freescale porting, work in progress

[helm.git] / helm / software / matita / contribs / ng_assembly / freescale / opcode_base_lemmas_opcode1.ma

diff --git a/helm/software/matita/contribs/ng_assembly/freescale/opcode_base_lemmas_opcode1.ma b/helm/software/matita/contribs/ng_assembly/freescale/opcode_base_lemmas_opcode1.ma
index 72803e9515d901ddf780c1b54a77840f7f4d3baf..ffc7eab82ac538f0409774ac1676242384eae50b 100755 (executable)
--- a/helm/software/matita/contribs/ng_assembly/freescale/opcode_base_lemmas_opcode1.ma
+++ b/helm/software/matita/contribs/ng_assembly/freescale/opcode_base_lemmas_opcode1.ma
@@ -27,944 +27,371 @@ include "freescale/opcode_base.ma".
 (* MATTONI BASE PER DEFINIRE LE TABELLE DELLE MCU *)
 (* ********************************************** *)
 
-ndefinition opcode_destruct1 : Πop2.ΠP:Prop.ADC = op2 → match op2 with [ ADC ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##1: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match ADC with [ ADC ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct2 : Πop2.ΠP:Prop.ADD = op2 → match op2 with [ ADD ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##2: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match ADD with [ ADD ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct3 : Πop2.ΠP:Prop.AIS = op2 → match op2 with [ AIS ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##3: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match AIS with [ AIS ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct4 : Πop2.ΠP:Prop.AIX = op2 → match op2 with [ AIX ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##4: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match AIX with [ AIX ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct5 : Πop2.ΠP:Prop.AND = op2 → match op2 with [ AND ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##5: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match AND with [ AND ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct6 : Πop2.ΠP:Prop.ASL = op2 → match op2 with [ ASL ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##6: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match ASL with [ ASL ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct7 : Πop2.ΠP:Prop.ASR = op2 → match op2 with [ ASR ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##7: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match ASR with [ ASR ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct8 : Πop2.ΠP:Prop.BCC = op2 → match op2 with [ BCC ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##8: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BCC with [ BCC ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct9 : Πop2.ΠP:Prop.BCLRn = op2 → match op2 with [ BCLRn ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##9: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BCLRn with [ BCLRn ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct10 : Πop2.ΠP:Prop.BCS = op2 → match op2 with [ BCS ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##10: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BCS with [ BCS ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct11 : Πop2.ΠP:Prop.BEQ = op2 → match op2 with [ BEQ ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##11: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BEQ with [ BEQ ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct12 : Πop2.ΠP:Prop.BGE = op2 → match op2 with [ BGE ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##12: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BGE with [ BGE ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct13 : Πop2.ΠP:Prop.BGND = op2 → match op2 with [ BGND ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##13: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BGND with [ BGND ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct14 : Πop2.ΠP:Prop.BGT = op2 → match op2 with [ BGT ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##14: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BGT with [ BGT ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct15 : Πop2.ΠP:Prop.BHCC = op2 → match op2 with [ BHCC ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##15: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BHCC with [ BHCC ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct16 : Πop2.ΠP:Prop.BHCS = op2 → match op2 with [ BHCS ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##16: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BHCS with [ BHCS ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct17 : Πop2.ΠP:Prop.BHI = op2 → match op2 with [ BHI ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##17: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BHI with [ BHI ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct18 : Πop2.ΠP:Prop.BIH = op2 → match op2 with [ BIH ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##18: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BIH with [ BIH ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct19 : Πop2.ΠP:Prop.BIL = op2 → match op2 with [ BIL ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##19: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BIL with [ BIL ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct20 : Πop2.ΠP:Prop.BIT = op2 → match op2 with [ BIT ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##20: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BIT with [ BIT ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct21 : Πop2.ΠP:Prop.BLE = op2 → match op2 with [ BLE ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##21: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BLE with [ BLE ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct22 : Πop2.ΠP:Prop.BLS = op2 → match op2 with [ BLS ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##22: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BLS with [ BLS ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct23 : Πop2.ΠP:Prop.BLT = op2 → match op2 with [ BLT ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##23: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BLT with [ BLT ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct24 : Πop2.ΠP:Prop.BMC = op2 → match op2 with [ BMC ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##24: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BMC with [ BMC ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct25 : Πop2.ΠP:Prop.BMI = op2 → match op2 with [ BMI ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##25: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BMI with [ BMI ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct26 : Πop2.ΠP:Prop.BMS = op2 → match op2 with [ BMS ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##26: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BMS with [ BMS ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct27 : Πop2.ΠP:Prop.BNE = op2 → match op2 with [ BNE ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##27: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BNE with [ BNE ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct28 : Πop2.ΠP:Prop.BPL = op2 → match op2 with [ BPL ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##28: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BPL with [ BPL ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct29 : Πop2.ΠP:Prop.BRA = op2 → match op2 with [ BRA ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##29: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BRA with [ BRA ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct30 : Πop2.ΠP:Prop.BRCLRn = op2 → match op2 with [ BRCLRn ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##30: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BRCLRn with [ BRCLRn ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct31 : Πop2.ΠP:Prop.BRN = op2 → match op2 with [ BRN ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##31: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BRN with [ BRN ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct32 : Πop2.ΠP:Prop.BRSETn = op2 → match op2 with [ BRSETn ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##32: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BRSETn with [ BRSETn ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct33 : Πop2.ΠP:Prop.BSETn = op2 → match op2 with [ BSETn ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##33: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BSETn with [ BSETn ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct34 : Πop2.ΠP:Prop.BSR = op2 → match op2 with [ BSR ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##34: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match BSR with [ BSR ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct35 : Πop2.ΠP:Prop.CBEQA = op2 → match op2 with [ CBEQA ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##35: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match CBEQA with [ CBEQA ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct36 : Πop2.ΠP:Prop.CBEQX = op2 → match op2 with [ CBEQX ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##36: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match CBEQX with [ CBEQX ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct37 : Πop2.ΠP:Prop.CLC = op2 → match op2 with [ CLC ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##37: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match CLC with [ CLC ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct38 : Πop2.ΠP:Prop.CLI = op2 → match op2 with [ CLI ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##38: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match CLI with [ CLI ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct39 : Πop2.ΠP:Prop.CLR = op2 → match op2 with [ CLR ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##39: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match CLR with [ CLR ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct40 : Πop2.ΠP:Prop.CMP = op2 → match op2 with [ CMP ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##40: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match CMP with [ CMP ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct41 : Πop2.ΠP:Prop.COM = op2 → match op2 with [ COM ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##41: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match COM with [ COM ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct42 : Πop2.ΠP:Prop.CPHX = op2 → match op2 with [ CPHX ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##42: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match CPHX with [ CPHX ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct43 : Πop2.ΠP:Prop.CPX = op2 → match op2 with [ CPX ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##43: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match CPX with [ CPX ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct44 : Πop2.ΠP:Prop.DAA = op2 → match op2 with [ DAA ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##44: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match DAA with [ DAA ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct45 : Πop2.ΠP:Prop.DBNZ = op2 → match op2 with [ DBNZ ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##45: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match DBNZ with [ DBNZ ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct46 : Πop2.ΠP:Prop.DEC = op2 → match op2 with [ DEC ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##46: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match DEC with [ DEC ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct47 : Πop2.ΠP:Prop.DIV = op2 → match op2 with [ DIV ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##47: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match DIV with [ DIV ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct48 : Πop2.ΠP:Prop.EOR = op2 → match op2 with [ EOR ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##48: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match EOR with [ EOR ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct49 : Πop2.ΠP:Prop.INC = op2 → match op2 with [ INC ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##49: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match INC with [ INC ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct50 : Πop2.ΠP:Prop.JMP = op2 → match op2 with [ JMP ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##50: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match JMP with [ JMP ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct51 : Πop2.ΠP:Prop.JSR = op2 → match op2 with [ JSR ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##51: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match JSR with [ JSR ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct52 : Πop2.ΠP:Prop.LDA = op2 → match op2 with [ LDA ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##52: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match LDA with [ LDA ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct53 : Πop2.ΠP:Prop.LDHX = op2 → match op2 with [ LDHX ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##53: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match LDHX with [ LDHX ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct54 : Πop2.ΠP:Prop.LDX = op2 → match op2 with [ LDX ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##54: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match LDX with [ LDX ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct55 : Πop2.ΠP:Prop.LSR = op2 → match op2 with [ LSR ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##55: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match LSR with [ LSR ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct56 : Πop2.ΠP:Prop.MOV = op2 → match op2 with [ MOV ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##56: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match MOV with [ MOV ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct57 : Πop2.ΠP:Prop.MUL = op2 → match op2 with [ MUL ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##57: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match MUL with [ MUL ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct58 : Πop2.ΠP:Prop.NEG = op2 → match op2 with [ NEG ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##58: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match NEG with [ NEG ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct59 : Πop2.ΠP:Prop.NOP = op2 → match op2 with [ NOP ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##59: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match NOP with [ NOP ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct60 : Πop2.ΠP:Prop.NSA = op2 → match op2 with [ NSA ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##60: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match NSA with [ NSA ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct61 : Πop2.ΠP:Prop.ORA = op2 → match op2 with [ ORA ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##61: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match ORA with [ ORA ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct62 : Πop2.ΠP:Prop.PSHA = op2 → match op2 with [ PSHA ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##62: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match PSHA with [ PSHA ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct63 : Πop2.ΠP:Prop.PSHH = op2 → match op2 with [ PSHH ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##63: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match PSHH with [ PSHH ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct64 : Πop2.ΠP:Prop.PSHX = op2 → match op2 with [ PSHX ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##64: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match PSHX with [ PSHX ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct65 : Πop2.ΠP:Prop.PULA = op2 → match op2 with [ PULA ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##65: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match PULA with [ PULA ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct66 : Πop2.ΠP:Prop.PULH = op2 → match op2 with [ PULH ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##66: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match PULH with [ PULH ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct67 : Πop2.ΠP:Prop.PULX = op2 → match op2 with [ PULX ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##67: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match PULX with [ PULX ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct68 : Πop2.ΠP:Prop.ROL = op2 → match op2 with [ ROL ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##68: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match ROL with [ ROL ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct69 : Πop2.ΠP:Prop.ROR = op2 → match op2 with [ ROR ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##69: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match ROR with [ ROR ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct70 : Πop2.ΠP:Prop.RSP = op2 → match op2 with [ RSP ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##70: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match RSP with [ RSP ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct71 : Πop2.ΠP:Prop.RTI = op2 → match op2 with [ RTI ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##71: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match RTI with [ RTI ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct72 : Πop2.ΠP:Prop.RTS = op2 → match op2 with [ RTS ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##72: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match RTS with [ RTS ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct73 : Πop2.ΠP:Prop.SBC = op2 → match op2 with [ SBC ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##73: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match SBC with [ SBC ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct74 : Πop2.ΠP:Prop.SEC = op2 → match op2 with [ SEC ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##74: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match SEC with [ SEC ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct75 : Πop2.ΠP:Prop.SEI = op2 → match op2 with [ SEI ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##75: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match SEI with [ SEI ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct76 : Πop2.ΠP:Prop.SHA = op2 → match op2 with [ SHA ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##76: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match SHA with [ SHA ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct77 : Πop2.ΠP:Prop.SLA = op2 → match op2 with [ SLA ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##77: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match SLA with [ SLA ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct78 : Πop2.ΠP:Prop.STA = op2 → match op2 with [ STA ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##78: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match STA with [ STA ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct79 : Πop2.ΠP:Prop.STHX = op2 → match op2 with [ STHX ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##79: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match STHX with [ STHX ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct80 : Πop2.ΠP:Prop.STOP = op2 → match op2 with [ STOP ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##80: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match STOP with [ STOP ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct81 : Πop2.ΠP:Prop.STX = op2 → match op2 with [ STX ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##81: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match STX with [ STX ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct82 : Πop2.ΠP:Prop.SUB = op2 → match op2 with [ SUB ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##82: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match SUB with [ SUB ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct83 : Πop2.ΠP:Prop.SWI = op2 → match op2 with [ SWI ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##83: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match SWI with [ SWI ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct84 : Πop2.ΠP:Prop.TAP = op2 → match op2 with [ TAP ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##84: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match TAP with [ TAP ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct85 : Πop2.ΠP:Prop.TAX = op2 → match op2 with [ TAX ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##85: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match TAX with [ TAX ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct86 : Πop2.ΠP:Prop.TPA = op2 → match op2 with [ TPA ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##86: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match TPA with [ TPA ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct87 : Πop2.ΠP:Prop.TST = op2 → match op2 with [ TST ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##87: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match TST with [ TST ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct88 : Πop2.ΠP:Prop.TSX = op2 → match op2 with [ TSX ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##88: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match TSX with [ TSX ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct89 : Πop2.ΠP:Prop.TXA = op2 → match op2 with [ TXA ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##89: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match TXA with [ TXA ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct90 : Πop2.ΠP:Prop.TXS = op2 → match op2 with [ TXS ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##90: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match TXS with [ TXS ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-ndefinition opcode_destruct91 : Πop2.ΠP:Prop.WAIT = op2 → match op2 with [ WAIT ⇒ P → P | _ ⇒ P ].
- #op2; #P; ncases op2; nnormalize;
- ##[ ##91: #H; napply (λx:P.x)
- ##| ##*: #H; napply False_ind;
-          nchange with (match WAIT with [ WAIT ⇒ False | _ ⇒ True ]);
-          nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
 ndefinition opcode_destruct_aux ≝
 Πop1,op2.ΠP:Prop.op1 = op2 →
- match op1 with
-  [ ADC ⇒ match op2 with [ ADC ⇒ P → P | _ ⇒ P ]
-  | ADD ⇒ match op2 with [ ADD ⇒ P → P | _ ⇒ P ]
-  | AIS ⇒ match op2 with [ AIS ⇒ P → P | _ ⇒ P ]
-  | AIX ⇒ match op2 with [ AIX ⇒ P → P | _ ⇒ P ]
-  | AND ⇒ match op2 with [ AND ⇒ P → P | _ ⇒ P ]
-  | ASL ⇒ match op2 with [ ASL ⇒ P → P | _ ⇒ P ]
-  | ASR ⇒ match op2 with [ ASR ⇒ P → P | _ ⇒ P ]
-  | BCC ⇒ match op2 with [ BCC ⇒ P → P | _ ⇒ P ]
-  | BCLRn ⇒ match op2 with [ BCLRn ⇒ P → P | _ ⇒ P ]
-  | BCS ⇒ match op2 with [ BCS ⇒ P → P | _ ⇒ P ]
-  | BEQ ⇒ match op2 with [ BEQ ⇒ P → P | _ ⇒ P ]
-  | BGE ⇒ match op2 with [ BGE ⇒ P → P | _ ⇒ P ]
-  | BGND ⇒ match op2 with [ BGND ⇒ P → P | _ ⇒ P ]
-  | BGT ⇒ match op2 with [ BGT ⇒ P → P | _ ⇒ P ]
-  | BHCC ⇒ match op2 with [ BHCC ⇒ P → P | _ ⇒ P ]
-  | BHCS ⇒ match op2 with [ BHCS ⇒ P → P | _ ⇒ P ]
-  | BHI ⇒ match op2 with [ BHI ⇒ P → P | _ ⇒ P ]
-  | BIH ⇒ match op2 with [ BIH ⇒ P → P | _ ⇒ P ]
-  | BIL ⇒ match op2 with [ BIL ⇒ P → P | _ ⇒ P ]
-  | BIT ⇒ match op2 with [ BIT ⇒ P → P | _ ⇒ P ]
-  | BLE ⇒ match op2 with [ BLE ⇒ P → P | _ ⇒ P ]
-  | BLS ⇒ match op2 with [ BLS ⇒ P → P | _ ⇒ P ]
-  | BLT ⇒ match op2 with [ BLT ⇒ P → P | _ ⇒ P ]
-  | BMC ⇒ match op2 with [ BMC ⇒ P → P | _ ⇒ P ]
-  | BMI ⇒ match op2 with [ BMI ⇒ P → P | _ ⇒ P ]
-  | BMS ⇒ match op2 with [ BMS ⇒ P → P | _ ⇒ P ]
-  | BNE ⇒ match op2 with [ BNE ⇒ P → P | _ ⇒ P ]
-  | BPL ⇒ match op2 with [ BPL ⇒ P → P | _ ⇒ P ]
-  | BRA ⇒ match op2 with [ BRA ⇒ P → P | _ ⇒ P ]
-  | BRCLRn ⇒ match op2 with [ BRCLRn ⇒ P → P | _ ⇒ P ]
-  | BRN ⇒ match op2 with [ BRN ⇒ P → P | _ ⇒ P ]
-  | BRSETn ⇒ match op2 with [ BRSETn ⇒ P → P | _ ⇒ P ]
-  | BSETn ⇒ match op2 with [ BSETn ⇒ P → P | _ ⇒ P ]
-  | BSR ⇒ match op2 with [ BSR ⇒ P → P | _ ⇒ P ]
-  | CBEQA ⇒ match op2 with [ CBEQA ⇒ P → P | _ ⇒ P ]
-  | CBEQX ⇒ match op2 with [ CBEQX ⇒ P → P | _ ⇒ P ]
-  | CLC ⇒ match op2 with [ CLC ⇒ P → P | _ ⇒ P ]
-  | CLI ⇒ match op2 with [ CLI ⇒ P → P | _ ⇒ P ]
-  | CLR ⇒ match op2 with [ CLR ⇒ P → P | _ ⇒ P ]
-  | CMP ⇒ match op2 with [ CMP ⇒ P → P | _ ⇒ P ]
-  | COM ⇒ match op2 with [ COM ⇒ P → P | _ ⇒ P ]
-  | CPHX ⇒ match op2 with [ CPHX ⇒ P → P | _ ⇒ P ]
-  | CPX ⇒ match op2 with [ CPX ⇒ P → P | _ ⇒ P ]
-  | DAA ⇒ match op2 with [ DAA ⇒ P → P | _ ⇒ P ]
-  | DBNZ ⇒ match op2 with [ DBNZ ⇒ P → P | _ ⇒ P ]
-  | DEC ⇒ match op2 with [ DEC ⇒ P → P | _ ⇒ P ]
-  | DIV ⇒ match op2 with [ DIV ⇒ P → P | _ ⇒ P ]
-  | EOR ⇒ match op2 with [ EOR ⇒ P → P | _ ⇒ P ]
-  | INC ⇒ match op2 with [ INC ⇒ P → P | _ ⇒ P ]
-  | JMP ⇒ match op2 with [ JMP ⇒ P → P | _ ⇒ P ]
-  | JSR ⇒ match op2 with [ JSR ⇒ P → P | _ ⇒ P ]
-  | LDA ⇒ match op2 with [ LDA ⇒ P → P | _ ⇒ P ]
-  | LDHX ⇒ match op2 with [ LDHX ⇒ P → P | _ ⇒ P ]
-  | LDX ⇒ match op2 with [ LDX ⇒ P → P | _ ⇒ P ]
-  | LSR ⇒ match op2 with [ LSR ⇒ P → P | _ ⇒ P ]
-  | MOV ⇒ match op2 with [ MOV ⇒ P → P | _ ⇒ P ]
-  | MUL ⇒ match op2 with [ MUL ⇒ P → P | _ ⇒ P ]
-  | NEG ⇒ match op2 with [ NEG ⇒ P → P | _ ⇒ P ]
-  | NOP ⇒ match op2 with [ NOP ⇒ P → P | _ ⇒ P ]
-  | NSA ⇒ match op2 with [ NSA ⇒ P → P | _ ⇒ P ]
-  | ORA ⇒ match op2 with [ ORA ⇒ P → P | _ ⇒ P ]
-  | PSHA ⇒ match op2 with [ PSHA ⇒ P → P | _ ⇒ P ]
-  | PSHH ⇒ match op2 with [ PSHH ⇒ P → P | _ ⇒ P ]
-  | PSHX ⇒ match op2 with [ PSHX ⇒ P → P | _ ⇒ P ]
-  | PULA ⇒ match op2 with [ PULA ⇒ P → P | _ ⇒ P ]
-  | PULH ⇒ match op2 with [ PULH ⇒ P → P | _ ⇒ P ]
-  | PULX ⇒ match op2 with [ PULX ⇒ P → P | _ ⇒ P ]
-  | ROL ⇒ match op2 with [ ROL ⇒ P → P | _ ⇒ P ]
-  | ROR ⇒ match op2 with [ ROR ⇒ P → P | _ ⇒ P ]
-  | RSP ⇒ match op2 with [ RSP ⇒ P → P | _ ⇒ P ]
-  | RTI ⇒ match op2 with [ RTI ⇒ P → P | _ ⇒ P ]
-  | RTS ⇒ match op2 with [ RTS ⇒ P → P | _ ⇒ P ]
-  | SBC ⇒ match op2 with [ SBC ⇒ P → P | _ ⇒ P ]
-  | SEC ⇒ match op2 with [ SEC ⇒ P → P | _ ⇒ P ]
-  | SEI ⇒ match op2 with [ SEI ⇒ P → P | _ ⇒ P ]
-  | SHA ⇒ match op2 with [ SHA ⇒ P → P | _ ⇒ P ]
-  | SLA ⇒ match op2 with [ SLA ⇒ P → P | _ ⇒ P ]
-  | STA ⇒ match op2 with [ STA ⇒ P → P | _ ⇒ P ]
-  | STHX ⇒ match op2 with [ STHX ⇒ P → P | _ ⇒ P ]
-  | STOP ⇒ match op2 with [ STOP ⇒ P → P | _ ⇒ P ]
-  | STX ⇒ match op2 with [ STX ⇒ P → P | _ ⇒ P ]
-  | SUB ⇒ match op2 with [ SUB ⇒ P → P | _ ⇒ P ]
-  | SWI ⇒ match op2 with [ SWI ⇒ P → P | _ ⇒ P ]
-  | TAP ⇒ match op2 with [ TAP ⇒ P → P | _ ⇒ P ]
-  | TAX ⇒ match op2 with [ TAX ⇒ P → P | _ ⇒ P ]
-  | TPA ⇒ match op2 with [ TPA ⇒ P → P | _ ⇒ P ]
-  | TST ⇒ match op2 with [ TST ⇒ P → P | _ ⇒ P ]
-  | TSX ⇒ match op2 with [ TSX ⇒ P → P | _ ⇒ P ]
-  | TXA ⇒ match op2 with [ TXA ⇒ P → P | _ ⇒ P ]
-  | TXS ⇒ match op2 with [ TXS ⇒ P → P | _ ⇒ P ]
-  | WAIT ⇒ match op2 with [ WAIT ⇒ P → P | _ ⇒ P ]
-  ].
+ 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 symmetric_eqop1 : ∀op2.eq_op ADC op2 = eq_op op2 ADC. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop2 : ∀op2.eq_op ADD op2 = eq_op op2 ADD. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop3 : ∀op2.eq_op AIS op2 = eq_op op2 AIS. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop4 : ∀op2.eq_op AIX op2 = eq_op op2 AIX. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop5 : ∀op2.eq_op AND op2 = eq_op op2 AND. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop6 : ∀op2.eq_op ASL op2 = eq_op op2 ASL. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop7 : ∀op2.eq_op ASR op2 = eq_op op2 ASR. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop8 : ∀op2.eq_op BCC op2 = eq_op op2 BCC. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop9 : ∀op2.eq_op BCLRn op2 = eq_op op2 BCLRn. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop10 : ∀op2.eq_op BCS op2 = eq_op op2 BCS. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop11 : ∀op2.eq_op BEQ op2 = eq_op op2 BEQ. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop12 : ∀op2.eq_op BGE op2 = eq_op op2 BGE. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop13 : ∀op2.eq_op BGND op2 = eq_op op2 BGND. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop14 : ∀op2.eq_op BGT op2 = eq_op op2 BGT. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop15 : ∀op2.eq_op BHCC op2 = eq_op op2 BHCC. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop16 : ∀op2.eq_op BHCS op2 = eq_op op2 BHCS. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop17 : ∀op2.eq_op BHI op2 = eq_op op2 BHI. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop18 : ∀op2.eq_op BIH op2 = eq_op op2 BIH. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop19 : ∀op2.eq_op BIL op2 = eq_op op2 BIL. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop20 : ∀op2.eq_op BIT op2 = eq_op op2 BIT. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop21 : ∀op2.eq_op BLE op2 = eq_op op2 BLE. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop22 : ∀op2.eq_op BLS op2 = eq_op op2 BLS. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop23 : ∀op2.eq_op BLT op2 = eq_op op2 BLT. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop24 : ∀op2.eq_op BMC op2 = eq_op op2 BMC. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop25 : ∀op2.eq_op BMI op2 = eq_op op2 BMI. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop26 : ∀op2.eq_op BMS op2 = eq_op op2 BMS. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop27 : ∀op2.eq_op BNE op2 = eq_op op2 BNE. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop28 : ∀op2.eq_op BPL op2 = eq_op op2 BPL. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop29 : ∀op2.eq_op BRA op2 = eq_op op2 BRA. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop30 : ∀op2.eq_op BRCLRn op2 = eq_op op2 BRCLRn. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop31 : ∀op2.eq_op BRN op2 = eq_op op2 BRN. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop32 : ∀op2.eq_op BRSETn op2 = eq_op op2 BRSETn. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop33 : ∀op2.eq_op BSETn op2 = eq_op op2 BSETn. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop34 : ∀op2.eq_op BSR op2 = eq_op op2 BSR. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop35 : ∀op2.eq_op CBEQA op2 = eq_op op2 CBEQA. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop36 : ∀op2.eq_op CBEQX op2 = eq_op op2 CBEQX. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop37 : ∀op2.eq_op CLC op2 = eq_op op2 CLC. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop38 : ∀op2.eq_op CLI op2 = eq_op op2 CLI. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop39 : ∀op2.eq_op CLR op2 = eq_op op2 CLR. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop40 : ∀op2.eq_op CMP op2 = eq_op op2 CMP. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop41 : ∀op2.eq_op COM op2 = eq_op op2 COM. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop42 : ∀op2.eq_op CPHX op2 = eq_op op2 CPHX. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop43 : ∀op2.eq_op CPX op2 = eq_op op2 CPX. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop44 : ∀op2.eq_op DAA op2 = eq_op op2 DAA. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop45 : ∀op2.eq_op DBNZ op2 = eq_op op2 DBNZ. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop46 : ∀op2.eq_op DEC op2 = eq_op op2 DEC. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop47 : ∀op2.eq_op DIV op2 = eq_op op2 DIV. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop48 : ∀op2.eq_op EOR op2 = eq_op op2 EOR. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop49 : ∀op2.eq_op INC op2 = eq_op op2 INC. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop50 : ∀op2.eq_op JMP op2 = eq_op op2 JMP. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop51 : ∀op2.eq_op JSR op2 = eq_op op2 JSR. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop52 : ∀op2.eq_op LDA op2 = eq_op op2 LDA. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop53 : ∀op2.eq_op LDHX op2 = eq_op op2 LDHX. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop54 : ∀op2.eq_op LDX op2 = eq_op op2 LDX. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop55 : ∀op2.eq_op LSR op2 = eq_op op2 LSR. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop56 : ∀op2.eq_op MOV op2 = eq_op op2 MOV. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop57 : ∀op2.eq_op MUL op2 = eq_op op2 MUL. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop58 : ∀op2.eq_op NEG op2 = eq_op op2 NEG. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop59 : ∀op2.eq_op NOP op2 = eq_op op2 NOP. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop60 : ∀op2.eq_op NSA op2 = eq_op op2 NSA. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop61 : ∀op2.eq_op ORA op2 = eq_op op2 ORA. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop62 : ∀op2.eq_op PSHA op2 = eq_op op2 PSHA. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop63 : ∀op2.eq_op PSHH op2 = eq_op op2 PSHH. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop64 : ∀op2.eq_op PSHX op2 = eq_op op2 PSHX. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop65 : ∀op2.eq_op PULA op2 = eq_op op2 PULA. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop66 : ∀op2.eq_op PULH op2 = eq_op op2 PULH. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop67 : ∀op2.eq_op PULX op2 = eq_op op2 PULX. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop68 : ∀op2.eq_op ROL op2 = eq_op op2 ROL. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop69 : ∀op2.eq_op ROR op2 = eq_op op2 ROR. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop70 : ∀op2.eq_op RSP op2 = eq_op op2 RSP. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop71 : ∀op2.eq_op RTI op2 = eq_op op2 RTI. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop72 : ∀op2.eq_op RTS op2 = eq_op op2 RTS. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop73 : ∀op2.eq_op SBC op2 = eq_op op2 SBC. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop74 : ∀op2.eq_op SEC op2 = eq_op op2 SEC. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop75 : ∀op2.eq_op SEI op2 = eq_op op2 SEI. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop76 : ∀op2.eq_op SHA op2 = eq_op op2 SHA. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop77 : ∀op2.eq_op SLA op2 = eq_op op2 SLA. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop78 : ∀op2.eq_op STA op2 = eq_op op2 STA. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop79 : ∀op2.eq_op STHX op2 = eq_op op2 STHX. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop80 : ∀op2.eq_op STOP op2 = eq_op op2 STOP. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop81 : ∀op2.eq_op STX op2 = eq_op op2 STX. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop82 : ∀op2.eq_op SUB op2 = eq_op op2 SUB. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop83 : ∀op2.eq_op SWI op2 = eq_op op2 SWI. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop84 : ∀op2.eq_op TAP op2 = eq_op op2 TAP. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop85 : ∀op2.eq_op TAX op2 = eq_op op2 TAX. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop86 : ∀op2.eq_op TPA op2 = eq_op op2 TPA. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop87 : ∀op2.eq_op TST op2 = eq_op op2 TST. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop88 : ∀op2.eq_op TSX op2 = eq_op op2 TSX. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop89 : ∀op2.eq_op TXA op2 = eq_op op2 TXA. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop90 : ∀op2.eq_op TXS op2 = eq_op op2 TXS. #op2; nnormalize; napply refl_eq.nqed.
+nlemma symmetric_eqop91 : ∀op2.eq_op WAIT op2 = eq_op op2 WAIT. #op2; nnormalize; napply refl_eq.nqed.
+
+nlemma symmetric_eqop : symmetricT opcode bool eq_op.
+ #op1; ncases op1;
+ ##[ ##1: napply symmetric_eqop1 ##| ##2: napply symmetric_eqop2 ##| ##3: napply symmetric_eqop3 ##| ##4: napply symmetric_eqop4
+ ##| ##5: napply symmetric_eqop5 ##| ##6: napply symmetric_eqop6 ##| ##7: napply symmetric_eqop7 ##| ##8: napply symmetric_eqop8
+ ##| ##9: napply symmetric_eqop9 ##| ##10: napply symmetric_eqop10 ##| ##11: napply symmetric_eqop11 ##| ##12: napply symmetric_eqop12
+ ##| ##13: napply symmetric_eqop13 ##| ##14: napply symmetric_eqop14 ##| ##15: napply symmetric_eqop15 ##| ##16: napply symmetric_eqop16
+ ##| ##17: napply symmetric_eqop17 ##| ##18: napply symmetric_eqop18 ##| ##19: napply symmetric_eqop19 ##| ##20: napply symmetric_eqop20
+ ##| ##21: napply symmetric_eqop21 ##| ##22: napply symmetric_eqop22 ##| ##23: napply symmetric_eqop23 ##| ##24: napply symmetric_eqop24
+ ##| ##25: napply symmetric_eqop25 ##| ##26: napply symmetric_eqop26 ##| ##27: napply symmetric_eqop27 ##| ##28: napply symmetric_eqop28
+ ##| ##29: napply symmetric_eqop29 ##| ##30: napply symmetric_eqop30 ##| ##31: napply symmetric_eqop31 ##| ##32: napply symmetric_eqop32
+ ##| ##33: napply symmetric_eqop33 ##| ##34: napply symmetric_eqop34 ##| ##35: napply symmetric_eqop35 ##| ##36: napply symmetric_eqop36
+ ##| ##37: napply symmetric_eqop37 ##| ##38: napply symmetric_eqop38 ##| ##39: napply symmetric_eqop39 ##| ##40: napply symmetric_eqop40
+ ##| ##41: napply symmetric_eqop41 ##| ##42: napply symmetric_eqop42 ##| ##43: napply symmetric_eqop43 ##| ##44: napply symmetric_eqop44
+ ##| ##45: napply symmetric_eqop45 ##| ##46: napply symmetric_eqop46 ##| ##47: napply symmetric_eqop47 ##| ##48: napply symmetric_eqop48
+ ##| ##49: napply symmetric_eqop49 ##| ##50: napply symmetric_eqop50 ##| ##51: napply symmetric_eqop51 ##| ##52: napply symmetric_eqop52
+ ##| ##53: napply symmetric_eqop53 ##| ##54: napply symmetric_eqop54 ##| ##55: napply symmetric_eqop55 ##| ##56: napply symmetric_eqop56
+ ##| ##57: napply symmetric_eqop57 ##| ##58: napply symmetric_eqop58 ##| ##59: napply symmetric_eqop59 ##| ##60: napply symmetric_eqop60
+ ##| ##61: napply symmetric_eqop61 ##| ##62: napply symmetric_eqop62 ##| ##63: napply symmetric_eqop63 ##| ##64: napply symmetric_eqop64
+ ##| ##65: napply symmetric_eqop65 ##| ##66: napply symmetric_eqop66 ##| ##67: napply symmetric_eqop67 ##| ##68: napply symmetric_eqop68
+ ##| ##69: napply symmetric_eqop69 ##| ##70: napply symmetric_eqop70 ##| ##71: napply symmetric_eqop71 ##| ##72: napply symmetric_eqop72
+ ##| ##73: napply symmetric_eqop73 ##| ##74: napply symmetric_eqop74 ##| ##75: napply symmetric_eqop75 ##| ##76: napply symmetric_eqop76
+ ##| ##77: napply symmetric_eqop77 ##| ##78: napply symmetric_eqop78 ##| ##79: napply symmetric_eqop79 ##| ##80: napply symmetric_eqop80
+ ##| ##81: napply symmetric_eqop81 ##| ##82: napply symmetric_eqop82 ##| ##83: napply symmetric_eqop83 ##| ##84: napply symmetric_eqop84
+ ##| ##85: napply symmetric_eqop85 ##| ##86: napply symmetric_eqop86 ##| ##87: napply symmetric_eqop87 ##| ##88: napply symmetric_eqop88
+ ##| ##89: napply symmetric_eqop89 ##| ##90: napply symmetric_eqop90 ##| ##91: napply symmetric_eqop91 ##]
+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 eq_to_eqop1 : ∀op2.ADC = op2 → eq_op ADC op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##1: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop2 : ∀op2.ADD = op2 → eq_op ADD op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##2: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop3 : ∀op2.AIS = op2 → eq_op AIS op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##3: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop4 : ∀op2.AIX = op2 → eq_op AIX op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##4: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop5 : ∀op2.AND = op2 → eq_op AND op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##5: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop6 : ∀op2.ASL = op2 → eq_op ASL op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##6: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop7 : ∀op2.ASR = op2 → eq_op ASR op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##7: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop8 : ∀op2.BCC = op2 → eq_op BCC op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##8: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop9 : ∀op2.BCLRn = op2 → eq_op BCLRn op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##9: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop10 : ∀op2.BCS = op2 → eq_op BCS op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##10: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop11 : ∀op2.BEQ = op2 → eq_op BEQ op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##11: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop12 : ∀op2.BGE = op2 → eq_op BGE op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##12: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop13 : ∀op2.BGND = op2 → eq_op BGND op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##13: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop14 : ∀op2.BGT = op2 → eq_op BGT op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##14: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop15 : ∀op2.BHCC = op2 → eq_op BHCC op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##15: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop16 : ∀op2.BHCS = op2 → eq_op BHCS op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##16: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop17 : ∀op2.BHI = op2 → eq_op BHI op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##17: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop18 : ∀op2.BIH = op2 → eq_op BIH op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##18: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop19 : ∀op2.BIL = op2 → eq_op BIL op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##19: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop20 : ∀op2.BIT = op2 → eq_op BIT op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##20: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop21 : ∀op2.BLE = op2 → eq_op BLE op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##21: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop22 : ∀op2.BLS = op2 → eq_op BLS op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##22: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop23 : ∀op2.BLT = op2 → eq_op BLT op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##23: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop24 : ∀op2.BMC = op2 → eq_op BMC op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##24: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop25 : ∀op2.BMI = op2 → eq_op BMI op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##25: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop26 : ∀op2.BMS = op2 → eq_op BMS op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##26: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop27 : ∀op2.BNE = op2 → eq_op BNE op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##27: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop28 : ∀op2.BPL = op2 → eq_op BPL op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##28: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop29 : ∀op2.BRA = op2 → eq_op BRA op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##29: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop30 : ∀op2.BRCLRn = op2 → eq_op BRCLRn op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##30: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop31 : ∀op2.BRN = op2 → eq_op BRN op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##31: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop32 : ∀op2.BRSETn = op2 → eq_op BRSETn op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##32: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop33 : ∀op2.BSETn = op2 → eq_op BSETn op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##33: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop34 : ∀op2.BSR = op2 → eq_op BSR op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##34: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop35 : ∀op2.CBEQA = op2 → eq_op CBEQA op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##35: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop36 : ∀op2.CBEQX = op2 → eq_op CBEQX op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##36: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop37 : ∀op2.CLC = op2 → eq_op CLC op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##37: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop38 : ∀op2.CLI = op2 → eq_op CLI op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##38: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop39 : ∀op2.CLR = op2 → eq_op CLR op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##39: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop40 : ∀op2.CMP = op2 → eq_op CMP op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##40: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop41 : ∀op2.COM = op2 → eq_op COM op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##41: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop42 : ∀op2.CPHX = op2 → eq_op CPHX op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##42: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop43 : ∀op2.CPX = op2 → eq_op CPX op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##43: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop44 : ∀op2.DAA = op2 → eq_op DAA op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##44: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop45 : ∀op2.DBNZ = op2 → eq_op DBNZ op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##45: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop46 : ∀op2.DEC = op2 → eq_op DEC op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##46: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop47 : ∀op2.DIV = op2 → eq_op DIV op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##47: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop48 : ∀op2.EOR = op2 → eq_op EOR op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##48: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop49 : ∀op2.INC = op2 → eq_op INC op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##49: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop50 : ∀op2.JMP = op2 → eq_op JMP op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##50: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop51 : ∀op2.JSR = op2 → eq_op JSR op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##51: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop52 : ∀op2.LDA = op2 → eq_op LDA op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##52: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop53 : ∀op2.LDHX = op2 → eq_op LDHX op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##53: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop54 : ∀op2.LDX = op2 → eq_op LDX op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##54: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop55 : ∀op2.LSR = op2 → eq_op LSR op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##55: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop56 : ∀op2.MOV = op2 → eq_op MOV op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##56: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop57 : ∀op2.MUL = op2 → eq_op MUL op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##57: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop58 : ∀op2.NEG = op2 → eq_op NEG op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##58: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop59 : ∀op2.NOP = op2 → eq_op NOP op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##59: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop60 : ∀op2.NSA = op2 → eq_op NSA op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##60: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop61 : ∀op2.ORA = op2 → eq_op ORA op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##61: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop62 : ∀op2.PSHA = op2 → eq_op PSHA op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##62: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop63 : ∀op2.PSHH = op2 → eq_op PSHH op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##63: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop64 : ∀op2.PSHX = op2 → eq_op PSHX op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##64: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop65 : ∀op2.PULA = op2 → eq_op PULA op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##65: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop66 : ∀op2.PULH = op2 → eq_op PULH op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##66: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop67 : ∀op2.PULX = op2 → eq_op PULX op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##67: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop68 : ∀op2.ROL = op2 → eq_op ROL op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##68: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop69 : ∀op2.ROR = op2 → eq_op ROR op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##69: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop70 : ∀op2.RSP = op2 → eq_op RSP op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##70: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop71 : ∀op2.RTI = op2 → eq_op RTI op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##71: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop72 : ∀op2.RTS = op2 → eq_op RTS op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##72: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop73 : ∀op2.SBC = op2 → eq_op SBC op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##73: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop74 : ∀op2.SEC = op2 → eq_op SEC op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##74: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop75 : ∀op2.SEI = op2 → eq_op SEI op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##75: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop76 : ∀op2.SHA = op2 → eq_op SHA op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##76: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop77 : ∀op2.SLA = op2 → eq_op SLA op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##77: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop78 : ∀op2.STA = op2 → eq_op STA op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##78: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop79 : ∀op2.STHX = op2 → eq_op STHX op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##79: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop80 : ∀op2.STOP = op2 → eq_op STOP op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##80: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop81 : ∀op2.STX = op2 → eq_op STX op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##81: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop82 : ∀op2.SUB = op2 → eq_op SUB op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##82: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop83 : ∀op2.SWI = op2 → eq_op SWI op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##83: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop84 : ∀op2.TAP = op2 → eq_op TAP op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##84: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop85 : ∀op2.TAX = op2 → eq_op TAX op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##85: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop86 : ∀op2.TPA = op2 → eq_op TPA op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##86: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop87 : ∀op2.TST = op2 → eq_op TST op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##87: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop88 : ∀op2.TSX = op2 → eq_op TSX op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##88: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop89 : ∀op2.TXA = op2 → eq_op TXA op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##89: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop90 : ∀op2.TXS = op2 → eq_op TXS op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##90: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+nlemma eq_to_eqop91 : ∀op2.WAIT = op2 → eq_op WAIT op2 = true. #op2; ncases op2; nnormalize; #H; ##[ ##91: napply refl_eq ##| ##*: napply (opcode_destruct … (false = true) H) ##]nqed.
+
+nlemma eq_to_eqop : ∀op1,op2.op1 = op2 → eq_op op1 op2 = true.
  #op1; ncases op1;
- ##[ ##1: napply opcode_destruct1 ##| ##2: napply opcode_destruct2 ##| ##3: napply opcode_destruct3 ##| ##4: napply opcode_destruct4
- ##| ##5: napply opcode_destruct5 ##| ##6: napply opcode_destruct6 ##| ##7: napply opcode_destruct7 ##| ##8: napply opcode_destruct8
- ##| ##9: napply opcode_destruct9 ##| ##10: napply opcode_destruct10 ##| ##11: napply opcode_destruct11 ##| ##12: napply opcode_destruct12
- ##| ##13: napply opcode_destruct13 ##| ##14: napply opcode_destruct14 ##| ##15: napply opcode_destruct15 ##| ##16: napply opcode_destruct16
- ##| ##17: napply opcode_destruct17 ##| ##18: napply opcode_destruct18 ##| ##19: napply opcode_destruct19 ##| ##20: napply opcode_destruct20
- ##| ##21: napply opcode_destruct21 ##| ##22: napply opcode_destruct22 ##| ##23: napply opcode_destruct23 ##| ##24: napply opcode_destruct24
- ##| ##25: napply opcode_destruct25 ##| ##26: napply opcode_destruct26 ##| ##27: napply opcode_destruct27 ##| ##28: napply opcode_destruct28
- ##| ##29: napply opcode_destruct29 ##| ##30: napply opcode_destruct30 ##| ##31: napply opcode_destruct31 ##| ##32: napply opcode_destruct32
- ##| ##33: napply opcode_destruct33 ##| ##34: napply opcode_destruct34 ##| ##35: napply opcode_destruct35 ##| ##36: napply opcode_destruct36
- ##| ##37: napply opcode_destruct37 ##| ##38: napply opcode_destruct38 ##| ##39: napply opcode_destruct39 ##| ##40: napply opcode_destruct40
- ##| ##41: napply opcode_destruct41 ##| ##42: napply opcode_destruct42 ##| ##43: napply opcode_destruct43 ##| ##44: napply opcode_destruct44
- ##| ##45: napply opcode_destruct45 ##| ##46: napply opcode_destruct46 ##| ##47: napply opcode_destruct47 ##| ##48: napply opcode_destruct48
- ##| ##49: napply opcode_destruct49 ##| ##50: napply opcode_destruct50 ##| ##51: napply opcode_destruct51 ##| ##52: napply opcode_destruct52
- ##| ##53: napply opcode_destruct53 ##| ##54: napply opcode_destruct54 ##| ##55: napply opcode_destruct55 ##| ##56: napply opcode_destruct56
- ##| ##57: napply opcode_destruct57 ##| ##58: napply opcode_destruct58 ##| ##59: napply opcode_destruct59 ##| ##60: napply opcode_destruct60
- ##| ##61: napply opcode_destruct61 ##| ##62: napply opcode_destruct62 ##| ##63: napply opcode_destruct63 ##| ##64: napply opcode_destruct64
- ##| ##65: napply opcode_destruct65 ##| ##66: napply opcode_destruct66 ##| ##67: napply opcode_destruct67 ##| ##68: napply opcode_destruct68
- ##| ##69: napply opcode_destruct69 ##| ##70: napply opcode_destruct70 ##| ##71: napply opcode_destruct71 ##| ##72: napply opcode_destruct72
- ##| ##73: napply opcode_destruct73 ##| ##74: napply opcode_destruct74 ##| ##75: napply opcode_destruct75 ##| ##76: napply opcode_destruct76
- ##| ##77: napply opcode_destruct77 ##| ##78: napply opcode_destruct78 ##| ##79: napply opcode_destruct79 ##| ##80: napply opcode_destruct80
- ##| ##81: napply opcode_destruct81 ##| ##82: napply opcode_destruct82 ##| ##83: napply opcode_destruct83 ##| ##84: napply opcode_destruct84
- ##| ##85: napply opcode_destruct85 ##| ##86: napply opcode_destruct86 ##| ##87: napply opcode_destruct87 ##| ##88: napply opcode_destruct88
- ##| ##89: napply opcode_destruct89 ##| ##90: napply opcode_destruct90 ##| ##91: napply opcode_destruct91 ##]
+ ##[ ##1: napply eq_to_eqop1 ##| ##2: napply eq_to_eqop2 ##| ##3: napply eq_to_eqop3 ##| ##4: napply eq_to_eqop4
+ ##| ##5: napply eq_to_eqop5 ##| ##6: napply eq_to_eqop6 ##| ##7: napply eq_to_eqop7 ##| ##8: napply eq_to_eqop8
+ ##| ##9: napply eq_to_eqop9 ##| ##10: napply eq_to_eqop10 ##| ##11: napply eq_to_eqop11 ##| ##12: napply eq_to_eqop12
+ ##| ##13: napply eq_to_eqop13 ##| ##14: napply eq_to_eqop14 ##| ##15: napply eq_to_eqop15 ##| ##16: napply eq_to_eqop16
+ ##| ##17: napply eq_to_eqop17 ##| ##18: napply eq_to_eqop18 ##| ##19: napply eq_to_eqop19 ##| ##20: napply eq_to_eqop20
+ ##| ##21: napply eq_to_eqop21 ##| ##22: napply eq_to_eqop22 ##| ##23: napply eq_to_eqop23 ##| ##24: napply eq_to_eqop24
+ ##| ##25: napply eq_to_eqop25 ##| ##26: napply eq_to_eqop26 ##| ##27: napply eq_to_eqop27 ##| ##28: napply eq_to_eqop28
+ ##| ##29: napply eq_to_eqop29 ##| ##30: napply eq_to_eqop30 ##| ##31: napply eq_to_eqop31 ##| ##32: napply eq_to_eqop32
+ ##| ##33: napply eq_to_eqop33 ##| ##34: napply eq_to_eqop34 ##| ##35: napply eq_to_eqop35 ##| ##36: napply eq_to_eqop36
+ ##| ##37: napply eq_to_eqop37 ##| ##38: napply eq_to_eqop38 ##| ##39: napply eq_to_eqop39 ##| ##40: napply eq_to_eqop40
+ ##| ##41: napply eq_to_eqop41 ##| ##42: napply eq_to_eqop42 ##| ##43: napply eq_to_eqop43 ##| ##44: napply eq_to_eqop44
+ ##| ##45: napply eq_to_eqop45 ##| ##46: napply eq_to_eqop46 ##| ##47: napply eq_to_eqop47 ##| ##48: napply eq_to_eqop48
+ ##| ##49: napply eq_to_eqop49 ##| ##50: napply eq_to_eqop50 ##| ##51: napply eq_to_eqop51 ##| ##52: napply eq_to_eqop52
+ ##| ##53: napply eq_to_eqop53 ##| ##54: napply eq_to_eqop54 ##| ##55: napply eq_to_eqop55 ##| ##56: napply eq_to_eqop56
+ ##| ##57: napply eq_to_eqop57 ##| ##58: napply eq_to_eqop58 ##| ##59: napply eq_to_eqop59 ##| ##60: napply eq_to_eqop60
+ ##| ##61: napply eq_to_eqop61 ##| ##62: napply eq_to_eqop62 ##| ##63: napply eq_to_eqop63 ##| ##64: napply eq_to_eqop64
+ ##| ##65: napply eq_to_eqop65 ##| ##66: napply eq_to_eqop66 ##| ##67: napply eq_to_eqop67 ##| ##68: napply eq_to_eqop68
+ ##| ##69: napply eq_to_eqop69 ##| ##70: napply eq_to_eqop70 ##| ##71: napply eq_to_eqop71 ##| ##72: napply eq_to_eqop72
+ ##| ##73: napply eq_to_eqop73 ##| ##74: napply eq_to_eqop74 ##| ##75: napply eq_to_eqop75 ##| ##76: napply eq_to_eqop76
+ ##| ##77: napply eq_to_eqop77 ##| ##78: napply eq_to_eqop78 ##| ##79: napply eq_to_eqop79 ##| ##80: napply eq_to_eqop80
+ ##| ##81: napply eq_to_eqop81 ##| ##82: napply eq_to_eqop82 ##| ##83: napply eq_to_eqop83 ##| ##84: napply eq_to_eqop84
+ ##| ##85: napply eq_to_eqop85 ##| ##86: napply eq_to_eqop86 ##| ##87: napply eq_to_eqop87 ##| ##88: napply eq_to_eqop88
+ ##| ##89: napply eq_to_eqop89 ##| ##90: napply eq_to_eqop90 ##| ##91: napply eq_to_eqop91 ##]
 nqed.