+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-(* ********************************************************************** *)
-(* Progetto FreeScale *)
-(* *)
-(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
-(* Ultima modifica: 05/08/2009 *)
-(* *)
-(* ********************************************************************** *)
-
-include "num/bool_lemmas.ma".
-include "freescale/opcode_base.ma".
-
-(* ********************************************** *)
-(* MATTONI BASE PER DEFINIRE LE TABELLE DELLE MCU *)
-(* ********************************************** *)
-
-ndefinition opcode_destruct_aux ≝
-Πop1,op2.ΠP:Prop.op1 = op2 →
- match eq_op op1 op2 with [ true ⇒ P → P | false ⇒ P ].
-
-ndefinition opcode_destruct : opcode_destruct_aux.
- #op1; #op2; #P; #H;
- nrewrite < H;
- nelim op1;
- nnormalize;
- napply (λx.x).
-nqed.
-
-nlemma eq_to_eqop : ∀n1,n2.n1 = n2 → eq_op n1 n2 = true.
- #n1; #n2; #H;
- nrewrite > H;
- nelim n2;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma neqop_to_neq : ∀n1,n2.eq_op n1 n2 = false → n1 ≠ n2.
- #n1; #n2; #H;
- napply (not_to_not (n1 = n2) (eq_op n1 n2 = true) …);
- ##[ ##1: napply (eq_to_eqop n1 n2)
- ##| ##2: napply (eqfalse_to_neqtrue … H)
- ##]
-nqed.
-
-nlemma eqop_to_eq1 : ∀op2.eq_op ADC op2 = true → ADC = op2. #op2; ncases op2; nnormalize; #H; ##[ ##1: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq2 : ∀op2.eq_op ADD op2 = true → ADD = op2. #op2; ncases op2; nnormalize; #H; ##[ ##2: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq3 : ∀op2.eq_op AIS op2 = true → AIS = op2. #op2; ncases op2; nnormalize; #H; ##[ ##3: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq4 : ∀op2.eq_op AIX op2 = true → AIX = op2. #op2; ncases op2; nnormalize; #H; ##[ ##4: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq5 : ∀op2.eq_op AND op2 = true → AND = op2. #op2; ncases op2; nnormalize; #H; ##[ ##5: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq6 : ∀op2.eq_op ASL op2 = true → ASL = op2. #op2; ncases op2; nnormalize; #H; ##[ ##6: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq7 : ∀op2.eq_op ASR op2 = true → ASR = op2. #op2; ncases op2; nnormalize; #H; ##[ ##7: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq8 : ∀op2.eq_op BCC op2 = true → BCC = op2. #op2; ncases op2; nnormalize; #H; ##[ ##8: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq9 : ∀op2.eq_op BCLRn op2 = true → BCLRn = op2. #op2; ncases op2; nnormalize; #H; ##[ ##9: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq10 : ∀op2.eq_op BCS op2 = true → BCS = op2. #op2; ncases op2; nnormalize; #H; ##[ ##10: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq11 : ∀op2.eq_op BEQ op2 = true → BEQ = op2. #op2; ncases op2; nnormalize; #H; ##[ ##11: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq12 : ∀op2.eq_op BGE op2 = true → BGE = op2. #op2; ncases op2; nnormalize; #H; ##[ ##12: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq13 : ∀op2.eq_op BGND op2 = true → BGND = op2. #op2; ncases op2; nnormalize; #H; ##[ ##13: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq14 : ∀op2.eq_op BGT op2 = true → BGT = op2. #op2; ncases op2; nnormalize; #H; ##[ ##14: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq15 : ∀op2.eq_op BHCC op2 = true → BHCC = op2. #op2; ncases op2; nnormalize; #H; ##[ ##15: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq16 : ∀op2.eq_op BHCS op2 = true → BHCS = op2. #op2; ncases op2; nnormalize; #H; ##[ ##16: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq17 : ∀op2.eq_op BHI op2 = true → BHI = op2. #op2; ncases op2; nnormalize; #H; ##[ ##17: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq18 : ∀op2.eq_op BIH op2 = true → BIH = op2. #op2; ncases op2; nnormalize; #H; ##[ ##18: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq19 : ∀op2.eq_op BIL op2 = true → BIL = op2. #op2; ncases op2; nnormalize; #H; ##[ ##19: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq20 : ∀op2.eq_op BIT op2 = true → BIT = op2. #op2; ncases op2; nnormalize; #H; ##[ ##20: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq21 : ∀op2.eq_op BLE op2 = true → BLE = op2. #op2; ncases op2; nnormalize; #H; ##[ ##21: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq22 : ∀op2.eq_op BLS op2 = true → BLS = op2. #op2; ncases op2; nnormalize; #H; ##[ ##22: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq23 : ∀op2.eq_op BLT op2 = true → BLT = op2. #op2; ncases op2; nnormalize; #H; ##[ ##23: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq24 : ∀op2.eq_op BMC op2 = true → BMC = op2. #op2; ncases op2; nnormalize; #H; ##[ ##24: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq25 : ∀op2.eq_op BMI op2 = true → BMI = op2. #op2; ncases op2; nnormalize; #H; ##[ ##25: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq26 : ∀op2.eq_op BMS op2 = true → BMS = op2. #op2; ncases op2; nnormalize; #H; ##[ ##26: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq27 : ∀op2.eq_op BNE op2 = true → BNE = op2. #op2; ncases op2; nnormalize; #H; ##[ ##27: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq28 : ∀op2.eq_op BPL op2 = true → BPL = op2. #op2; ncases op2; nnormalize; #H; ##[ ##28: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq29 : ∀op2.eq_op BRA op2 = true → BRA = op2. #op2; ncases op2; nnormalize; #H; ##[ ##29: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq30 : ∀op2.eq_op BRCLRn op2 = true → BRCLRn = op2. #op2; ncases op2; nnormalize; #H; ##[ ##30: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq31 : ∀op2.eq_op BRN op2 = true → BRN = op2. #op2; ncases op2; nnormalize; #H; ##[ ##31: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq32 : ∀op2.eq_op BRSETn op2 = true → BRSETn = op2. #op2; ncases op2; nnormalize; #H; ##[ ##32: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq33 : ∀op2.eq_op BSETn op2 = true → BSETn = op2. #op2; ncases op2; nnormalize; #H; ##[ ##33: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq34 : ∀op2.eq_op BSR op2 = true → BSR = op2. #op2; ncases op2; nnormalize; #H; ##[ ##34: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq35 : ∀op2.eq_op CBEQA op2 = true → CBEQA = op2. #op2; ncases op2; nnormalize; #H; ##[ ##35: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq36 : ∀op2.eq_op CBEQX op2 = true → CBEQX = op2. #op2; ncases op2; nnormalize; #H; ##[ ##36: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq37 : ∀op2.eq_op CLC op2 = true → CLC = op2. #op2; ncases op2; nnormalize; #H; ##[ ##37: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq38 : ∀op2.eq_op CLI op2 = true → CLI = op2. #op2; ncases op2; nnormalize; #H; ##[ ##38: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq39 : ∀op2.eq_op CLR op2 = true → CLR = op2. #op2; ncases op2; nnormalize; #H; ##[ ##39: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq40 : ∀op2.eq_op CMP op2 = true → CMP = op2. #op2; ncases op2; nnormalize; #H; ##[ ##40: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq41 : ∀op2.eq_op COM op2 = true → COM = op2. #op2; ncases op2; nnormalize; #H; ##[ ##41: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq42 : ∀op2.eq_op CPHX op2 = true → CPHX = op2. #op2; ncases op2; nnormalize; #H; ##[ ##42: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq43 : ∀op2.eq_op CPX op2 = true → CPX = op2. #op2; ncases op2; nnormalize; #H; ##[ ##43: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq44 : ∀op2.eq_op DAA op2 = true → DAA = op2. #op2; ncases op2; nnormalize; #H; ##[ ##44: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq45 : ∀op2.eq_op DBNZ op2 = true → DBNZ = op2. #op2; ncases op2; nnormalize; #H; ##[ ##45: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq46 : ∀op2.eq_op DEC op2 = true → DEC = op2. #op2; ncases op2; nnormalize; #H; ##[ ##46: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq47 : ∀op2.eq_op DIV op2 = true → DIV = op2. #op2; ncases op2; nnormalize; #H; ##[ ##47: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq48 : ∀op2.eq_op EOR op2 = true → EOR = op2. #op2; ncases op2; nnormalize; #H; ##[ ##48: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq49 : ∀op2.eq_op INC op2 = true → INC = op2. #op2; ncases op2; nnormalize; #H; ##[ ##49: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq50 : ∀op2.eq_op JMP op2 = true → JMP = op2. #op2; ncases op2; nnormalize; #H; ##[ ##50: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq51 : ∀op2.eq_op JSR op2 = true → JSR = op2. #op2; ncases op2; nnormalize; #H; ##[ ##51: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq52 : ∀op2.eq_op LDA op2 = true → LDA = op2. #op2; ncases op2; nnormalize; #H; ##[ ##52: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq53 : ∀op2.eq_op LDHX op2 = true → LDHX = op2. #op2; ncases op2; nnormalize; #H; ##[ ##53: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq54 : ∀op2.eq_op LDX op2 = true → LDX = op2. #op2; ncases op2; nnormalize; #H; ##[ ##54: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq55 : ∀op2.eq_op LSR op2 = true → LSR = op2. #op2; ncases op2; nnormalize; #H; ##[ ##55: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq56 : ∀op2.eq_op MOV op2 = true → MOV = op2. #op2; ncases op2; nnormalize; #H; ##[ ##56: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq57 : ∀op2.eq_op MUL op2 = true → MUL = op2. #op2; ncases op2; nnormalize; #H; ##[ ##57: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq58 : ∀op2.eq_op NEG op2 = true → NEG = op2. #op2; ncases op2; nnormalize; #H; ##[ ##58: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq59 : ∀op2.eq_op NOP op2 = true → NOP = op2. #op2; ncases op2; nnormalize; #H; ##[ ##59: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq60 : ∀op2.eq_op NSA op2 = true → NSA = op2. #op2; ncases op2; nnormalize; #H; ##[ ##60: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq61 : ∀op2.eq_op ORA op2 = true → ORA = op2. #op2; ncases op2; nnormalize; #H; ##[ ##61: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq62 : ∀op2.eq_op PSHA op2 = true → PSHA = op2. #op2; ncases op2; nnormalize; #H; ##[ ##62: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq63 : ∀op2.eq_op PSHH op2 = true → PSHH = op2. #op2; ncases op2; nnormalize; #H; ##[ ##63: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq64 : ∀op2.eq_op PSHX op2 = true → PSHX = op2. #op2; ncases op2; nnormalize; #H; ##[ ##64: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq65 : ∀op2.eq_op PULA op2 = true → PULA = op2. #op2; ncases op2; nnormalize; #H; ##[ ##65: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq66 : ∀op2.eq_op PULH op2 = true → PULH = op2. #op2; ncases op2; nnormalize; #H; ##[ ##66: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq67 : ∀op2.eq_op PULX op2 = true → PULX = op2. #op2; ncases op2; nnormalize; #H; ##[ ##67: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq68 : ∀op2.eq_op ROL op2 = true → ROL = op2. #op2; ncases op2; nnormalize; #H; ##[ ##68: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq69 : ∀op2.eq_op ROR op2 = true → ROR = op2. #op2; ncases op2; nnormalize; #H; ##[ ##69: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq70 : ∀op2.eq_op RSP op2 = true → RSP = op2. #op2; ncases op2; nnormalize; #H; ##[ ##70: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq71 : ∀op2.eq_op RTI op2 = true → RTI = op2. #op2; ncases op2; nnormalize; #H; ##[ ##71: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq72 : ∀op2.eq_op RTS op2 = true → RTS = op2. #op2; ncases op2; nnormalize; #H; ##[ ##72: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq73 : ∀op2.eq_op SBC op2 = true → SBC = op2. #op2; ncases op2; nnormalize; #H; ##[ ##73: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq74 : ∀op2.eq_op SEC op2 = true → SEC = op2. #op2; ncases op2; nnormalize; #H; ##[ ##74: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq75 : ∀op2.eq_op SEI op2 = true → SEI = op2. #op2; ncases op2; nnormalize; #H; ##[ ##75: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq76 : ∀op2.eq_op SHA op2 = true → SHA = op2. #op2; ncases op2; nnormalize; #H; ##[ ##76: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq77 : ∀op2.eq_op SLA op2 = true → SLA = op2. #op2; ncases op2; nnormalize; #H; ##[ ##77: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq78 : ∀op2.eq_op STA op2 = true → STA = op2. #op2; ncases op2; nnormalize; #H; ##[ ##78: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq79 : ∀op2.eq_op STHX op2 = true → STHX = op2. #op2; ncases op2; nnormalize; #H; ##[ ##79: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq80 : ∀op2.eq_op STOP op2 = true → STOP = op2. #op2; ncases op2; nnormalize; #H; ##[ ##80: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq81 : ∀op2.eq_op STX op2 = true → STX = op2. #op2; ncases op2; nnormalize; #H; ##[ ##81: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq82 : ∀op2.eq_op SUB op2 = true → SUB = op2. #op2; ncases op2; nnormalize; #H; ##[ ##82: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq83 : ∀op2.eq_op SWI op2 = true → SWI = op2. #op2; ncases op2; nnormalize; #H; ##[ ##83: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq84 : ∀op2.eq_op TAP op2 = true → TAP = op2. #op2; ncases op2; nnormalize; #H; ##[ ##84: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq85 : ∀op2.eq_op TAX op2 = true → TAX = op2. #op2; ncases op2; nnormalize; #H; ##[ ##85: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq86 : ∀op2.eq_op TPA op2 = true → TPA = op2. #op2; ncases op2; nnormalize; #H; ##[ ##86: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq87 : ∀op2.eq_op TST op2 = true → TST = op2. #op2; ncases op2; nnormalize; #H; ##[ ##87: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq88 : ∀op2.eq_op TSX op2 = true → TSX = op2. #op2; ncases op2; nnormalize; #H; ##[ ##88: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq89 : ∀op2.eq_op TXA op2 = true → TXA = op2. #op2; ncases op2; nnormalize; #H; ##[ ##89: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq90 : ∀op2.eq_op TXS op2 = true → TXS = op2. #op2; ncases op2; nnormalize; #H; ##[ ##90: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-nlemma eqop_to_eq91 : ∀op2.eq_op WAIT op2 = true → WAIT = op2. #op2; ncases op2; nnormalize; #H; ##[ ##91: napply refl_eq ##| ##*: napply (bool_destruct … H) ##]nqed.
-
-nlemma eqop_to_eq : ∀op1,op2.eq_op op1 op2 = true → op1 = op2.
- #op1; ncases op1;
- ##[ ##1: napply eqop_to_eq1 ##| ##2: napply eqop_to_eq2 ##| ##3: napply eqop_to_eq3 ##| ##4: napply eqop_to_eq4
- ##| ##5: napply eqop_to_eq5 ##| ##6: napply eqop_to_eq6 ##| ##7: napply eqop_to_eq7 ##| ##8: napply eqop_to_eq8
- ##| ##9: napply eqop_to_eq9 ##| ##10: napply eqop_to_eq10 ##| ##11: napply eqop_to_eq11 ##| ##12: napply eqop_to_eq12
- ##| ##13: napply eqop_to_eq13 ##| ##14: napply eqop_to_eq14 ##| ##15: napply eqop_to_eq15 ##| ##16: napply eqop_to_eq16
- ##| ##17: napply eqop_to_eq17 ##| ##18: napply eqop_to_eq18 ##| ##19: napply eqop_to_eq19 ##| ##20: napply eqop_to_eq20
- ##| ##21: napply eqop_to_eq21 ##| ##22: napply eqop_to_eq22 ##| ##23: napply eqop_to_eq23 ##| ##24: napply eqop_to_eq24
- ##| ##25: napply eqop_to_eq25 ##| ##26: napply eqop_to_eq26 ##| ##27: napply eqop_to_eq27 ##| ##28: napply eqop_to_eq28
- ##| ##29: napply eqop_to_eq29 ##| ##30: napply eqop_to_eq30 ##| ##31: napply eqop_to_eq31 ##| ##32: napply eqop_to_eq32
- ##| ##33: napply eqop_to_eq33 ##| ##34: napply eqop_to_eq34 ##| ##35: napply eqop_to_eq35 ##| ##36: napply eqop_to_eq36
- ##| ##37: napply eqop_to_eq37 ##| ##38: napply eqop_to_eq38 ##| ##39: napply eqop_to_eq39 ##| ##40: napply eqop_to_eq40
- ##| ##41: napply eqop_to_eq41 ##| ##42: napply eqop_to_eq42 ##| ##43: napply eqop_to_eq43 ##| ##44: napply eqop_to_eq44
- ##| ##45: napply eqop_to_eq45 ##| ##46: napply eqop_to_eq46 ##| ##47: napply eqop_to_eq47 ##| ##48: napply eqop_to_eq48
- ##| ##49: napply eqop_to_eq49 ##| ##50: napply eqop_to_eq50 ##| ##51: napply eqop_to_eq51 ##| ##52: napply eqop_to_eq52
- ##| ##53: napply eqop_to_eq53 ##| ##54: napply eqop_to_eq54 ##| ##55: napply eqop_to_eq55 ##| ##56: napply eqop_to_eq56
- ##| ##57: napply eqop_to_eq57 ##| ##58: napply eqop_to_eq58 ##| ##59: napply eqop_to_eq59 ##| ##60: napply eqop_to_eq60
- ##| ##61: napply eqop_to_eq61 ##| ##62: napply eqop_to_eq62 ##| ##63: napply eqop_to_eq63 ##| ##64: napply eqop_to_eq64
- ##| ##65: napply eqop_to_eq65 ##| ##66: napply eqop_to_eq66 ##| ##67: napply eqop_to_eq67 ##| ##68: napply eqop_to_eq68
- ##| ##69: napply eqop_to_eq69 ##| ##70: napply eqop_to_eq70 ##| ##71: napply eqop_to_eq71 ##| ##72: napply eqop_to_eq72
- ##| ##73: napply eqop_to_eq73 ##| ##74: napply eqop_to_eq74 ##| ##75: napply eqop_to_eq75 ##| ##76: napply eqop_to_eq76
- ##| ##77: napply eqop_to_eq77 ##| ##78: napply eqop_to_eq78 ##| ##79: napply eqop_to_eq79 ##| ##80: napply eqop_to_eq80
- ##| ##81: napply eqop_to_eq81 ##| ##82: napply eqop_to_eq82 ##| ##83: napply eqop_to_eq83 ##| ##84: napply eqop_to_eq84
- ##| ##85: napply eqop_to_eq85 ##| ##86: napply eqop_to_eq86 ##| ##87: napply eqop_to_eq87 ##| ##88: napply eqop_to_eq88
- ##| ##89: napply eqop_to_eq89 ##| ##90: napply eqop_to_eq90 ##| ##91: napply eqop_to_eq91 ##]
-nqed.
-
-nlemma neq_to_neqop : ∀n1,n2.n1 ≠ n2 → eq_op n1 n2 = false.
- #n1; #n2; #H;
- napply (neqtrue_to_eqfalse (eq_op n1 n2));
- napply (not_to_not (eq_op n1 n2 = true) (n1 = n2) ? H);
- napply (eqop_to_eq n1 n2).
-nqed.
-
-nlemma decidable_op : ∀x,y:opcode.decidable (x = y).
- #x; #y; nnormalize;
- napply (or2_elim (eq_op x y = true) (eq_op x y = false) ? (decidable_bexpr ?));
- ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqop_to_eq … H))
- ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqop_to_neq … H))
- ##]
-nqed.
-
-nlemma symmetric_eqop : symmetricT opcode bool eq_op.
- #n1; #n2;
- napply (or2_elim (n1 = n2) (n1 ≠ n2) ? (decidable_op n1 n2));
- ##[ ##1: #H; nrewrite > H; napply refl_eq
- ##| ##2: #H; nrewrite > (neq_to_neqop n1 n2 H);
- napply (symmetric_eq ? (eq_op n2 n1) false);
- napply (neq_to_neqop n2 n1 (symmetric_neq ? n1 n2 H))
- ##]
-nqed.
projects / helm.git / blobdiff