex46@dTest_random_ex47@
+ dTest_random_ex48@dTest_random_ex49@dTest_random_ex4A@dTest_random_ex4B@
+ dTest_random_ex4C@dTest_random_ex4D@dTest_random_ex4E@dTest_random_ex4F@
+ dTest_random_ex50@dTest_random_ex51@dTest_random_ex52@dTest_random_ex53@
+ dTest_random_ex54@dTest_random_ex55@dTest_random_ex56@dTest_random_ex57@
+ dTest_random_ex58@dTest_random_ex59@dTest_random_ex5A@dTest_random_ex5B@
+ dTest_random_ex5C@dTest_random_ex5D@dTest_random_ex5E@dTest_random_ex5F.
+
+(* campitura di 128 0x00 *)
+ndefinition dTest_bytes_aux : list byte8 ≝
+[
+〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;
+〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;
+〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;
+〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;
+〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;
+〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;
+〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;
+〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉;〈x0,x0〉
+].
+
+(* blocco di 0x00 lungo 0x0380 da caricare dopo dati per azzerare
+ counters, index, position, e stack di esecuzione *)
+ndefinition dTest_zeros : list byte8 ≝
+ dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux.
+
+ndefinition dTest_zeros3K : list byte8 ≝
+ dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@
+ dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@
+ dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@
+ dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux@dTest_bytes_aux.
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/memory_func.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/memory_trees.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/memory_struct.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/aux_bases.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/memory_struct.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/status.ma".
(* modelli di HCS08 *)
ninductive HCS08_mcu_model : Type ≝
- MC9S08AW60 : HCS08_mcu_model
+ MC9S08GB60 : HCS08_mcu_model
(*..*).
-ndefinition HCS08_mcu_model_ind : ΠP:HCS08_mcu_model → Prop.P MC9S08AW60 → Πh:HCS08_mcu_model.P h ≝
-λP:HCS08_mcu_model → Prop.λp:P MC9S08AW60.λh:HCS08_mcu_model.
- match h with [ MC9S08AW60 ⇒ p ].
+ndefinition HCS08_mcu_model_ind : ΠP:HCS08_mcu_model → Prop.P MC9S08GB60 → Πh:HCS08_mcu_model.P h ≝
+λP:HCS08_mcu_model → Prop.λp:P MC9S08GB60.λh:HCS08_mcu_model.
+ match h with [ MC9S08GB60 ⇒ p ].
-ndefinition HCS08_mcu_model_rec : ΠP:HCS08_mcu_model → Set.P MC9S08AW60 → Πh:HCS08_mcu_model.P h ≝
-λP:HCS08_mcu_model → Set.λp:P MC9S08AW60.λh:HCS08_mcu_model.
- match h with [ MC9S08AW60 ⇒ p ].
+ndefinition HCS08_mcu_model_rec : ΠP:HCS08_mcu_model → Set.P MC9S08GB60 → Πh:HCS08_mcu_model.P h ≝
+λP:HCS08_mcu_model → Set.λp:P MC9S08GB60.λh:HCS08_mcu_model.
+ match h with [ MC9S08GB60 ⇒ p ].
-ndefinition HCS08_mcu_model_rect : ΠP:HCS08_mcu_model → Type.P MC9S08AW60 → Πh:HCS08_mcu_model.P h ≝
-λP:HCS08_mcu_model → Type.λp:P MC9S08AW60.λh:HCS08_mcu_model.
- match h with [ MC9S08AW60 ⇒ p ].
+ndefinition HCS08_mcu_model_rect : ΠP:HCS08_mcu_model → Type.P MC9S08GB60 → Πh:HCS08_mcu_model.P h ≝
+λP:HCS08_mcu_model → Type.λp:P MC9S08GB60.λh:HCS08_mcu_model.
+ match h with [ MC9S08GB60 ⇒ p ].
(* modelli di RS08 *)
ninductive RS08_mcu_model : Type ≝
(* memoria degli HCS08 *)
ndefinition memory_type_of_FamilyHCS08 ≝
λm:HCS08_mcu_model.match m with
- [ MC9S08AW60 ⇒
+ [ MC9S08GB60 ⇒
[
(* astraggo molto *)
(* 0x0000-0x006F,0x1800-0x185F: sarebbe memory mapped IO *)
- triple ??? 〈〈x0,x0〉:〈x7,x0〉〉 〈〈x0,x8〉:〈x6,xF〉〉 MEM_READ_WRITE (* 2048B RAM *)
- ; triple ??? 〈〈x0,x8〉:〈x7,x0〉〉 〈〈x1,x7〉:〈xF,xF〉〉 MEM_READ_ONLY (* 3984B FLASH *)
- ; triple ??? 〈〈x1,x8〉:〈x6,x0〉〉 〈〈xF,xF〉:〈xF,xF〉〉 MEM_READ_ONLY (* 59296B FLASH *) ]
+ triple ??? 〈〈x0,x0〉:〈x8,x0〉〉 〈〈x1,x0〉:〈x7,xF〉〉 MEM_READ_WRITE (* 4096B RAM *)
+ ; triple ??? 〈〈x1,x0〉:〈x8,x0〉〉 〈〈x1,x7〉:〈xF,xF〉〉 MEM_READ_ONLY (* 1920B FLASH *)
+ ; triple ??? 〈〈x1,x8〉:〈x2,xC〉〉 〈〈xF,xF〉:〈xF,xF〉〉 MEM_READ_ONLY (* 59348B FLASH *) ]
].
(* memoria dei RS08 *)
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/load_write.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/pts.ma".
| (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).
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/bool_lemmas.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/opcode_base.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/aux_bases.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/bool_lemmas.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/opcode_base_lemmas_opcode2.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/aux_bases_lemmas.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/opcode_base_lemmas_instrmode1.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/bool_lemmas.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/opcode_base_lemmas_opcode1.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/bool.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/bool_lemmas.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/bool.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/bool_lemmas.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
universe constraint Type[0] < Type[1].
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/memory_abs.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/word16_lemmas.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/opcode.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/table_HC05.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/opcode.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/table_HC08.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/opcode.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/table_HCS08.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/opcode.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/table_RS08.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/pts.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/table_HC05.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/byte8.ma".
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/byte8_lemmas.ma".
(**************************************************************************)
(* ********************************************************************** *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
(* ********************************************************************** *)
(**************************************************************************)
(* ********************************************************************** *)
-(* Progetto FreeScale *)
+(* Progetto FreeScale *)
(* *)
-(* Sviluppato da: *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
(* *)
-(* Questo materiale fa parte della tesi: *)
-(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
-(* *)
-(* data ultima modifica 15/11/2007 *)
(* ********************************************************************** *)
include "freescale/word16_lemmas.ma".
--- /dev/null
+
+include "utility/utility.ma".
+
+(*
+nlemma fold_right_neList2_aux3 :
+\forall T. \forall h,h',t,t'.len_neList T (h§§t) = len_neList T (h'§§t') → len_neList T t = len_neList T t'.
+ #T; #h; #h'; #t; #t';
+ napply (ne_list_ind T ??? t);
+ napply (ne_list_ind T ??? t');
+ ##[ ##1: nnormalize; #x; #y; #H; napply (refl_eq ??)
+ ##| ##2: #a; #l'; #H; #x; #H1;
+ nchange in H1:(%) with ((S (len_neList T «£x»)) = (S (len_neList T (a§§l'))));
+ nrewrite > (nat_destruct_S_S ?? H1);
+ napply (refl_eq ??)
+ ##| ##3: #x; #a; #l'; #H; #H1;
+ nchange in H1:(%) with ((S (len_neList T (a§§l')))= (S (len_neList T «£x»)));
+ nrewrite > (nat_destruct_S_S ?? H1);
+ napply (refl_eq ??)
+ ##| ##4: #a; #l; #H; #a1; #l1; #H1; #H2;
+ (* sarebbe nchange in H2:(%) with ((S (len_neList T (a1§§l1))) = (S (len_neList T (a§§l)))); *)
+ (* ma fa passare il seguente errato ... *)
+ nchange in H2:(%) with ((S (len_neList T (a§§l1))) = (S (len_neList T (a§§l))));
+*)
+
+include "freescale/byte8_lemmas.ma".
+
+(*
+nlemma associative_plusb8_aux
+ : \forall e1,e2,e3,e4.
+ match plus_ex_d_dc e2 e4 with
+ [ pair l c ⇒ 〈plus_ex_dc_d e1 e3 c,l〉 ] =
+ 〈plus_ex_dc_d e1 e3 (snd ?? (plus_ex_d_dc e2 e4)),(fst ?? (plus_ex_d_dc e2 e4))〉.
+ #e1; #e2; #e3; #e4;
+ (* anche qui appare un T1 *)
+ ncases (plus_ex_d_dc e2 e4);
+ #e5; #c;
+ napply (refl_eq ??).
+nqed.
+
+nlemma associative_plusb8
+ : \forall b1,b2,b3.(plus_b8_d_d (plus_b8_d_d b1 b2) b3) = (plus_b8_d_d b1 (plus_b8_d_d b2 b3)).
+ #b1; ncases b1; #e1; #e2;
+ #b2; ncases b2; #e3; #e4;
+ #b3; ncases b3; #e5; #e6;
+
+(* perche' volendo posso introdurre anche 2 premesse diverse con lo stesso nome? tipo #e2; #e2 *)
+
+ nchange with (
+ match plus_ex_d_dc (b8l (match plus_ex_d_dc e2 e4 with
+ [ pair l1 c1 ⇒ 〈plus_ex_dc_d e1 e3 c1,l1〉 ])) e6 with
+ [ pair l2 c2 ⇒ 〈plus_ex_dc_d (b8h (match plus_ex_d_dc e2 e4 with
+ [ pair l3 c3 ⇒ 〈plus_ex_dc_d e1 e3 c3,l3〉 ])) e5 c2,l2〉 ] =
+ match plus_ex_d_dc e2 (b8l (match plus_ex_d_dc e4 e6 with
+ [ pair l4 c4 ⇒ 〈plus_ex_dc_d e3 e5 c4,l4〉 ])) with
+ [ pair l5 c5 ⇒ 〈plus_ex_dc_d e1 (b8h (match plus_ex_d_dc e4 e6 with
+ [ pair l6 c6 ⇒ 〈plus_ex_dc_d e3 e5 c6,l6〉 ])) c5,l5〉 ]);
+
+(* gia' qua ci sono T1, T2 che appaiono dal nulla al posto delle variabili *)
+
+ nrewrite > (associative_plusb8_aux e1 e2 e3 e4);
+ nrewrite > (associative_plusb8_aux e3 e4 e5 e6);
+ nrewrite > (plusex_d_dc_to_d_c e2 e4);
+ nrewrite > (plusex_d_dc_to_d_d e2 e4);
+ nrewrite > (plusex_d_dc_to_d_c e4 e6);
+
+ (* nel visualizzatore era (snd ?? (plus_ex_d_dc e5 T2)) ma ha accettato la versione corretta *)
+
+ nrewrite > (plusex_d_dc_to_d_d e4 e6);
+
+ (*...*)
+*)
--- /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".
+
+(* ************************** *)
+(* DEFINIZIONE ASCII MINIMALE *)
+(* ************************** *)
+
+ninductive ascii : Type ≝
+(* numeri *)
+ ch_0: ascii
+| ch_1: ascii
+| ch_2: ascii
+| ch_3: ascii
+| ch_4: ascii
+| ch_5: ascii
+| ch_6: ascii
+| ch_7: ascii
+| ch_8: ascii
+| ch_9: ascii
+
+(* simboli *)
+| ch__: ascii
+
+(* maiuscole *)
+| ch_A: ascii
+| ch_B: ascii
+| ch_C: ascii
+| ch_D: ascii
+| ch_E: ascii
+| ch_F: ascii
+| ch_G: ascii
+| ch_H: ascii
+| ch_I: ascii
+| ch_J: ascii
+| ch_K: ascii
+| ch_L: ascii
+| ch_M: ascii
+| ch_N: ascii
+| ch_O: ascii
+| ch_P: ascii
+| ch_Q: ascii
+| ch_R: ascii
+| ch_S: ascii
+| ch_T: ascii
+| ch_U: ascii
+| ch_V: ascii
+| ch_W: ascii
+| ch_X: ascii
+| ch_Y: ascii
+| ch_Z: ascii
+
+(* minuscole *)
+| ch_a: ascii
+| ch_b: ascii
+| ch_c: ascii
+| ch_d: ascii
+| ch_e: ascii
+| ch_f: ascii
+| ch_g: ascii
+| ch_h: ascii
+| ch_i: ascii
+| ch_j: ascii
+| ch_k: ascii
+| ch_l: ascii
+| ch_m: ascii
+| ch_n: ascii
+| ch_o: ascii
+| ch_p: ascii
+| ch_q: ascii
+| ch_r: ascii
+| ch_s: ascii
+| ch_t: ascii
+| ch_u: ascii
+| ch_v: ascii
+| ch_w: ascii
+| ch_x: ascii
+| ch_y: ascii
+| ch_z: ascii.
+
+ndefinition ascii_ind
+ : ΠP:ascii → Prop.
+ P ch_0 → P ch_1 → P ch_2 → P ch_3 → P ch_4 → P ch_5 → P ch_6 → P ch_7 → P ch_8 → P ch_9 → P ch__ →
+ P ch_A → P ch_B → P ch_C → P ch_D → P ch_E → P ch_F → P ch_G → P ch_H → P ch_I → P ch_J → P ch_K →
+ P ch_L → P ch_M → P ch_N → P ch_O → P ch_P → P ch_Q → P ch_R → P ch_S → P ch_T → P ch_U → P ch_V →
+ P ch_W → P ch_X → P ch_Y → P ch_Z → P ch_a → P ch_b → P ch_c → P ch_d → P ch_e → P ch_f → P ch_g →
+ P ch_h → P ch_i → P ch_j → P ch_k → P ch_l → P ch_m → P ch_n → P ch_o → P ch_p → P ch_q → P ch_r →
+ P ch_s → P ch_t → P ch_u → P ch_v → P ch_w → P ch_x → P ch_y → P ch_z → Πa:ascii.P a ≝
+λP:ascii → Prop.
+λp:P ch_0.λp1:P ch_1.λp2:P ch_2.λp3:P ch_3.λp4:P ch_4.λp5:P ch_5.λp6:P ch_6.λp7:P ch_7.λp8:P ch_8.λp9:P ch_9.
+λp10:P ch__.λp11:P ch_A.λp12:P ch_B.λp13:P ch_C.λp14:P ch_D.λp15:P ch_E.λp16:P ch_F.λp17:P ch_G.λp18:P ch_H.
+λp19:P ch_I.λp20:P ch_J.λp21:P ch_K.λp22:P ch_L.λp23:P ch_M.λp24:P ch_N.λp25:P ch_O.λp26:P ch_P.λp27:P ch_Q.
+λp28:P ch_R.λp29:P ch_S.λp30:P ch_T.λp31:P ch_U.λp32:P ch_V.λp33:P ch_W.λp34:P ch_X.λp35:P ch_Y.λp36:P ch_Z.
+λp37:P ch_a.λp38:P ch_b.λp39:P ch_c.λp40:P ch_d.λp41:P ch_e.λp42:P ch_f.λp43:P ch_g.λp44:P ch_h.λp45:P ch_i.
+λp46:P ch_j.λp47:P ch_k.λp48:P ch_l.λp49:P ch_m.λp50:P ch_n.λp51:P ch_o.λp52:P ch_p.λp53:P ch_q.λp54:P ch_r.
+λp55:P ch_s.λp56:P ch_t.λp57:P ch_u.λp58:P ch_v.λp59:P ch_w.λp60:P ch_x.λp61:P ch_y.λp62:P ch_z.λa:ascii.
+ match a with
+ [ ch_0 ⇒ p | ch_1 ⇒ p1 | ch_2 ⇒ p2 | ch_3 ⇒ p3 | ch_4 ⇒ p4 | ch_5 ⇒ p5 | ch_6 ⇒ p6 | ch_7 ⇒ p7
+ | ch_8 ⇒ p8 | ch_9 ⇒ p9 | ch__ ⇒ p10 | ch_A ⇒ p11 | ch_B ⇒ p12 | ch_C ⇒ p13 | ch_D ⇒ p14 | ch_E ⇒ p15
+ | ch_F ⇒ p16 | ch_G ⇒ p17 | ch_H ⇒ p18 | ch_I ⇒ p19 | ch_J ⇒ p20 | ch_K ⇒ p21 | ch_L ⇒ p22 | ch_M ⇒ p23
+ | ch_N ⇒ p24 | ch_O ⇒ p25 | ch_P ⇒ p26 | ch_Q ⇒ p27 | ch_R ⇒ p28 | ch_S ⇒ p29 | ch_T ⇒ p30 | ch_U ⇒ p31
+ | ch_V ⇒ p32 | ch_W ⇒ p33 | ch_X ⇒ p34 | ch_Y ⇒ p35 | ch_Z ⇒ p36 | ch_a ⇒ p37 | ch_b ⇒ p38 | ch_c ⇒ p39
+ | ch_d ⇒ p40 | ch_e ⇒ p41 | ch_f ⇒ p42 | ch_g ⇒ p43 | ch_h ⇒ p44 | ch_i ⇒ p45 | ch_j ⇒ p46 | ch_k ⇒ p47
+ | ch_l ⇒ p48 | ch_m ⇒ p49 | ch_n ⇒ p50 | ch_o ⇒ p51 | ch_p ⇒ p52 | ch_q ⇒ p53 | ch_r ⇒ p54 | ch_s ⇒ p55
+ | ch_t ⇒ p56 | ch_u ⇒ p57 | ch_v ⇒ p58 | ch_w ⇒ p59 | ch_x ⇒ p60 | ch_y ⇒ p61 | ch_z ⇒ p62 ].
+
+ndefinition ascii_rec
+ : ΠP:ascii → Set.
+ P ch_0 → P ch_1 → P ch_2 → P ch_3 → P ch_4 → P ch_5 → P ch_6 → P ch_7 → P ch_8 → P ch_9 → P ch__ →
+ P ch_A → P ch_B → P ch_C → P ch_D → P ch_E → P ch_F → P ch_G → P ch_H → P ch_I → P ch_J → P ch_K →
+ P ch_L → P ch_M → P ch_N → P ch_O → P ch_P → P ch_Q → P ch_R → P ch_S → P ch_T → P ch_U → P ch_V →
+ P ch_W → P ch_X → P ch_Y → P ch_Z → P ch_a → P ch_b → P ch_c → P ch_d → P ch_e → P ch_f → P ch_g →
+ P ch_h → P ch_i → P ch_j → P ch_k → P ch_l → P ch_m → P ch_n → P ch_o → P ch_p → P ch_q → P ch_r →
+ P ch_s → P ch_t → P ch_u → P ch_v → P ch_w → P ch_x → P ch_y → P ch_z → Πa:ascii.P a ≝
+λP:ascii → Set.
+λp:P ch_0.λp1:P ch_1.λp2:P ch_2.λp3:P ch_3.λp4:P ch_4.λp5:P ch_5.λp6:P ch_6.λp7:P ch_7.λp8:P ch_8.λp9:P ch_9.
+λp10:P ch__.λp11:P ch_A.λp12:P ch_B.λp13:P ch_C.λp14:P ch_D.λp15:P ch_E.λp16:P ch_F.λp17:P ch_G.λp18:P ch_H.
+λp19:P ch_I.λp20:P ch_J.λp21:P ch_K.λp22:P ch_L.λp23:P ch_M.λp24:P ch_N.λp25:P ch_O.λp26:P ch_P.λp27:P ch_Q.
+λp28:P ch_R.λp29:P ch_S.λp30:P ch_T.λp31:P ch_U.λp32:P ch_V.λp33:P ch_W.λp34:P ch_X.λp35:P ch_Y.λp36:P ch_Z.
+λp37:P ch_a.λp38:P ch_b.λp39:P ch_c.λp40:P ch_d.λp41:P ch_e.λp42:P ch_f.λp43:P ch_g.λp44:P ch_h.λp45:P ch_i.
+λp46:P ch_j.λp47:P ch_k.λp48:P ch_l.λp49:P ch_m.λp50:P ch_n.λp51:P ch_o.λp52:P ch_p.λp53:P ch_q.λp54:P ch_r.
+λp55:P ch_s.λp56:P ch_t.λp57:P ch_u.λp58:P ch_v.λp59:P ch_w.λp60:P ch_x.λp61:P ch_y.λp62:P ch_z.λa:ascii.
+ match a with
+ [ ch_0 ⇒ p | ch_1 ⇒ p1 | ch_2 ⇒ p2 | ch_3 ⇒ p3 | ch_4 ⇒ p4 | ch_5 ⇒ p5 | ch_6 ⇒ p6 | ch_7 ⇒ p7
+ | ch_8 ⇒ p8 | ch_9 ⇒ p9 | ch__ ⇒ p10 | ch_A ⇒ p11 | ch_B ⇒ p12 | ch_C ⇒ p13 | ch_D ⇒ p14 | ch_E ⇒ p15
+ | ch_F ⇒ p16 | ch_G ⇒ p17 | ch_H ⇒ p18 | ch_I ⇒ p19 | ch_J ⇒ p20 | ch_K ⇒ p21 | ch_L ⇒ p22 | ch_M ⇒ p23
+ | ch_N ⇒ p24 | ch_O ⇒ p25 | ch_P ⇒ p26 | ch_Q ⇒ p27 | ch_R ⇒ p28 | ch_S ⇒ p29 | ch_T ⇒ p30 | ch_U ⇒ p31
+ | ch_V ⇒ p32 | ch_W ⇒ p33 | ch_X ⇒ p34 | ch_Y ⇒ p35 | ch_Z ⇒ p36 | ch_a ⇒ p37 | ch_b ⇒ p38 | ch_c ⇒ p39
+ | ch_d ⇒ p40 | ch_e ⇒ p41 | ch_f ⇒ p42 | ch_g ⇒ p43 | ch_h ⇒ p44 | ch_i ⇒ p45 | ch_j ⇒ p46 | ch_k ⇒ p47
+ | ch_l ⇒ p48 | ch_m ⇒ p49 | ch_n ⇒ p50 | ch_o ⇒ p51 | ch_p ⇒ p52 | ch_q ⇒ p53 | ch_r ⇒ p54 | ch_s ⇒ p55
+ | ch_t ⇒ p56 | ch_u ⇒ p57 | ch_v ⇒ p58 | ch_w ⇒ p59 | ch_x ⇒ p60 | ch_y ⇒ p61 | ch_z ⇒ p62 ].
+
+ndefinition ascii_rect
+ : ΠP:ascii → Type.
+ P ch_0 → P ch_1 → P ch_2 → P ch_3 → P ch_4 → P ch_5 → P ch_6 → P ch_7 → P ch_8 → P ch_9 → P ch__ →
+ P ch_A → P ch_B → P ch_C → P ch_D → P ch_E → P ch_F → P ch_G → P ch_H → P ch_I → P ch_J → P ch_K →
+ P ch_L → P ch_M → P ch_N → P ch_O → P ch_P → P ch_Q → P ch_R → P ch_S → P ch_T → P ch_U → P ch_V →
+ P ch_W → P ch_X → P ch_Y → P ch_Z → P ch_a → P ch_b → P ch_c → P ch_d → P ch_e → P ch_f → P ch_g →
+ P ch_h → P ch_i → P ch_j → P ch_k → P ch_l → P ch_m → P ch_n → P ch_o → P ch_p → P ch_q → P ch_r →
+ P ch_s → P ch_t → P ch_u → P ch_v → P ch_w → P ch_x → P ch_y → P ch_z → Πa:ascii.P a ≝
+λP:ascii → Type.
+λp:P ch_0.λp1:P ch_1.λp2:P ch_2.λp3:P ch_3.λp4:P ch_4.λp5:P ch_5.λp6:P ch_6.λp7:P ch_7.λp8:P ch_8.λp9:P ch_9.
+λp10:P ch__.λp11:P ch_A.λp12:P ch_B.λp13:P ch_C.λp14:P ch_D.λp15:P ch_E.λp16:P ch_F.λp17:P ch_G.λp18:P ch_H.
+λp19:P ch_I.λp20:P ch_J.λp21:P ch_K.λp22:P ch_L.λp23:P ch_M.λp24:P ch_N.λp25:P ch_O.λp26:P ch_P.λp27:P ch_Q.
+λp28:P ch_R.λp29:P ch_S.λp30:P ch_T.λp31:P ch_U.λp32:P ch_V.λp33:P ch_W.λp34:P ch_X.λp35:P ch_Y.λp36:P ch_Z.
+λp37:P ch_a.λp38:P ch_b.λp39:P ch_c.λp40:P ch_d.λp41:P ch_e.λp42:P ch_f.λp43:P ch_g.λp44:P ch_h.λp45:P ch_i.
+λp46:P ch_j.λp47:P ch_k.λp48:P ch_l.λp49:P ch_m.λp50:P ch_n.λp51:P ch_o.λp52:P ch_p.λp53:P ch_q.λp54:P ch_r.
+λp55:P ch_s.λp56:P ch_t.λp57:P ch_u.λp58:P ch_v.λp59:P ch_w.λp60:P ch_x.λp61:P ch_y.λp62:P ch_z.λa:ascii.
+ match a with
+ [ ch_0 ⇒ p | ch_1 ⇒ p1 | ch_2 ⇒ p2 | ch_3 ⇒ p3 | ch_4 ⇒ p4 | ch_5 ⇒ p5 | ch_6 ⇒ p6 | ch_7 ⇒ p7
+ | ch_8 ⇒ p8 | ch_9 ⇒ p9 | ch__ ⇒ p10 | ch_A ⇒ p11 | ch_B ⇒ p12 | ch_C ⇒ p13 | ch_D ⇒ p14 | ch_E ⇒ p15
+ | ch_F ⇒ p16 | ch_G ⇒ p17 | ch_H ⇒ p18 | ch_I ⇒ p19 | ch_J ⇒ p20 | ch_K ⇒ p21 | ch_L ⇒ p22 | ch_M ⇒ p23
+ | ch_N ⇒ p24 | ch_O ⇒ p25 | ch_P ⇒ p26 | ch_Q ⇒ p27 | ch_R ⇒ p28 | ch_S ⇒ p29 | ch_T ⇒ p30 | ch_U ⇒ p31
+ | ch_V ⇒ p32 | ch_W ⇒ p33 | ch_X ⇒ p34 | ch_Y ⇒ p35 | ch_Z ⇒ p36 | ch_a ⇒ p37 | ch_b ⇒ p38 | ch_c ⇒ p39
+ | ch_d ⇒ p40 | ch_e ⇒ p41 | ch_f ⇒ p42 | ch_g ⇒ p43 | ch_h ⇒ p44 | ch_i ⇒ p45 | ch_j ⇒ p46 | ch_k ⇒ p47
+ | ch_l ⇒ p48 | ch_m ⇒ p49 | ch_n ⇒ p50 | ch_o ⇒ p51 | ch_p ⇒ p52 | ch_q ⇒ p53 | ch_r ⇒ p54 | ch_s ⇒ p55
+ | ch_t ⇒ p56 | ch_u ⇒ p57 | ch_v ⇒ p58 | ch_w ⇒ p59 | ch_x ⇒ p60 | ch_y ⇒ p61 | ch_z ⇒ p62 ].
+
+(* confronto fra ascii *)
+ndefinition eq_ascii ≝
+λc,c':ascii.match c with
+ [ ch_0 ⇒ match c' with [ ch_0 ⇒ true | _ ⇒ false ]
+ | ch_1 ⇒ match c' with [ ch_1 ⇒ true | _ ⇒ false ]
+ | ch_2 ⇒ match c' with [ ch_2 ⇒ true | _ ⇒ false ]
+ | ch_3 ⇒ match c' with [ ch_3 ⇒ true | _ ⇒ false ]
+ | ch_4 ⇒ match c' with [ ch_4 ⇒ true | _ ⇒ false ]
+ | ch_5 ⇒ match c' with [ ch_5 ⇒ true | _ ⇒ false ]
+ | ch_6 ⇒ match c' with [ ch_6 ⇒ true | _ ⇒ false ]
+ | ch_7 ⇒ match c' with [ ch_7 ⇒ true | _ ⇒ false ]
+ | ch_8 ⇒ match c' with [ ch_8 ⇒ true | _ ⇒ false ]
+ | ch_9 ⇒ match c' with [ ch_9 ⇒ true | _ ⇒ false ]
+ | ch__ ⇒ match c' with [ ch__ ⇒ true | _ ⇒ false ]
+ | ch_A ⇒ match c' with [ ch_A ⇒ true | _ ⇒ false ]
+ | ch_B ⇒ match c' with [ ch_B ⇒ true | _ ⇒ false ]
+ | ch_C ⇒ match c' with [ ch_C ⇒ true | _ ⇒ false ]
+ | ch_D ⇒ match c' with [ ch_D ⇒ true | _ ⇒ false ]
+ | ch_E ⇒ match c' with [ ch_E ⇒ true | _ ⇒ false ]
+ | ch_F ⇒ match c' with [ ch_F ⇒ true | _ ⇒ false ]
+ | ch_G ⇒ match c' with [ ch_G ⇒ true | _ ⇒ false ]
+ | ch_H ⇒ match c' with [ ch_H ⇒ true | _ ⇒ false ]
+ | ch_I ⇒ match c' with [ ch_I ⇒ true | _ ⇒ false ]
+ | ch_J ⇒ match c' with [ ch_J ⇒ true | _ ⇒ false ]
+ | ch_K ⇒ match c' with [ ch_K ⇒ true | _ ⇒ false ]
+ | ch_L ⇒ match c' with [ ch_L ⇒ true | _ ⇒ false ]
+ | ch_M ⇒ match c' with [ ch_M ⇒ true | _ ⇒ false ]
+ | ch_N ⇒ match c' with [ ch_N ⇒ true | _ ⇒ false ]
+ | ch_O ⇒ match c' with [ ch_O ⇒ true | _ ⇒ false ]
+ | ch_P ⇒ match c' with [ ch_P ⇒ true | _ ⇒ false ]
+ | ch_Q ⇒ match c' with [ ch_Q ⇒ true | _ ⇒ false ]
+ | ch_R ⇒ match c' with [ ch_R ⇒ true | _ ⇒ false ]
+ | ch_S ⇒ match c' with [ ch_S ⇒ true | _ ⇒ false ]
+ | ch_T ⇒ match c' with [ ch_T ⇒ true | _ ⇒ false ]
+ | ch_U ⇒ match c' with [ ch_U ⇒ true | _ ⇒ false ]
+ | ch_V ⇒ match c' with [ ch_V ⇒ true | _ ⇒ false ]
+ | ch_W ⇒ match c' with [ ch_W ⇒ true | _ ⇒ false ]
+ | ch_X ⇒ match c' with [ ch_X ⇒ true | _ ⇒ false ]
+ | ch_Y ⇒ match c' with [ ch_Y ⇒ true | _ ⇒ false ]
+ | ch_Z ⇒ match c' with [ ch_Z ⇒ true | _ ⇒ false ]
+ | ch_a ⇒ match c' with [ ch_a ⇒ true | _ ⇒ false ]
+ | ch_b ⇒ match c' with [ ch_b ⇒ true | _ ⇒ false ]
+ | ch_c ⇒ match c' with [ ch_c ⇒ true | _ ⇒ false ]
+ | ch_d ⇒ match c' with [ ch_d ⇒ true | _ ⇒ false ]
+ | ch_e ⇒ match c' with [ ch_e ⇒ true | _ ⇒ false ]
+ | ch_f ⇒ match c' with [ ch_f ⇒ true | _ ⇒ false ]
+ | ch_g ⇒ match c' with [ ch_g ⇒ true | _ ⇒ false ]
+ | ch_h ⇒ match c' with [ ch_h ⇒ true | _ ⇒ false ]
+ | ch_i ⇒ match c' with [ ch_i ⇒ true | _ ⇒ false ]
+ | ch_j ⇒ match c' with [ ch_j ⇒ true | _ ⇒ false ]
+ | ch_k ⇒ match c' with [ ch_k ⇒ true | _ ⇒ false ]
+ | ch_l ⇒ match c' with [ ch_l ⇒ true | _ ⇒ false ]
+ | ch_m ⇒ match c' with [ ch_m ⇒ true | _ ⇒ false ]
+ | ch_n ⇒ match c' with [ ch_n ⇒ true | _ ⇒ false ]
+ | ch_o ⇒ match c' with [ ch_o ⇒ true | _ ⇒ false ]
+ | ch_p ⇒ match c' with [ ch_p ⇒ true | _ ⇒ false ]
+ | ch_q ⇒ match c' with [ ch_q ⇒ true | _ ⇒ false ]
+ | ch_r ⇒ match c' with [ ch_r ⇒ true | _ ⇒ false ]
+ | ch_s ⇒ match c' with [ ch_s ⇒ true | _ ⇒ false ]
+ | ch_t ⇒ match c' with [ ch_t ⇒ true | _ ⇒ false ]
+ | ch_u ⇒ match c' with [ ch_u ⇒ true | _ ⇒ false ]
+ | ch_v ⇒ match c' with [ ch_v ⇒ true | _ ⇒ false ]
+ | ch_w ⇒ match c' with [ ch_w ⇒ true | _ ⇒ false ]
+ | ch_x ⇒ match c' with [ ch_x ⇒ true | _ ⇒ false ]
+ | ch_y ⇒ match c' with [ ch_y ⇒ true | _ ⇒ false ]
+ | ch_z ⇒ match c' with [ ch_z ⇒ true | _ ⇒ false ]
+ ].
--- /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 "utility/ascii.ma".
+include "freescale/theory.ma".
+
+(* ************************** *)
+(* DEFINIZIONE ASCII MINIMALE *)
+(* ************************** *)
+
+ndefinition ascii_destruct1 : Πc2.ΠP:Prop.ch_0 = c2 → match c2 with [ ch_0 ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##1: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_0 with [ ch_0 ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct2 : Πc2.ΠP:Prop.ch_1 = c2 → match c2 with [ ch_1 ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##2: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_1 with [ ch_1 ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct3 : Πc2.ΠP:Prop.ch_2 = c2 → match c2 with [ ch_2 ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##3: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_2 with [ ch_2 ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct4 : Πc2.ΠP:Prop.ch_3 = c2 → match c2 with [ ch_3 ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##4: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_3 with [ ch_3 ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct5 : Πc2.ΠP:Prop.ch_4 = c2 → match c2 with [ ch_4 ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##5: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_4 with [ ch_4 ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct6 : Πc2.ΠP:Prop.ch_5 = c2 → match c2 with [ ch_5 ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##6: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_5 with [ ch_5 ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct7 : Πc2.ΠP:Prop.ch_6 = c2 → match c2 with [ ch_6 ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##7: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_6 with [ ch_6 ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct8 : Πc2.ΠP:Prop.ch_7 = c2 → match c2 with [ ch_7 ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##8: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_7 with [ ch_7 ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct9 : Πc2.ΠP:Prop.ch_8 = c2 → match c2 with [ ch_8 ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##9: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_8 with [ ch_8 ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct10 : Πc2.ΠP:Prop.ch_9 = c2 → match c2 with [ ch_9 ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##10: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_9 with [ ch_9 ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct11 : Πc2.ΠP:Prop.ch__ = c2 → match c2 with [ ch__ ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##11: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch__ with [ ch__ ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct12 : Πc2.ΠP:Prop.ch_A = c2 → match c2 with [ ch_A ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##12: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_A with [ ch_A ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct13 : Πc2.ΠP:Prop.ch_B = c2 → match c2 with [ ch_B ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##13: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_B with [ ch_B ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct14 : Πc2.ΠP:Prop.ch_C = c2 → match c2 with [ ch_C ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##14: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_C with [ ch_C ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct15 : Πc2.ΠP:Prop.ch_D = c2 → match c2 with [ ch_D ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##15: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_D with [ ch_D ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct16 : Πc2.ΠP:Prop.ch_E = c2 → match c2 with [ ch_E ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##16: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_E with [ ch_E ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct17 : Πc2.ΠP:Prop.ch_F = c2 → match c2 with [ ch_F ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##17: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_F with [ ch_F ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct18 : Πc2.ΠP:Prop.ch_G = c2 → match c2 with [ ch_G ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##18: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_G with [ ch_G ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct19 : Πc2.ΠP:Prop.ch_H = c2 → match c2 with [ ch_H ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##19: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_H with [ ch_H ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct20 : Πc2.ΠP:Prop.ch_I = c2 → match c2 with [ ch_I ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##20: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_I with [ ch_I ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct21 : Πc2.ΠP:Prop.ch_J = c2 → match c2 with [ ch_J ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##21: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_J with [ ch_J ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct22 : Πc2.ΠP:Prop.ch_K = c2 → match c2 with [ ch_K ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##22: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_K with [ ch_K ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct23 : Πc2.ΠP:Prop.ch_L = c2 → match c2 with [ ch_L ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##23: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_L with [ ch_L ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct24 : Πc2.ΠP:Prop.ch_M = c2 → match c2 with [ ch_M ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##24: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_M with [ ch_M ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct25 : Πc2.ΠP:Prop.ch_N = c2 → match c2 with [ ch_N ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##25: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_N with [ ch_N ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct26 : Πc2.ΠP:Prop.ch_O = c2 → match c2 with [ ch_O ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##26: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_O with [ ch_O ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct27 : Πc2.ΠP:Prop.ch_P = c2 → match c2 with [ ch_P ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##27: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_P with [ ch_P ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct28 : Πc2.ΠP:Prop.ch_Q = c2 → match c2 with [ ch_Q ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##28: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_Q with [ ch_Q ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct29 : Πc2.ΠP:Prop.ch_R = c2 → match c2 with [ ch_R ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##29: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_R with [ ch_R ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct30 : Πc2.ΠP:Prop.ch_S = c2 → match c2 with [ ch_S ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##30: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_S with [ ch_S ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct31 : Πc2.ΠP:Prop.ch_T = c2 → match c2 with [ ch_T ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##31: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_T with [ ch_T ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct32 : Πc2.ΠP:Prop.ch_U = c2 → match c2 with [ ch_U ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##32: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_U with [ ch_U ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct33 : Πc2.ΠP:Prop.ch_V = c2 → match c2 with [ ch_V ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##33: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_V with [ ch_V ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct34 : Πc2.ΠP:Prop.ch_W = c2 → match c2 with [ ch_W ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##34: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_W with [ ch_W ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct35 : Πc2.ΠP:Prop.ch_X = c2 → match c2 with [ ch_X ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##35: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_X with [ ch_X ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct36 : Πc2.ΠP:Prop.ch_Y = c2 → match c2 with [ ch_Y ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##36: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_Y with [ ch_Y ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct37 : Πc2.ΠP:Prop.ch_Z = c2 → match c2 with [ ch_Z ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##37: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_Z with [ ch_Z ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct38 : Πc2.ΠP:Prop.ch_a = c2 → match c2 with [ ch_a ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##38: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_a with [ ch_a ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct39 : Πc2.ΠP:Prop.ch_b = c2 → match c2 with [ ch_b ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##39: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_b with [ ch_b ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct40 : Πc2.ΠP:Prop.ch_c = c2 → match c2 with [ ch_c ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##40: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_c with [ ch_c ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct41 : Πc2.ΠP:Prop.ch_d = c2 → match c2 with [ ch_d ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##41: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_d with [ ch_d ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct42 : Πc2.ΠP:Prop.ch_e = c2 → match c2 with [ ch_e ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##42: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_e with [ ch_e ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct43 : Πc2.ΠP:Prop.ch_f = c2 → match c2 with [ ch_f ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##43: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_f with [ ch_f ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct44 : Πc2.ΠP:Prop.ch_g = c2 → match c2 with [ ch_g ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##44: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_g with [ ch_g ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct45 : Πc2.ΠP:Prop.ch_h = c2 → match c2 with [ ch_h ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##45: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_h with [ ch_h ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct46 : Πc2.ΠP:Prop.ch_i = c2 → match c2 with [ ch_i ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##46: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_i with [ ch_i ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct47 : Πc2.ΠP:Prop.ch_j = c2 → match c2 with [ ch_j ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##47: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_j with [ ch_j ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct48 : Πc2.ΠP:Prop.ch_k = c2 → match c2 with [ ch_k ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##48: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_k with [ ch_k ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct49 : Πc2.ΠP:Prop.ch_l = c2 → match c2 with [ ch_l ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##49: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_l with [ ch_l ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct50 : Πc2.ΠP:Prop.ch_m = c2 → match c2 with [ ch_m ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##50: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_m with [ ch_m ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct51 : Πc2.ΠP:Prop.ch_n = c2 → match c2 with [ ch_n ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##51: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_n with [ ch_n ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct52 : Πc2.ΠP:Prop.ch_o = c2 → match c2 with [ ch_o ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##52: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_o with [ ch_o ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct53 : Πc2.ΠP:Prop.ch_p = c2 → match c2 with [ ch_p ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##53: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_p with [ ch_p ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct54 : Πc2.ΠP:Prop.ch_q = c2 → match c2 with [ ch_q ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##54: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_q with [ ch_q ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct55 : Πc2.ΠP:Prop.ch_r = c2 → match c2 with [ ch_r ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##55: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_r with [ ch_r ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct56 : Πc2.ΠP:Prop.ch_s = c2 → match c2 with [ ch_s ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##56: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_s with [ ch_s ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct57 : Πc2.ΠP:Prop.ch_t = c2 → match c2 with [ ch_t ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##57: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_t with [ ch_t ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct58 : Πc2.ΠP:Prop.ch_u = c2 → match c2 with [ ch_u ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##58: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_u with [ ch_u ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct59 : Πc2.ΠP:Prop.ch_v = c2 → match c2 with [ ch_v ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##59: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_v with [ ch_v ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct60 : Πc2.ΠP:Prop.ch_w = c2 → match c2 with [ ch_w ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##60: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_w with [ ch_w ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct61 : Πc2.ΠP:Prop.ch_x = c2 → match c2 with [ ch_x ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##61: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_x with [ ch_x ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct62 : Πc2.ΠP:Prop.ch_y = c2 → match c2 with [ ch_y ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##62: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_y with [ ch_y ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct63 : Πc2.ΠP:Prop.ch_z = c2 → match c2 with [ ch_z ⇒ P → P | _ ⇒ P ].
+ #c2; #P; ncases c2; nnormalize;
+ ##[ ##63: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (False_ind ??); nchange with (match ch_z with [ ch_z ⇒ False | _ ⇒ True ]); nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition ascii_destruct_aux ≝
+Πc1,c2.ΠP:Prop.c1 = c2 →
+ match c1 with
+ [ ch_0 ⇒ match c2 with [ ch_0 ⇒ P → P | _ ⇒ P ] | ch_1 ⇒ match c2 with [ ch_1 ⇒ P → P | _ ⇒ P ]
+ | ch_2 ⇒ match c2 with [ ch_2 ⇒ P → P | _ ⇒ P ] | ch_3 ⇒ match c2 with [ ch_3 ⇒ P → P | _ ⇒ P ]
+ | ch_4 ⇒ match c2 with [ ch_4 ⇒ P → P | _ ⇒ P ] | ch_5 ⇒ match c2 with [ ch_5 ⇒ P → P | _ ⇒ P ]
+ | ch_6 ⇒ match c2 with [ ch_6 ⇒ P → P | _ ⇒ P ] | ch_7 ⇒ match c2 with [ ch_7 ⇒ P → P | _ ⇒ P ]
+ | ch_8 ⇒ match c2 with [ ch_8 ⇒ P → P | _ ⇒ P ] | ch_9 ⇒ match c2 with [ ch_9 ⇒ P → P | _ ⇒ P ]
+ | ch__ ⇒ match c2 with [ ch__ ⇒ P → P | _ ⇒ P ] | ch_A ⇒ match c2 with [ ch_A ⇒ P → P | _ ⇒ P ]
+ | ch_B ⇒ match c2 with [ ch_B ⇒ P → P | _ ⇒ P ] | ch_C ⇒ match c2 with [ ch_C ⇒ P → P | _ ⇒ P ]
+ | ch_D ⇒ match c2 with [ ch_D ⇒ P → P | _ ⇒ P ] | ch_E ⇒ match c2 with [ ch_E ⇒ P → P | _ ⇒ P ]
+ | ch_F ⇒ match c2 with [ ch_F ⇒ P → P | _ ⇒ P ] | ch_G ⇒ match c2 with [ ch_G ⇒ P → P | _ ⇒ P ]
+ | ch_H ⇒ match c2 with [ ch_H ⇒ P → P | _ ⇒ P ] | ch_I ⇒ match c2 with [ ch_I ⇒ P → P | _ ⇒ P ]
+ | ch_J ⇒ match c2 with [ ch_J ⇒ P → P | _ ⇒ P ] | ch_K ⇒ match c2 with [ ch_K ⇒ P → P | _ ⇒ P ]
+ | ch_L ⇒ match c2 with [ ch_L ⇒ P → P | _ ⇒ P ] | ch_M ⇒ match c2 with [ ch_M ⇒ P → P | _ ⇒ P ]
+ | ch_N ⇒ match c2 with [ ch_N ⇒ P → P | _ ⇒ P ] | ch_O ⇒ match c2 with [ ch_O ⇒ P → P | _ ⇒ P ]
+ | ch_P ⇒ match c2 with [ ch_P ⇒ P → P | _ ⇒ P ] | ch_Q ⇒ match c2 with [ ch_Q ⇒ P → P | _ ⇒ P ]
+ | ch_R ⇒ match c2 with [ ch_R ⇒ P → P | _ ⇒ P ] | ch_S ⇒ match c2 with [ ch_S ⇒ P → P | _ ⇒ P ]
+ | ch_T ⇒ match c2 with [ ch_T ⇒ P → P | _ ⇒ P ] | ch_U ⇒ match c2 with [ ch_U ⇒ P → P | _ ⇒ P ]
+ | ch_V ⇒ match c2 with [ ch_V ⇒ P → P | _ ⇒ P ] | ch_W ⇒ match c2 with [ ch_W ⇒ P → P | _ ⇒ P ]
+ | ch_X ⇒ match c2 with [ ch_X ⇒ P → P | _ ⇒ P ] | ch_Y ⇒ match c2 with [ ch_Y ⇒ P → P | _ ⇒ P ]
+ | ch_Z ⇒ match c2 with [ ch_Z ⇒ P → P | _ ⇒ P ] | ch_a ⇒ match c2 with [ ch_a ⇒ P → P | _ ⇒ P ]
+ | ch_b ⇒ match c2 with [ ch_b ⇒ P → P | _ ⇒ P ] | ch_c ⇒ match c2 with [ ch_c ⇒ P → P | _ ⇒ P ]
+ | ch_d ⇒ match c2 with [ ch_d ⇒ P → P | _ ⇒ P ] | ch_e ⇒ match c2 with [ ch_e ⇒ P → P | _ ⇒ P ]
+ | ch_f ⇒ match c2 with [ ch_f ⇒ P → P | _ ⇒ P ] | ch_g ⇒ match c2 with [ ch_g ⇒ P → P | _ ⇒ P ]
+ | ch_h ⇒ match c2 with [ ch_h ⇒ P → P | _ ⇒ P ] | ch_i ⇒ match c2 with [ ch_i ⇒ P → P | _ ⇒ P ]
+ | ch_j ⇒ match c2 with [ ch_j ⇒ P → P | _ ⇒ P ] | ch_k ⇒ match c2 with [ ch_k ⇒ P → P | _ ⇒ P ]
+ | ch_l ⇒ match c2 with [ ch_l ⇒ P → P | _ ⇒ P ] | ch_m ⇒ match c2 with [ ch_m ⇒ P → P | _ ⇒ P ]
+ | ch_n ⇒ match c2 with [ ch_n ⇒ P → P | _ ⇒ P ] | ch_o ⇒ match c2 with [ ch_o ⇒ P → P | _ ⇒ P ]
+ | ch_p ⇒ match c2 with [ ch_p ⇒ P → P | _ ⇒ P ] | ch_q ⇒ match c2 with [ ch_q ⇒ P → P | _ ⇒ P ]
+ | ch_r ⇒ match c2 with [ ch_r ⇒ P → P | _ ⇒ P ] | ch_s ⇒ match c2 with [ ch_s ⇒ P → P | _ ⇒ P ]
+ | ch_t ⇒ match c2 with [ ch_t ⇒ P → P | _ ⇒ P ] | ch_u ⇒ match c2 with [ ch_u ⇒ P → P | _ ⇒ P ]
+ | ch_v ⇒ match c2 with [ ch_v ⇒ P → P | _ ⇒ P ] | ch_w ⇒ match c2 with [ ch_w ⇒ P → P | _ ⇒ P ]
+ | ch_x ⇒ match c2 with [ ch_x ⇒ P → P | _ ⇒ P ] | ch_y ⇒ match c2 with [ ch_y ⇒ P → P | _ ⇒ P ]
+ | ch_z ⇒ match c2 with [ ch_z ⇒ P → P | _ ⇒ P ]].
+
+nlemma ascii_destruct : ascii_destruct_aux.
+ #c1; ncases c1;
+ ##[ ##1: napply ascii_destruct1 ##| ##2: napply ascii_destruct2
+ ##| ##3: napply ascii_destruct3 ##| ##4: napply ascii_destruct4
+ ##| ##5: napply ascii_destruct5 ##| ##6: napply ascii_destruct6
+ ##| ##7: napply ascii_destruct7 ##| ##8: napply ascii_destruct8
+ ##| ##9: napply ascii_destruct9 ##| ##10: napply ascii_destruct10
+ ##| ##11: napply ascii_destruct11 ##| ##12: napply ascii_destruct12
+ ##| ##13: napply ascii_destruct13 ##| ##14: napply ascii_destruct14
+ ##| ##15: napply ascii_destruct15 ##| ##16: napply ascii_destruct16
+ ##| ##17: napply ascii_destruct17 ##| ##18: napply ascii_destruct18
+ ##| ##19: napply ascii_destruct19 ##| ##20: napply ascii_destruct20
+ ##| ##21: napply ascii_destruct21 ##| ##22: napply ascii_destruct22
+ ##| ##23: napply ascii_destruct23 ##| ##24: napply ascii_destruct24
+ ##| ##25: napply ascii_destruct25 ##| ##26: napply ascii_destruct26
+ ##| ##27: napply ascii_destruct27 ##| ##28: napply ascii_destruct28
+ ##| ##29: napply ascii_destruct29 ##| ##30: napply ascii_destruct30
+ ##| ##31: napply ascii_destruct31 ##| ##32: napply ascii_destruct32
+ ##| ##33: napply ascii_destruct33 ##| ##34: napply ascii_destruct34
+ ##| ##35: napply ascii_destruct35 ##| ##36: napply ascii_destruct36
+ ##| ##37: napply ascii_destruct37 ##| ##38: napply ascii_destruct38
+ ##| ##39: napply ascii_destruct39 ##| ##40: napply ascii_destruct40
+ ##| ##41: napply ascii_destruct41 ##| ##42: napply ascii_destruct42
+ ##| ##43: napply ascii_destruct43 ##| ##44: napply ascii_destruct44
+ ##| ##45: napply ascii_destruct45 ##| ##46: napply ascii_destruct46
+ ##| ##47: napply ascii_destruct47 ##| ##48: napply ascii_destruct48
+ ##| ##49: napply ascii_destruct49 ##| ##50: napply ascii_destruct50
+ ##| ##51: napply ascii_destruct51 ##| ##52: napply ascii_destruct52
+ ##| ##53: napply ascii_destruct53 ##| ##54: napply ascii_destruct54
+ ##| ##55: napply ascii_destruct55 ##| ##56: napply ascii_destruct56
+ ##| ##57: napply ascii_destruct57 ##| ##58: napply ascii_destruct58
+ ##| ##59: napply ascii_destruct59 ##| ##60: napply ascii_destruct60
+ ##| ##61: napply ascii_destruct61 ##| ##62: napply ascii_destruct62
+ ##| ##63: napply ascii_destruct63 ##]
+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 "utility/ascii_lemmas1.ma".
+include "freescale/bool_lemmas.ma".
+
+(* ************************** *)
+(* DEFINIZIONE ASCII MINIMALE *)
+(* ************************** *)
+
+nlemma symmetric_eqascii1 : ∀a2.eq_ascii ch_0 a2 = eq_ascii a2 ch_0. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii2 : ∀a2.eq_ascii ch_1 a2 = eq_ascii a2 ch_1. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii3 : ∀a2.eq_ascii ch_2 a2 = eq_ascii a2 ch_2. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii4 : ∀a2.eq_ascii ch_3 a2 = eq_ascii a2 ch_3. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii5 : ∀a2.eq_ascii ch_4 a2 = eq_ascii a2 ch_4. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii6 : ∀a2.eq_ascii ch_5 a2 = eq_ascii a2 ch_5. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii7 : ∀a2.eq_ascii ch_6 a2 = eq_ascii a2 ch_6. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii8 : ∀a2.eq_ascii ch_7 a2 = eq_ascii a2 ch_7. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii9 : ∀a2.eq_ascii ch_8 a2 = eq_ascii a2 ch_8. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii10 : ∀a2.eq_ascii ch_9 a2 = eq_ascii a2 ch_9. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii11 : ∀a2.eq_ascii ch__ a2 = eq_ascii a2 ch__. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii12 : ∀a2.eq_ascii ch_A a2 = eq_ascii a2 ch_A. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii13 : ∀a2.eq_ascii ch_B a2 = eq_ascii a2 ch_B. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii14 : ∀a2.eq_ascii ch_C a2 = eq_ascii a2 ch_C. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii15 : ∀a2.eq_ascii ch_D a2 = eq_ascii a2 ch_D. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii16 : ∀a2.eq_ascii ch_E a2 = eq_ascii a2 ch_E. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii17 : ∀a2.eq_ascii ch_F a2 = eq_ascii a2 ch_F. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii18 : ∀a2.eq_ascii ch_G a2 = eq_ascii a2 ch_G. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii19 : ∀a2.eq_ascii ch_H a2 = eq_ascii a2 ch_H. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii20 : ∀a2.eq_ascii ch_I a2 = eq_ascii a2 ch_I. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii21 : ∀a2.eq_ascii ch_J a2 = eq_ascii a2 ch_J. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii22 : ∀a2.eq_ascii ch_K a2 = eq_ascii a2 ch_K. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii23 : ∀a2.eq_ascii ch_L a2 = eq_ascii a2 ch_L. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii24 : ∀a2.eq_ascii ch_M a2 = eq_ascii a2 ch_M. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii25 : ∀a2.eq_ascii ch_N a2 = eq_ascii a2 ch_N. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii26 : ∀a2.eq_ascii ch_O a2 = eq_ascii a2 ch_O. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii27 : ∀a2.eq_ascii ch_P a2 = eq_ascii a2 ch_P. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii28 : ∀a2.eq_ascii ch_Q a2 = eq_ascii a2 ch_Q. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii29 : ∀a2.eq_ascii ch_R a2 = eq_ascii a2 ch_R. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii30 : ∀a2.eq_ascii ch_S a2 = eq_ascii a2 ch_S. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii31 : ∀a2.eq_ascii ch_T a2 = eq_ascii a2 ch_T. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii32 : ∀a2.eq_ascii ch_U a2 = eq_ascii a2 ch_U. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii33 : ∀a2.eq_ascii ch_V a2 = eq_ascii a2 ch_V. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii34 : ∀a2.eq_ascii ch_W a2 = eq_ascii a2 ch_W. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii35 : ∀a2.eq_ascii ch_X a2 = eq_ascii a2 ch_X. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii36 : ∀a2.eq_ascii ch_Y a2 = eq_ascii a2 ch_Y. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii37 : ∀a2.eq_ascii ch_Z a2 = eq_ascii a2 ch_Z. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii38 : ∀a2.eq_ascii ch_a a2 = eq_ascii a2 ch_a. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii39 : ∀a2.eq_ascii ch_b a2 = eq_ascii a2 ch_b. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii40 : ∀a2.eq_ascii ch_c a2 = eq_ascii a2 ch_c. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii41 : ∀a2.eq_ascii ch_d a2 = eq_ascii a2 ch_d. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii42 : ∀a2.eq_ascii ch_e a2 = eq_ascii a2 ch_e. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii43 : ∀a2.eq_ascii ch_f a2 = eq_ascii a2 ch_f. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii44 : ∀a2.eq_ascii ch_g a2 = eq_ascii a2 ch_g. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii45 : ∀a2.eq_ascii ch_h a2 = eq_ascii a2 ch_h. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii46 : ∀a2.eq_ascii ch_i a2 = eq_ascii a2 ch_i. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii47 : ∀a2.eq_ascii ch_j a2 = eq_ascii a2 ch_j. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii48 : ∀a2.eq_ascii ch_k a2 = eq_ascii a2 ch_k. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii49 : ∀a2.eq_ascii ch_l a2 = eq_ascii a2 ch_l. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii50 : ∀a2.eq_ascii ch_m a2 = eq_ascii a2 ch_m. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii51 : ∀a2.eq_ascii ch_n a2 = eq_ascii a2 ch_n. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii52 : ∀a2.eq_ascii ch_o a2 = eq_ascii a2 ch_o. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii53 : ∀a2.eq_ascii ch_p a2 = eq_ascii a2 ch_p. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii54 : ∀a2.eq_ascii ch_q a2 = eq_ascii a2 ch_q. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii55 : ∀a2.eq_ascii ch_r a2 = eq_ascii a2 ch_r. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii56 : ∀a2.eq_ascii ch_s a2 = eq_ascii a2 ch_s. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii57 : ∀a2.eq_ascii ch_t a2 = eq_ascii a2 ch_t. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii58 : ∀a2.eq_ascii ch_u a2 = eq_ascii a2 ch_u. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii59 : ∀a2.eq_ascii ch_v a2 = eq_ascii a2 ch_v. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii60 : ∀a2.eq_ascii ch_w a2 = eq_ascii a2 ch_w. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii61 : ∀a2.eq_ascii ch_x a2 = eq_ascii a2 ch_x. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii62 : ∀a2.eq_ascii ch_y a2 = eq_ascii a2 ch_y. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+nlemma symmetric_eqascii63 : ∀a2.eq_ascii ch_z a2 = eq_ascii a2 ch_z. #a2; ncases a2; nnormalize; napply (refl_eq ??).nqed.
+
+nlemma symmetric_eqascii : symmetricT ascii bool eq_ascii.
+ #a1; ncases a1;
+ ##[ ##1: napply symmetric_eqascii1 ##| ##2: napply symmetric_eqascii2
+ ##| ##3: napply symmetric_eqascii3 ##| ##4: napply symmetric_eqascii4
+ ##| ##5: napply symmetric_eqascii5 ##| ##6: napply symmetric_eqascii6
+ ##| ##7: napply symmetric_eqascii7 ##| ##8: napply symmetric_eqascii8
+ ##| ##9: napply symmetric_eqascii9 ##| ##10: napply symmetric_eqascii10
+ ##| ##11: napply symmetric_eqascii11 ##| ##12: napply symmetric_eqascii12
+ ##| ##13: napply symmetric_eqascii13 ##| ##14: napply symmetric_eqascii14
+ ##| ##15: napply symmetric_eqascii15 ##| ##16: napply symmetric_eqascii16
+ ##| ##17: napply symmetric_eqascii17 ##| ##18: napply symmetric_eqascii18
+ ##| ##19: napply symmetric_eqascii19 ##| ##20: napply symmetric_eqascii20
+ ##| ##21: napply symmetric_eqascii21 ##| ##22: napply symmetric_eqascii22
+ ##| ##23: napply symmetric_eqascii23 ##| ##24: napply symmetric_eqascii24
+ ##| ##25: napply symmetric_eqascii25 ##| ##26: napply symmetric_eqascii26
+ ##| ##27: napply symmetric_eqascii27 ##| ##28: napply symmetric_eqascii28
+ ##| ##29: napply symmetric_eqascii29 ##| ##30: napply symmetric_eqascii30
+ ##| ##31: napply symmetric_eqascii31 ##| ##32: napply symmetric_eqascii32
+ ##| ##33: napply symmetric_eqascii33 ##| ##34: napply symmetric_eqascii34
+ ##| ##35: napply symmetric_eqascii35 ##| ##36: napply symmetric_eqascii36
+ ##| ##37: napply symmetric_eqascii37 ##| ##38: napply symmetric_eqascii38
+ ##| ##39: napply symmetric_eqascii39 ##| ##40: napply symmetric_eqascii40
+ ##| ##41: napply symmetric_eqascii41 ##| ##42: napply symmetric_eqascii42
+ ##| ##43: napply symmetric_eqascii43 ##| ##44: napply symmetric_eqascii44
+ ##| ##45: napply symmetric_eqascii45 ##| ##46: napply symmetric_eqascii46
+ ##| ##47: napply symmetric_eqascii47 ##| ##48: napply symmetric_eqascii48
+ ##| ##49: napply symmetric_eqascii49 ##| ##50: napply symmetric_eqascii50
+ ##| ##51: napply symmetric_eqascii51 ##| ##52: napply symmetric_eqascii52
+ ##| ##53: napply symmetric_eqascii53 ##| ##54: napply symmetric_eqascii54
+ ##| ##55: napply symmetric_eqascii55 ##| ##56: napply symmetric_eqascii56
+ ##| ##57: napply symmetric_eqascii57 ##| ##58: napply symmetric_eqascii58
+ ##| ##59: napply symmetric_eqascii59 ##| ##60: napply symmetric_eqascii60
+ ##| ##61: napply symmetric_eqascii61 ##| ##62: napply symmetric_eqascii62
+ ##| ##63: napply symmetric_eqascii63 ##]
+nqed.
+
+nlemma eqascii_to_eq1 : ∀a2.eq_ascii ch_0 a2 = true → ch_0 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##1: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq2 : ∀a2.eq_ascii ch_1 a2 = true → ch_1 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##2: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq3 : ∀a2.eq_ascii ch_2 a2 = true → ch_2 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##3: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq4 : ∀a2.eq_ascii ch_3 a2 = true → ch_3 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##4: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq5 : ∀a2.eq_ascii ch_4 a2 = true → ch_4 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##5: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq6 : ∀a2.eq_ascii ch_5 a2 = true → ch_5 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##6: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq7 : ∀a2.eq_ascii ch_6 a2 = true → ch_6 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##7: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq8 : ∀a2.eq_ascii ch_7 a2 = true → ch_7 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##8: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq9 : ∀a2.eq_ascii ch_8 a2 = true → ch_8 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##9: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq10 : ∀a2.eq_ascii ch_9 a2 = true → ch_9 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##10: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq11 : ∀a2.eq_ascii ch__ a2 = true → ch__ = a2. #a2; ncases a2; nnormalize; #H; ##[ ##11: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq12 : ∀a2.eq_ascii ch_A a2 = true → ch_A = a2. #a2; ncases a2; nnormalize; #H; ##[ ##12: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq13 : ∀a2.eq_ascii ch_B a2 = true → ch_B = a2. #a2; ncases a2; nnormalize; #H; ##[ ##13: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq14 : ∀a2.eq_ascii ch_C a2 = true → ch_C = a2. #a2; ncases a2; nnormalize; #H; ##[ ##14: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq15 : ∀a2.eq_ascii ch_D a2 = true → ch_D = a2. #a2; ncases a2; nnormalize; #H; ##[ ##15: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq16 : ∀a2.eq_ascii ch_E a2 = true → ch_E = a2. #a2; ncases a2; nnormalize; #H; ##[ ##16: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq17 : ∀a2.eq_ascii ch_F a2 = true → ch_F = a2. #a2; ncases a2; nnormalize; #H; ##[ ##17: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq18 : ∀a2.eq_ascii ch_G a2 = true → ch_G = a2. #a2; ncases a2; nnormalize; #H; ##[ ##18: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq19 : ∀a2.eq_ascii ch_H a2 = true → ch_H = a2. #a2; ncases a2; nnormalize; #H; ##[ ##19: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq20 : ∀a2.eq_ascii ch_I a2 = true → ch_I = a2. #a2; ncases a2; nnormalize; #H; ##[ ##20: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq21 : ∀a2.eq_ascii ch_J a2 = true → ch_J = a2. #a2; ncases a2; nnormalize; #H; ##[ ##21: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq22 : ∀a2.eq_ascii ch_K a2 = true → ch_K = a2. #a2; ncases a2; nnormalize; #H; ##[ ##22: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq23 : ∀a2.eq_ascii ch_L a2 = true → ch_L = a2. #a2; ncases a2; nnormalize; #H; ##[ ##23: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq24 : ∀a2.eq_ascii ch_M a2 = true → ch_M = a2. #a2; ncases a2; nnormalize; #H; ##[ ##24: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq25 : ∀a2.eq_ascii ch_N a2 = true → ch_N = a2. #a2; ncases a2; nnormalize; #H; ##[ ##25: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq26 : ∀a2.eq_ascii ch_O a2 = true → ch_O = a2. #a2; ncases a2; nnormalize; #H; ##[ ##26: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq27 : ∀a2.eq_ascii ch_P a2 = true → ch_P = a2. #a2; ncases a2; nnormalize; #H; ##[ ##27: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq28 : ∀a2.eq_ascii ch_Q a2 = true → ch_Q = a2. #a2; ncases a2; nnormalize; #H; ##[ ##28: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq29 : ∀a2.eq_ascii ch_R a2 = true → ch_R = a2. #a2; ncases a2; nnormalize; #H; ##[ ##29: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq30 : ∀a2.eq_ascii ch_S a2 = true → ch_S = a2. #a2; ncases a2; nnormalize; #H; ##[ ##30: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq31 : ∀a2.eq_ascii ch_T a2 = true → ch_T = a2. #a2; ncases a2; nnormalize; #H; ##[ ##31: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq32 : ∀a2.eq_ascii ch_U a2 = true → ch_U = a2. #a2; ncases a2; nnormalize; #H; ##[ ##32: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq33 : ∀a2.eq_ascii ch_V a2 = true → ch_V = a2. #a2; ncases a2; nnormalize; #H; ##[ ##33: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq34 : ∀a2.eq_ascii ch_W a2 = true → ch_W = a2. #a2; ncases a2; nnormalize; #H; ##[ ##34: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq35 : ∀a2.eq_ascii ch_X a2 = true → ch_X = a2. #a2; ncases a2; nnormalize; #H; ##[ ##35: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq36 : ∀a2.eq_ascii ch_Y a2 = true → ch_Y = a2. #a2; ncases a2; nnormalize; #H; ##[ ##36: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq37 : ∀a2.eq_ascii ch_Z a2 = true → ch_Z = a2. #a2; ncases a2; nnormalize; #H; ##[ ##37: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq38 : ∀a2.eq_ascii ch_a a2 = true → ch_a = a2. #a2; ncases a2; nnormalize; #H; ##[ ##38: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq39 : ∀a2.eq_ascii ch_b a2 = true → ch_b = a2. #a2; ncases a2; nnormalize; #H; ##[ ##39: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq40 : ∀a2.eq_ascii ch_c a2 = true → ch_c = a2. #a2; ncases a2; nnormalize; #H; ##[ ##40: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq41 : ∀a2.eq_ascii ch_d a2 = true → ch_d = a2. #a2; ncases a2; nnormalize; #H; ##[ ##41: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq42 : ∀a2.eq_ascii ch_e a2 = true → ch_e = a2. #a2; ncases a2; nnormalize; #H; ##[ ##42: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq43 : ∀a2.eq_ascii ch_f a2 = true → ch_f = a2. #a2; ncases a2; nnormalize; #H; ##[ ##43: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq44 : ∀a2.eq_ascii ch_g a2 = true → ch_g = a2. #a2; ncases a2; nnormalize; #H; ##[ ##44: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq45 : ∀a2.eq_ascii ch_h a2 = true → ch_h = a2. #a2; ncases a2; nnormalize; #H; ##[ ##45: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq46 : ∀a2.eq_ascii ch_i a2 = true → ch_i = a2. #a2; ncases a2; nnormalize; #H; ##[ ##46: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq47 : ∀a2.eq_ascii ch_j a2 = true → ch_j = a2. #a2; ncases a2; nnormalize; #H; ##[ ##47: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq48 : ∀a2.eq_ascii ch_k a2 = true → ch_k = a2. #a2; ncases a2; nnormalize; #H; ##[ ##48: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq49 : ∀a2.eq_ascii ch_l a2 = true → ch_l = a2. #a2; ncases a2; nnormalize; #H; ##[ ##49: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq50 : ∀a2.eq_ascii ch_m a2 = true → ch_m = a2. #a2; ncases a2; nnormalize; #H; ##[ ##50: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq51 : ∀a2.eq_ascii ch_n a2 = true → ch_n = a2. #a2; ncases a2; nnormalize; #H; ##[ ##51: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq52 : ∀a2.eq_ascii ch_o a2 = true → ch_o = a2. #a2; ncases a2; nnormalize; #H; ##[ ##52: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq53 : ∀a2.eq_ascii ch_p a2 = true → ch_p = a2. #a2; ncases a2; nnormalize; #H; ##[ ##53: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq54 : ∀a2.eq_ascii ch_q a2 = true → ch_q = a2. #a2; ncases a2; nnormalize; #H; ##[ ##54: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq55 : ∀a2.eq_ascii ch_r a2 = true → ch_r = a2. #a2; ncases a2; nnormalize; #H; ##[ ##55: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq56 : ∀a2.eq_ascii ch_s a2 = true → ch_s = a2. #a2; ncases a2; nnormalize; #H; ##[ ##56: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq57 : ∀a2.eq_ascii ch_t a2 = true → ch_t = a2. #a2; ncases a2; nnormalize; #H; ##[ ##57: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq58 : ∀a2.eq_ascii ch_u a2 = true → ch_u = a2. #a2; ncases a2; nnormalize; #H; ##[ ##58: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq59 : ∀a2.eq_ascii ch_v a2 = true → ch_v = a2. #a2; ncases a2; nnormalize; #H; ##[ ##59: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq60 : ∀a2.eq_ascii ch_w a2 = true → ch_w = a2. #a2; ncases a2; nnormalize; #H; ##[ ##60: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq61 : ∀a2.eq_ascii ch_x a2 = true → ch_x = a2. #a2; ncases a2; nnormalize; #H; ##[ ##61: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq62 : ∀a2.eq_ascii ch_y a2 = true → ch_y = a2. #a2; ncases a2; nnormalize; #H; ##[ ##62: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+nlemma eqascii_to_eq63 : ∀a2.eq_ascii ch_z a2 = true → ch_z = a2. #a2; ncases a2; nnormalize; #H; ##[ ##63: napply (refl_eq ??) | ##*: napply (bool_destruct ??? H) ##] nqed.
+
+nlemma eqascii_to_eq : ∀c1,c2.eq_ascii c1 c2 = true → c1 = c2.
+ #c1; ncases c1;
+ ##[ ##1: napply eqascii_to_eq1 ##| ##2: napply eqascii_to_eq2
+ ##| ##3: napply eqascii_to_eq3 ##| ##4: napply eqascii_to_eq4
+ ##| ##5: napply eqascii_to_eq5 ##| ##6: napply eqascii_to_eq6
+ ##| ##7: napply eqascii_to_eq7 ##| ##8: napply eqascii_to_eq8
+ ##| ##9: napply eqascii_to_eq9 ##| ##10: napply eqascii_to_eq10
+ ##| ##11: napply eqascii_to_eq11 ##| ##12: napply eqascii_to_eq12
+ ##| ##13: napply eqascii_to_eq13 ##| ##14: napply eqascii_to_eq14
+ ##| ##15: napply eqascii_to_eq15 ##| ##16: napply eqascii_to_eq16
+ ##| ##17: napply eqascii_to_eq17 ##| ##18: napply eqascii_to_eq18
+ ##| ##19: napply eqascii_to_eq19 ##| ##20: napply eqascii_to_eq20
+ ##| ##21: napply eqascii_to_eq21 ##| ##22: napply eqascii_to_eq22
+ ##| ##23: napply eqascii_to_eq23 ##| ##24: napply eqascii_to_eq24
+ ##| ##25: napply eqascii_to_eq25 ##| ##26: napply eqascii_to_eq26
+ ##| ##27: napply eqascii_to_eq27 ##| ##28: napply eqascii_to_eq28
+ ##| ##29: napply eqascii_to_eq29 ##| ##30: napply eqascii_to_eq30
+ ##| ##31: napply eqascii_to_eq31 ##| ##32: napply eqascii_to_eq32
+ ##| ##33: napply eqascii_to_eq33 ##| ##34: napply eqascii_to_eq34
+ ##| ##35: napply eqascii_to_eq35 ##| ##36: napply eqascii_to_eq36
+ ##| ##37: napply eqascii_to_eq37 ##| ##38: napply eqascii_to_eq38
+ ##| ##39: napply eqascii_to_eq39 ##| ##40: napply eqascii_to_eq40
+ ##| ##41: napply eqascii_to_eq41 ##| ##42: napply eqascii_to_eq42
+ ##| ##43: napply eqascii_to_eq43 ##| ##44: napply eqascii_to_eq44
+ ##| ##45: napply eqascii_to_eq45 ##| ##46: napply eqascii_to_eq46
+ ##| ##47: napply eqascii_to_eq47 ##| ##48: napply eqascii_to_eq48
+ ##| ##49: napply eqascii_to_eq49 ##| ##50: napply eqascii_to_eq50
+ ##| ##51: napply eqascii_to_eq51 ##| ##52: napply eqascii_to_eq52
+ ##| ##53: napply eqascii_to_eq53 ##| ##54: napply eqascii_to_eq54
+ ##| ##55: napply eqascii_to_eq55 ##| ##56: napply eqascii_to_eq56
+ ##| ##57: napply eqascii_to_eq57 ##| ##58: napply eqascii_to_eq58
+ ##| ##59: napply eqascii_to_eq59 ##| ##60: napply eqascii_to_eq60
+ ##| ##61: napply eqascii_to_eq61 ##| ##62: napply eqascii_to_eq62
+ ##| ##63: napply eqascii_to_eq63 ##]
+nqed.
+
+nlemma eq_to_eqascii1 : ∀a2.ch_0 = a2 → eq_ascii ch_0 a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##1: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii2 : ∀a2.ch_1 = a2 → eq_ascii ch_1 a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##2: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii3 : ∀a2.ch_2 = a2 → eq_ascii ch_2 a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##3: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii4 : ∀a2.ch_3 = a2 → eq_ascii ch_3 a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##4: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii5 : ∀a2.ch_4 = a2 → eq_ascii ch_4 a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##5: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii6 : ∀a2.ch_5 = a2 → eq_ascii ch_5 a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##6: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii7 : ∀a2.ch_6 = a2 → eq_ascii ch_6 a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##7: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii8 : ∀a2.ch_7 = a2 → eq_ascii ch_7 a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##8: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii9 : ∀a2.ch_8 = a2 → eq_ascii ch_8 a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##9: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii10 : ∀a2.ch_9 = a2 → eq_ascii ch_9 a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##10: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii11 : ∀a2.ch__ = a2 → eq_ascii ch__ a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##11: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii12 : ∀a2.ch_A = a2 → eq_ascii ch_A a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##12: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii13 : ∀a2.ch_B = a2 → eq_ascii ch_B a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##13: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii14 : ∀a2.ch_C = a2 → eq_ascii ch_C a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##14: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii15 : ∀a2.ch_D = a2 → eq_ascii ch_D a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##15: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii16 : ∀a2.ch_E = a2 → eq_ascii ch_E a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##16: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii17 : ∀a2.ch_F = a2 → eq_ascii ch_F a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##17: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii18 : ∀a2.ch_G = a2 → eq_ascii ch_G a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##18: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii19 : ∀a2.ch_H = a2 → eq_ascii ch_H a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##19: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii20 : ∀a2.ch_I = a2 → eq_ascii ch_I a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##20: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii21 : ∀a2.ch_J = a2 → eq_ascii ch_J a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##21: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii22 : ∀a2.ch_K = a2 → eq_ascii ch_K a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##22: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii23 : ∀a2.ch_L = a2 → eq_ascii ch_L a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##23: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii24 : ∀a2.ch_M = a2 → eq_ascii ch_M a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##24: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii25 : ∀a2.ch_N = a2 → eq_ascii ch_N a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##25: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii26 : ∀a2.ch_O = a2 → eq_ascii ch_O a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##26: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii27 : ∀a2.ch_P = a2 → eq_ascii ch_P a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##27: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii28 : ∀a2.ch_Q = a2 → eq_ascii ch_Q a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##28: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii29 : ∀a2.ch_R = a2 → eq_ascii ch_R a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##29: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii30 : ∀a2.ch_S = a2 → eq_ascii ch_S a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##30: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii31 : ∀a2.ch_T = a2 → eq_ascii ch_T a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##31: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii32 : ∀a2.ch_U = a2 → eq_ascii ch_U a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##32: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii33 : ∀a2.ch_V = a2 → eq_ascii ch_V a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##33: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii34 : ∀a2.ch_W = a2 → eq_ascii ch_W a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##34: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii35 : ∀a2.ch_X = a2 → eq_ascii ch_X a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##35: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii36 : ∀a2.ch_Y = a2 → eq_ascii ch_Y a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##36: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii37 : ∀a2.ch_Z = a2 → eq_ascii ch_Z a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##37: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii38 : ∀a2.ch_a = a2 → eq_ascii ch_a a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##38: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii39 : ∀a2.ch_b = a2 → eq_ascii ch_b a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##39: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii40 : ∀a2.ch_c = a2 → eq_ascii ch_c a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##40: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii41 : ∀a2.ch_d = a2 → eq_ascii ch_d a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##41: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii42 : ∀a2.ch_e = a2 → eq_ascii ch_e a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##42: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii43 : ∀a2.ch_f = a2 → eq_ascii ch_f a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##43: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii44 : ∀a2.ch_g = a2 → eq_ascii ch_g a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##44: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii45 : ∀a2.ch_h = a2 → eq_ascii ch_h a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##45: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii46 : ∀a2.ch_i = a2 → eq_ascii ch_i a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##46: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii47 : ∀a2.ch_j = a2 → eq_ascii ch_j a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##47: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii48 : ∀a2.ch_k = a2 → eq_ascii ch_k a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##48: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii49 : ∀a2.ch_l = a2 → eq_ascii ch_l a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##49: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii50 : ∀a2.ch_m = a2 → eq_ascii ch_m a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##50: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii51 : ∀a2.ch_n = a2 → eq_ascii ch_n a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##51: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii52 : ∀a2.ch_o = a2 → eq_ascii ch_o a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##52: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii53 : ∀a2.ch_p = a2 → eq_ascii ch_p a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##53: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii54 : ∀a2.ch_q = a2 → eq_ascii ch_q a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##54: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii55 : ∀a2.ch_r = a2 → eq_ascii ch_r a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##55: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii56 : ∀a2.ch_s = a2 → eq_ascii ch_s a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##56: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii57 : ∀a2.ch_t = a2 → eq_ascii ch_t a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##57: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii58 : ∀a2.ch_u = a2 → eq_ascii ch_u a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##58: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii59 : ∀a2.ch_v = a2 → eq_ascii ch_v a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##59: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii60 : ∀a2.ch_w = a2 → eq_ascii ch_w a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##60: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii61 : ∀a2.ch_x = a2 → eq_ascii ch_x a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##61: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii62 : ∀a2.ch_y = a2 → eq_ascii ch_y a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##62: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+nlemma eq_to_eqascii63 : ∀a2.ch_z = a2 → eq_ascii ch_z a2 = true. #a2; ncases a2; nnormalize; #H; ##[ ##63: napply (refl_eq ??) | ##*: napply (ascii_destruct ??? H) ##] nqed.
+
+nlemma eq_to_eqascii : ∀c1,c2.c1 = c2 → eq_ascii c1 c2 = true.
+ #c1; ncases c1;
+ ##[ ##1: napply eq_to_eqascii1 ##| ##2: napply eq_to_eqascii2
+ ##| ##3: napply eq_to_eqascii3 ##| ##4: napply eq_to_eqascii4
+ ##| ##5: napply eq_to_eqascii5 ##| ##6: napply eq_to_eqascii6
+ ##| ##7: napply eq_to_eqascii7 ##| ##8: napply eq_to_eqascii8
+ ##| ##9: napply eq_to_eqascii9 ##| ##10: napply eq_to_eqascii10
+ ##| ##11: napply eq_to_eqascii11 ##| ##12: napply eq_to_eqascii12
+ ##| ##13: napply eq_to_eqascii13 ##| ##14: napply eq_to_eqascii14
+ ##| ##15: napply eq_to_eqascii15 ##| ##16: napply eq_to_eqascii16
+ ##| ##17: napply eq_to_eqascii17 ##| ##18: napply eq_to_eqascii18
+ ##| ##19: napply eq_to_eqascii19 ##| ##20: napply eq_to_eqascii20
+ ##| ##21: napply eq_to_eqascii21 ##| ##22: napply eq_to_eqascii22
+ ##| ##23: napply eq_to_eqascii23 ##| ##24: napply eq_to_eqascii24
+ ##| ##25: napply eq_to_eqascii25 ##| ##26: napply eq_to_eqascii26
+ ##| ##27: napply eq_to_eqascii27 ##| ##28: napply eq_to_eqascii28
+ ##| ##29: napply eq_to_eqascii29 ##| ##30: napply eq_to_eqascii30
+ ##| ##31: napply eq_to_eqascii31 ##| ##32: napply eq_to_eqascii32
+ ##| ##33: napply eq_to_eqascii33 ##| ##34: napply eq_to_eqascii34
+ ##| ##35: napply eq_to_eqascii35 ##| ##36: napply eq_to_eqascii36
+ ##| ##37: napply eq_to_eqascii37 ##| ##38: napply eq_to_eqascii38
+ ##| ##39: napply eq_to_eqascii39 ##| ##40: napply eq_to_eqascii40
+ ##| ##41: napply eq_to_eqascii41 ##| ##42: napply eq_to_eqascii42
+ ##| ##43: napply eq_to_eqascii43 ##| ##44: napply eq_to_eqascii44
+ ##| ##45: napply eq_to_eqascii45 ##| ##46: napply eq_to_eqascii46
+ ##| ##47: napply eq_to_eqascii47 ##| ##48: napply eq_to_eqascii48
+ ##| ##49: napply eq_to_eqascii49 ##| ##50: napply eq_to_eqascii50
+ ##| ##51: napply eq_to_eqascii51 ##| ##52: napply eq_to_eqascii52
+ ##| ##53: napply eq_to_eqascii53 ##| ##54: napply eq_to_eqascii54
+ ##| ##55: napply eq_to_eqascii55 ##| ##56: napply eq_to_eqascii56
+ ##| ##57: napply eq_to_eqascii57 ##| ##58: napply eq_to_eqascii58
+ ##| ##59: napply eq_to_eqascii59 ##| ##60: napply eq_to_eqascii60
+ ##| ##61: napply eq_to_eqascii61 ##| ##62: napply eq_to_eqascii62
+ ##| ##63: napply eq_to_eqascii63 ##]
+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 "utility/ascii.ma".
+include "utility/utility.ma".
+
+(* ************************ *)
+(* MANIPOLAZIONE DI STRINGA *)
+(* ************************ *)
+
+(* tipo pubblico *)
+ndefinition aux_str_type ≝ list ascii.
+
+(* empty string *)
+ndefinition empty_str ≝ nil ascii.
+
+(* is empty ? *)
+ndefinition isNull_str ≝
+λstr:aux_str_type.match str with
+ [ nil ⇒ true | cons _ _ ⇒ false ].
+
+(* strcmp *)
+nlet rec eq_str (str,str':aux_str_type) ≝
+ match str with
+ [ nil ⇒ match str' with
+ [ nil => true
+ | cons _ _ => false ]
+ | cons h t ⇒ match str' with
+ [ nil ⇒ false
+ | cons h' t' ⇒ (eq_ascii h h')⊗(eq_str t t')
+ ]
+ ].
+
+(* strcat *)
+ndefinition strCat_str ≝
+λstr,str':aux_str_type.str@str'.
+
+(* strlen *)
+ndefinition strLen_str ≝ len_list ascii.
+
+(* ************ *)
+(* STRINGA + ID *)
+(* ************ *)
+
+(* tipo pubblico *)
+ninductive aux_strId_type : Type ≝
+ STR_ID: aux_str_type → nat → aux_strId_type.
+
+ndefinition aux_strId_type_ind : ΠP:aux_strId_type → Prop.(Πl,n.P (STR_ID l n)) → Πa:aux_strId_type.P a ≝
+λP:aux_strId_type → Prop.λf:Πl,n.P (STR_ID l n).λa:aux_strId_type.
+ match a with [ STR_ID l n ⇒ f l n ].
+
+ndefinition aux_strId_type_rec : ΠP:aux_strId_type → Set.(Πl,n.P (STR_ID l n)) → Πa:aux_strId_type.P a ≝
+λP:aux_strId_type → Set.λf:Πl,n.P (STR_ID l n).λa:aux_strId_type.
+ match a with [ STR_ID l n ⇒ f l n ].
+
+ndefinition aux_strId_type_rect : ΠP:aux_strId_type → Type.(Πl,n.P (STR_ID l n)) → Πa:aux_strId_type.P a ≝
+λP:aux_strId_type → Type.λf:Πl,n.P (STR_ID l n).λa:aux_strId_type.
+ match a with [ STR_ID l n ⇒ f l n ].
+
+(* getter *)
+ndefinition get_name_strId ≝ λsid:aux_strId_type.match sid with [ STR_ID n _ ⇒ n ].
+ndefinition get_id_strId ≝ λsid:aux_strId_type.match sid with [ STR_ID _ d ⇒ d ].
+
+(* confronto *)
+ndefinition eq_strId ≝
+λsid,sid':aux_strId_type.(eq_str (get_name_strId sid) (get_name_strId sid'))⊗(eq_nat (get_id_strId sid) (get_id_strId sid')).
--- /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 "utility/string.ma".
+include "utility/ascii_lemmas2.ma".
+
+(* ************************ *)
+(* MANIPOLAZIONE DI STRINGA *)
+(* ************************ *)
+
+nlemma symmetric_eqstr : symmetricT aux_str_type bool eq_str.
+ #l1;
+ napply (list_ind ascii ??? l1);
+ ##[ ##1: #l2; ncases l2;
+ ##[ ##1: nnormalize; napply (refl_eq ??)
+ ##| ##2: #x; #y; nnormalize; napply (refl_eq ??)
+ ##]
+ ##| ##2: #x1; #x2; #H; #l2; ncases l2;
+ ##[ ##1: nnormalize; napply (refl_eq ??)
+ ##| ##2: #y1; #y2;
+ nchange with (((eq_ascii x1 y1)⊗(eq_str x2 y2)) = ((eq_ascii y1 x1)⊗(eq_str y2 x2)));
+ nrewrite > (symmetric_eqascii x1 y1);
+ nrewrite > (H y2);
+ napply (refl_eq ??)
+ ##]
+ ##]
+nqed.
+
+nlemma eqstr_to_eq : ∀s,s'.eq_str s s' = true → s = s'.
+ #l1;
+ napply (list_ind ascii ??? l1);
+ ##[ ##1: #l2; ncases l2;
+ ##[ ##1: nnormalize; #H; napply (refl_eq ??)
+ ##| ##2: #x1; #x2; nnormalize; #H; napply (bool_destruct ??? H)
+ ##]
+ ##| ##2: #x1; #x2; #H; #l2; ncases l2;
+ ##[ ##1: nnormalize; #H1; napply (bool_destruct ??? H1)
+ ##| ##2: #y1; #y2; #H1;
+ nchange in H1:(%) with (((eq_ascii x1 y1)⊗(eq_str x2 y2)) = true);
+ nrewrite > (eqascii_to_eq x1 y1 (andb_true_true_l ?? H1));
+ nrewrite > (H y2 (andb_true_true_r ?? H1));
+ napply (refl_eq ??)
+ ##]
+ ##]
+nqed.
+
+nlemma eq_to_eqstr : ∀s,s'.s = s' → eq_str s s' = true.
+ #l1;
+ napply (list_ind ascii ??? l1);
+ ##[ ##1: #l2; ncases l2;
+ ##[ ##1: nnormalize; #H; napply (refl_eq ??)
+ ##| ##2: #x1; #x2; nnormalize; #H; nelim (list_destruct_nil_cons ascii ?? H)
+ ##]
+ ##| ##2: #x1; #x2; #H; #l2; ncases l2;
+ ##[ ##1: #H; nelim (list_destruct_cons_nil ascii ?? H)
+ ##| ##2: #y1; #y2; #H1;
+ nrewrite > (list_destruct_1 ascii ???? H1);
+ nchange with (((eq_ascii y1 y1)⊗(eq_str x2 y2)) = true);
+ nrewrite > (H y2 (list_destruct_2 ascii ???? H1));
+ nrewrite > (eq_to_eqascii y1 y1 (refl_eq ??));
+ nnormalize;
+ napply (refl_eq ??)
+ ##]
+ ##]
+nqed.
+
+(* ************ *)
+(* STRINGA + ID *)
+(* ************ *)
+
+nlemma strid_destruct_1 : ∀x1,x2,y1,y2.STR_ID x1 y1 = STR_ID x2 y2 → x1 = x2.
+ #x1; #x2; #y1; #y2; #H;
+ nchange with (match STR_ID x2 y2 with [ STR_ID a _ ⇒ x1 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply (refl_eq ??).
+nqed.
+
+nlemma strid_destruct_2 : ∀x1,x2,y1,y2.STR_ID x1 y1 = STR_ID x2 y2 → y1 = y2.
+ #x1; #x2; #y1; #y2; #H;
+ nchange with (match STR_ID x2 y2 with [ STR_ID _ b ⇒ y1 = b ]);
+ nrewrite < H;
+ nnormalize;
+ napply (refl_eq ??).
+nqed.
+
+nlemma symmetric_eqstrid : symmetricT aux_strId_type bool eq_strId.
+ #si1; #si2;
+ ncases si1;
+ #l1; #n1;
+ ncases si2;
+ #l2; #n2;
+ nchange with (((eq_str l1 l2)⊗(eq_nat n1 n2)) = ((eq_str l2 l1)⊗(eq_nat n2 n1)));
+ nrewrite > (symmetric_eqstr l1 l2);
+ nrewrite > (symmetric_eqnat n1 n2);
+ napply (refl_eq ??).
+nqed.
+
+nlemma eqstrid_to_eq : ∀s,s'.eq_strId s s' = true → s = s'.
+ #si1; #si2;
+ ncases si1;
+ #l1; #n1;
+ ncases si2;
+ #l2; #n2; #H;
+ nchange in H:(%) with (((eq_str l1 l2)⊗(eq_nat n1 n2)) = true);
+ nrewrite > (eqstr_to_eq l1 l2 (andb_true_true_l ?? H));
+ nrewrite > (eqnat_to_eq n1 n2 (andb_true_true_r ?? H));
+ napply (refl_eq ??).
+nqed.
+
+nlemma eq_to_eqstrid : ∀s,s'.s = s' → eq_strId s s' = true.
+ #si1; #si2;
+ ncases si1;
+ #l1; #n1;
+ ncases si2;
+ #l2; #n2; #H;
+ nchange with (((eq_str l1 l2)⊗(eq_nat n1 n2)) = true);
+ nrewrite > (strid_destruct_1 ???? H);
+ nrewrite > (strid_destruct_2 ???? H);
+ nrewrite > (eq_to_eqstr l2 l2 (refl_eq ??));
+ nrewrite > (eq_to_eqnat n2 n2 (refl_eq ??));
+ nnormalize;
+ 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/theory.ma".
+include "freescale/nat_lemmas.ma".
+include "freescale/option.ma".
+
+(* ************** *)
+(* Non-Empty List *)
+(* ************** *)
+
+(* lista non vuota *)
+ninductive ne_list (A:Type) : Type ≝
+ | ne_nil: A → ne_list A
+ | ne_cons: A → ne_list A → ne_list A.
+
+nlet rec ne_list_ind (A:Type) (P:ne_list A → Prop) (f:Πd.P (ne_nil A d)) (f1:(Πa:A.Πl':ne_list A.P l' → P (ne_cons A a l'))) (l:ne_list A) on l ≝
+ match l with [ ne_nil d ⇒ f d | ne_cons h t ⇒ f1 h t (ne_list_ind A P f f1 t) ].
+
+nlet rec ne_list_rec (A:Type) (P:ne_list A → Set) (f:Πd.P (ne_nil A d)) (f1:(Πa:A.Πl':ne_list A.P l' → P (ne_cons A a l'))) (l:ne_list A) on l ≝
+ match l with [ ne_nil d ⇒ f d | ne_cons h t ⇒ f1 h t (ne_list_rec A P f f1 t) ].
+
+nlet rec ne_list_rect (A:Type) (P:ne_list A → Type) (f:Πd.P (ne_nil A d)) (f1:(Πa:A.Πl':ne_list A.P l' → P (ne_cons A a l'))) (l:ne_list A) on l ≝
+ match l with [ ne_nil d ⇒ f d | ne_cons h t ⇒ f1 h t (ne_list_rect A P f f1 t) ].
+
+(* append *)
+nlet rec ne_append (A:Type) (l1,l2:ne_list A) on l1 ≝
+ match l1 with
+ [ ne_nil hd ⇒ ne_cons A hd l2
+ | ne_cons hd tl ⇒ ne_cons A hd (ne_append A tl l2) ].
+
+notation "hvbox(hd break §§ tl)"
+ right associative with precedence 46
+ for @{'ne_cons $hd $tl}.
+
+notation "« list0 x sep ; break £ y break »"
+ non associative with precedence 90
+ for ${fold right @{'ne_nil $y } rec acc @{'ne_cons $x $acc}}.
+
+notation "hvbox(l1 break & l2)"
+ right associative with precedence 47
+ for @{'ne_append $l1 $l2 }.
+
+interpretation "ne_nil" 'ne_nil hd = (ne_nil ? hd).
+interpretation "ne_cons" 'ne_cons hd tl = (ne_cons ? hd tl).
+interpretation "ne_append" 'ne_append l1 l2 = (ne_append ? l1 l2).
+
+(* ************ *)
+(* List Utility *)
+(* ************ *)
+
+(* listlen *)
+nlet rec len_list (T:Type) (l:list T) on l ≝
+ match l with [ nil ⇒ O | cons _ t ⇒ S (len_list T t) ].
+
+nlet rec len_neList (T:Type) (nl:ne_list T) on nl ≝
+ match nl with [ ne_nil _ ⇒ 1 | ne_cons _ t ⇒ S (len_neList T t) ].
+
+(* vuota? *)
+ndefinition is_empty_list ≝
+λT:Type.λl:list T.match l with [ nil ⇒ True | cons _ _ ⇒ False ].
+
+ndefinition isb_empty_list ≝
+λT:Type.λl:list T.match l with [ nil ⇒ true | cons _ _ ⇒ false ].
+
+ndefinition isnot_empty_list ≝
+λT:Type.λl:list T.match l with [ nil ⇒ False | cons _ _ ⇒ True ].
+
+ndefinition isnotb_empty_list ≝
+λT:Type.λl:list T.match l with [ nil ⇒ false | cons _ _ ⇒ true ].
+
+(* conversione *)
+nlet rec neList_to_list (T:Type) (nl:ne_list T) on nl : list T ≝
+ match nl with [ ne_nil h ⇒ [h] | ne_cons h t ⇒ [h]@(neList_to_list T t) ].
+
+nlet rec list_to_neList_aux (T:Type) (l:list T) on l : option (ne_list T) ≝
+ match l with
+ [ nil ⇒ None (ne_list T)
+ | cons h t ⇒ match list_to_neList_aux T t with
+ [ None ⇒ Some (ne_list T) «£h»
+ | Some t' ⇒ Some (ne_list T) («£h»&t') ]].
+
+ndefinition list_to_neList ≝
+λT:Type.λl:list T.
+ match l
+ return λl:list T.isnot_empty_list T l → ne_list T
+ with
+ [ nil ⇒ λp:isnot_empty_list T (nil T).False_rect ? p
+ | cons h t ⇒ λp:isnot_empty_list T (cons T h t).
+ match list_to_neList_aux T t with
+ [ None ⇒ «£h»
+ | Some t' ⇒ «£h»&t'
+ ]
+ ].
+
+(* nth elem *)
+nlet rec nth_list (T:Type) (l:list T) (n:nat) on l ≝
+ match l with
+ [ nil ⇒ None ?
+ | cons h t ⇒ match n with
+ [ O ⇒ Some ? h | S n' ⇒ nth_list T t n' ]
+ ].
+
+nlet rec nth_neList (T:Type) (nl:ne_list T) (n:nat) on nl ≝
+ match nl with
+ [ ne_nil h ⇒ match n with
+ [ O ⇒ Some ? h | S _ ⇒ None ? ]
+ | ne_cons h t ⇒ match n with
+ [ O ⇒ Some ? h | S n' ⇒ nth_neList T t n' ]
+ ].
+
+nlet rec abs_nth_neList (T:Type) (nl:ne_list T) (n:nat) on nl ≝
+ match nl with
+ [ ne_nil h ⇒ h
+ | ne_cons h t ⇒ match n with
+ [ O ⇒ h | S n' ⇒ abs_nth_neList T t n' ]
+ ].
+
+(* reverse *)
+nlet rec reverse_list (T:Type) (l:list T) on l ≝
+ match l with
+ [ nil ⇒ nil T
+ | cons h t ⇒ (reverse_list T t)@[h]
+ ].
+
+nlet rec reverse_neList (T:Type) (nl:ne_list T) on nl ≝
+ match nl with
+ [ ne_nil h ⇒ ne_nil T h
+ | ne_cons h t ⇒ (reverse_neList T t)&(ne_nil T h)
+ ].
+
+(* getLast *)
+ndefinition get_last_list ≝
+λT:Type.λl:list T.match reverse_list T l with
+ [ nil ⇒ None ?
+ | cons h _ ⇒ Some ? h ].
+
+ndefinition get_last_neList ≝
+λT:Type.λnl:ne_list T.match reverse_neList T nl with
+ [ ne_nil h ⇒ h
+ | ne_cons h _ ⇒ h ].
+
+(* cutLast *)
+ndefinition cut_last_list ≝
+λT:Type.λl:list T.match reverse_list T l with
+ [ nil ⇒ nil T
+ | cons _ t ⇒ reverse_list T t ].
+
+ndefinition cut_last_neList ≝
+λT:Type.λnl:ne_list T.match reverse_neList T nl with
+ [ ne_nil h ⇒ ne_nil T h
+ | ne_cons _ t ⇒ reverse_neList T t ].
+
+(* getFirst *)
+ndefinition get_first_list ≝
+λT:Type.λl:list T.match l with
+ [ nil ⇒ None ?
+ | cons h _ ⇒ Some ? h ].
+
+ndefinition get_first_neList ≝
+λT:Type.λnl:ne_list T.match nl with
+ [ ne_nil h ⇒ h
+ | ne_cons h _ ⇒ h ].
+
+(* cutFirst *)
+ndefinition cut_first_list ≝
+λT:Type.λl:list T.match l with
+ [ nil ⇒ nil T
+ | cons _ t ⇒ t ].
+
+ndefinition cut_first_neList ≝
+λT:Type.λnl:ne_list T.match nl with
+ [ ne_nil h ⇒ ne_nil T h
+ | ne_cons _ t ⇒ t ].
+
+(* apply f *)
+nlet rec apply_f_list (T1,T2:Type) (l:list T1) (f:T1 → T2) on l ≝
+match l with
+ [ nil ⇒ nil T2
+ | cons h t ⇒ cons T2 (f h) (apply_f_list T1 T2 t f) ].
+
+nlet rec apply_f_neList (T1,T2:Type) (nl:ne_list T1) (f:T1 → T2) on nl ≝
+match nl with
+ [ ne_nil h ⇒ ne_nil T2 (f h)
+ | ne_cons h t ⇒ ne_cons T2 (f h) (apply_f_neList T1 T2 t f) ].
+
+(* fold right *)
+nlet rec fold_right_list (T1,T2:Type) (f:T1 → T2 → T2) (acc:T2) (l:list T1) on l ≝
+ match l with
+ [ nil ⇒ acc
+ | cons h t ⇒ f h (fold_right_list T1 T2 f acc t)
+ ].
+
+nlet rec fold_right_neList (T1,T2:Type) (f:T1 → T2 → T2) (acc:T2) (nl:ne_list T1) on nl ≝
+ match nl with
+ [ ne_nil h ⇒ f h acc
+ | ne_cons h t ⇒ f h (fold_right_neList T1 T2 f acc t)
+ ].
+
+(* double fold right *)
+nlemma fold_right_list2_aux1 :
+∀T.∀h,t.len_list T [] = len_list T (h::t) → False.
+ #T; #h; #t;
+ nnormalize;
+ #H;
+ napply (nat_destruct_0_S ? H).
+nqed.
+
+nlemma fold_right_list2_aux2 :
+∀T.∀h,t.len_list T (h::t) = len_list T [] → False.
+ #T; #h; #t;
+ nnormalize;
+ #H;
+ napply (nat_destruct_S_0 ? H).
+nqed.
+
+nlemma fold_right_list2_aux3 :
+∀T.∀h,h',t,t'.len_list T (h::t) = len_list T (h'::t') → len_list T t = len_list T t'.
+ #T; #h; #h'; #t; #t';
+ napply (list_ind T ??? t);
+ napply (list_ind T ??? t');
+ ##[ ##1: nnormalize; #H; napply (refl_eq ??)
+ ##| ##2: #a; #l'; #H; #H1;
+ nchange in H1:(%) with ((S O) = (S (S (len_list T l'))));
+ nelim (nat_destruct_0_S ? (nat_destruct_S_S ?? H1))
+ ##| ##3: #a; #l'; #H; #H1;
+ nchange in H1:(%) with ((S (S (len_list T l'))) = (S O));
+ nelim (nat_destruct_S_0 ? (nat_destruct_S_S ?? H1))
+ ##| ##4: #a; #l; #H; #a1; #l1; #H1; #H2;
+ nchange in H2:(%) with ((S (S (len_list T l1))) = (S (S (len_list T l))));
+ nchange with ((S (len_list T l1)) = (S (len_list T l)));
+ nrewrite > (nat_destruct_S_S ?? H2);
+ napply (refl_eq ??)
+ ##]
+nqed.
+
+nlet rec fold_right_list2 (T1,T2:Type) (f:T1 → T1 → T2 → T2) (acc:T2) (l1:list T1) on l1 ≝
+ match l1
+ return λl1.Πl2.len_list T1 l1 = len_list T1 l2 → T2
+ with
+ [ nil ⇒ λl2.match l2 return λl2.len_list T1 [] = len_list T1 l2 → T2 with
+ [ nil ⇒ λp:len_list T1 [] = len_list T1 [].acc
+ | cons h t ⇒ λp:len_list T1 [] = len_list T1 (h::t).
+ False_rect ? (fold_right_list2_aux1 T1 h t p)
+ ]
+ | cons h t ⇒ λl2.match l2 return λl2.len_list T1 (h::t) = len_list T1 l2 → T2 with
+ [ nil ⇒ λp:len_list T1 (h::t) = len_list T1 [].
+ False_rect ? (fold_right_list2_aux2 T1 h t p)
+ | cons h' t' ⇒ λp:len_list T1 (h::t) = len_list T1 (h'::t').
+ f h h' (fold_right_list2 T1 T2 f acc t t' (fold_right_list2_aux3 T1 h h' t t' p))
+ ]
+ ].
+
+nlemma fold_right_neList2_aux1 :
+∀T.∀h,h',t'.len_neList T «£h» = len_neList T (h'§§t') → False.
+ #T; #h; #h'; #t';
+ nnormalize;
+ ncases t';
+ nnormalize;
+ ##[ ##1: #x; #H; nelim (nat_destruct_0_S ? (nat_destruct_S_S ?? H))
+ ##| ##2: #x; #l; #H; nelim (nat_destruct_0_S ? (nat_destruct_S_S ?? H))
+ ##]
+nqed.
+
+nlemma fold_right_neList2_aux2 :
+∀T.∀h,h',t.len_neList T (h§§t) = len_neList T «£h'» → False.
+ #T; #h; #h'; #t;
+ nnormalize;
+ ncases t;
+ nnormalize;
+ ##[ ##1: #x; #H; nelim (nat_destruct_S_0 ? (nat_destruct_S_S ?? H))
+ ##| ##2: #x; #l; #H; nelim (nat_destruct_S_0 ? (nat_destruct_S_S ?? H))
+ ##]
+nqed.
+
+nlemma fold_right_neList2_aux3 :
+∀T.∀h,h',t,t'.len_neList T (h§§t) = len_neList T (h'§§t') → len_neList T t = len_neList T t'.
+ #T; #h; #h'; #t; #t';
+ napply (ne_list_ind T ??? t);
+ napply (ne_list_ind T ??? t');
+ ##[ ##1: nnormalize; #x; #y; #H; napply (refl_eq ??)
+ ##| ##2: #a; #l'; #H; #x; #H1;
+ nchange in H1:(%) with ((S (len_neList T «£x»)) = (S (len_neList T (a§§l'))));
+ nrewrite > (nat_destruct_S_S ?? H1);
+ napply (refl_eq ??)
+ ##| ##3: #x; #a; #l'; #H; #H1;
+ nchange in H1:(%) with ((S (len_neList T (a§§l')))= (S (len_neList T «£x»)));
+ nrewrite > (nat_destruct_S_S ?? H1);
+ napply (refl_eq ??)
+ ##| ##4: #a; #l; #H; #a1; #l1; #H1; #H2;
+ nchange in H2:(%) with ((S (len_neList T (a1§§l1))) = (S (len_neList T (a§§l))));
+ nrewrite > (nat_destruct_S_S ?? H2);
+ napply (refl_eq ??)
+ ##]
+nqed.
+
+nlet rec fold_right_neList2 (T1,T2:Type) (f:T1 → T1 → T2 → T2) (acc:T2) (l1:ne_list T1) on l1 ≝
+ match l1
+ return λl1.Πl2.len_neList T1 l1 = len_neList T1 l2 → T2
+ with
+ [ ne_nil h ⇒ λl2.match l2 return λl2.len_neList T1 «£h» = len_neList T1 l2 → T2 with
+ [ ne_nil h' ⇒ λp:len_neList T1 «£h» = len_neList T1 «£h'».
+ f h h' acc
+ | ne_cons h' t' ⇒ λp:len_neList T1 «£h» = len_neList T1 (h'§§t').
+ False_rect ? (fold_right_neList2_aux1 T1 h h' t' p)
+ ]
+ | ne_cons h t ⇒ λl2.match l2 return λl2.len_neList T1 (h§§t) = len_neList T1 l2 → T2 with
+ [ ne_nil h' ⇒ λp:len_neList T1 (h§§t) = len_neList T1 «£h'».
+ False_rect ? (fold_right_neList2_aux2 T1 h h' t p)
+ | ne_cons h' t' ⇒ λp:len_neList T1 (h§§t) = len_neList T1 (h'§§t').
+ f h h' (fold_right_neList2 T1 T2 f acc t t' (fold_right_neList2_aux3 T1 h h' t t' p))
+ ]
+ ].
+
+(* ******** *)
+(* naturali *)
+(* ******** *)
+
+ndefinition isZero ≝ λn:nat.match n with [ O ⇒ True | S _ ⇒ False ].
+
+ndefinition isZerob ≝ λn:nat.match n with [ O ⇒ true | S _ ⇒ false ].
+
+ndefinition ltb ≝ λn1,n2:nat.(le_nat n1 n2) ⊗ (⊖ (eq_nat n1 n2)).
+
+ndefinition geb ≝ λn1,n2:nat.(⊖ (le_nat n1 n2)) ⊕ (eq_nat n1 n2).
+
+ndefinition gtb ≝ λn1,n2:nat.⊖ (le_nat n1 n2).
--- /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 "utility/utility.ma".
+
+(* ************ *)
+(* List Utility *)
+(* ************ *)
+
+nlemma nelist_destruct_nil_nil : ∀T.∀x1,x2:T.ne_nil T x1 = ne_nil T x2 → x1 = x2.
+ #T; #x1; #x2; #H;
+ nchange with (match ne_nil T x2 with [ ne_cons _ _ ⇒ False | ne_nil a ⇒ x1 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply (refl_eq ??).
+nqed.
+
+nlemma nelist_destruct_cons_cons_1 : ∀T.∀x1,x2:T.∀y1,y2:ne_list T.ne_cons T x1 y1 = ne_cons T x2 y2 → x1 = x2.
+ #T; #x1; #x2; #y1; #y2; #H;
+ nchange with (match ne_cons T x2 y2 with [ ne_nil _ ⇒ False | ne_cons a _ ⇒ x1 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply (refl_eq ??).
+nqed.
+
+nlemma nelist_destruct_cons_cons_2 : ∀T.∀x1,x2:T.∀y1,y2:ne_list T.ne_cons T x1 y1 = ne_cons T x2 y2 → y1 = y2.
+ #T; #x1; #x2; #y1; #y2; #H;
+ nchange with (match ne_cons T x2 y2 with [ ne_nil _ ⇒ False | ne_cons _ b ⇒ y1 = b ]);
+ nrewrite < H;
+ nnormalize;
+ napply (refl_eq ??).
+nqed.
+
+nlemma nelist_destruct_cons_nil : ∀T.∀x1,x2:T.∀y1:ne_list T.ne_cons T x1 y1 = ne_nil T x2 → False.
+ #T; #x1; #x2; #y1; #H;
+ nchange with (match ne_cons T x1 y1 with [ ne_nil _ ⇒ True | ne_cons a b ⇒ False ]);
+ nrewrite > H;
+ nnormalize;
+ napply I.
+nqed.
+
+nlemma list_destruct_nil_cons : ∀T.∀x1,x2:T.∀y2:ne_list T.ne_nil T x1 = ne_cons T x2 y2 → False.
+ #T; #x1; #x2; #y2; #H;
+ nchange with (match ne_cons T x2 y2 with [ ne_nil _ ⇒ True | ne_cons a b ⇒ False ]);
+ nrewrite < H;
+ nnormalize;
+ napply I.
+nqed.
+
+nlemma isbemptylist_to_isemptylist : ∀T,l.isb_empty_list T l = true → is_empty_list T l.
+ #T; #l;
+ ncases l;
+ nnormalize;
+ ##[ ##1: #H; napply I
+ ##| ##2: #x; #l; #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma isnotbemptylist_to_isnotemptylist : ∀T,l.isnotb_empty_list T l = true → isnot_empty_list T l.
+ #T; #l;
+ ncases l;
+ nnormalize;
+ ##[ ##1: #H; napply (bool_destruct ??? H)
+ ##| ##2: #x; #l; #H; napply I
+ ##]
+nqed.
+
+(* ******** *)
+(* naturali *)
+(* ******** *)
+
+nlemma iszerob_to_iszero : ∀n.isZerob n = true → isZero n.
+ #n;
+ ncases n;
+ ##[ ##1: nnormalize; #H; napply I
+ ##| ##2: #n1; nnormalize; #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
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