X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_assembly%2Ffreescale%2Faux_bases_lemmas.ma;h=55ef3df2367d79e1a56441ff9899ea087eec39be;hb=c3fc204cc02f1031b5d17fb0f2be1fc01e5c452f;hp=c85df6e61b4d27528e74dae147e4b6532044a418;hpb=3e5c359c75874748cfed8a9046031b62396e0e6d;p=helm.git diff --git a/helm/software/matita/contribs/ng_assembly/freescale/aux_bases_lemmas.ma b/helm/software/matita/contribs/ng_assembly/freescale/aux_bases_lemmas.ma index c85df6e61..55ef3df23 100755 --- a/helm/software/matita/contribs/ng_assembly/freescale/aux_bases_lemmas.ma +++ b/helm/software/matita/contribs/ng_assembly/freescale/aux_bases_lemmas.ma @@ -104,25 +104,23 @@ nlemma symmetric_eqoct : symmetricT oct bool eq_oct. napply (refl_eq ??). nqed. -nlemma eqoct_to_eq : ∀o1,o2.eq_oct o1 o2 = true → o1 = o2. - #n1; #n2; #H; - nletin K ≝ (bool_destruct ?? (n1 = n2) H); - nelim n1 in K:(%) ⊢ %; - nelim n2; +nlemma eqoct_to_eq : ∀n1,n2.eq_oct n1 n2 = true → n1 = n2. + #n1; #n2; + ncases n1; + ncases n2; nnormalize; ##[ ##1,10,19,28,37,46,55,64: #H; napply (refl_eq ??) - ##| ##*: #H; napply H + ##| ##*: #H; napply (bool_destruct ??? H) ##] nqed. nlemma eq_to_eqoct : ∀n1,n2.n1 = n2 → eq_oct n1 n2 = true. - #n1; #n2; #H; - nletin K ≝ (oct_destruct ?? (eq_oct n1 n2 = true) H); - nelim n1 in K:(%) ⊢ %; - nelim n2; + #n1; #n2; + ncases n1; + ncases n2; nnormalize; ##[ ##1,10,19,28,37,46,55,64: #H; napply (refl_eq ??) - ##| ##*: #H; napply H + ##| ##*: #H; napply (oct_destruct ??? H) ##] nqed. @@ -402,271 +400,269 @@ nlemma symmetric_eqbitrig : symmetricT bitrigesim bool eq_bitrig. nqed. nlemma eqbitrig_to_eq : ∀t1,t2.eq_bitrig t1 t2 = true → t1 = t2. - #t1; #t2; #H; - nletin K ≝ (bool_destruct ?? (t1 = t2) H); - nelim t1 in K:(%) ⊢ %; - ##[ ##1: nelim t2; nnormalize; #H; + #t1; #t2; + ncases t1; + ##[ ##1: ncases t2; nnormalize; #H; ##[ ##1: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##2: nelim t2; nnormalize; #H; + ##| ##2: ncases t2; nnormalize; #H; ##[ ##2: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##3: nelim t2; nnormalize; #H; + ##| ##3: ncases t2; nnormalize; #H; ##[ ##3: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##4: nelim t2; nnormalize; #H; + ##| ##4: ncases t2; nnormalize; #H; ##[ ##4: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##5: nelim t2; nnormalize; #H; + ##| ##5: ncases t2; nnormalize; #H; ##[ ##5: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##6: nelim t2; nnormalize; #H; + ##| ##6: ncases t2; nnormalize; #H; ##[ ##6: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*:napply (bool_destruct ??? H) ##] - ##| ##7: nelim t2; nnormalize; #H; + ##| ##7: ncases t2; nnormalize; #H; ##[ ##7: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##8: nelim t2; nnormalize; #H; + ##| ##8: ncases t2; nnormalize; #H; ##[ ##8: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##9: nelim t2; nnormalize; #H; + ##| ##9: ncases t2; nnormalize; #H; ##[ ##9: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##10: nelim t2; nnormalize; #H; + ##| ##10: ncases t2; nnormalize; #H; ##[ ##10: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##11: nelim t2; nnormalize; #H; + ##| ##11: ncases t2; nnormalize; #H; ##[ ##11: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##12: nelim t2; nnormalize; #H; + ##| ##12: ncases t2; nnormalize; #H; ##[ ##12: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##13: nelim t2; nnormalize; #H; + ##| ##13: ncases t2; nnormalize; #H; ##[ ##13: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##14: nelim t2; nnormalize; #H; + ##| ##14: ncases t2; nnormalize; #H; ##[ ##14: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##15: nelim t2; nnormalize; #H; + ##| ##15: ncases t2; nnormalize; #H; ##[ ##15: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##16: nelim t2; nnormalize; #H; + ##| ##16: ncases t2; nnormalize; #H; ##[ ##16: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##17: nelim t2; nnormalize; #H; + ##| ##17: ncases t2; nnormalize; #H; ##[ ##17: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##18: nelim t2; nnormalize; #H; + ##| ##18: ncases t2; nnormalize; #H; ##[ ##18: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##19: nelim t2; nnormalize; #H; + ##| ##19: ncases t2; nnormalize; #H; ##[ ##19: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##20: nelim t2; nnormalize; #H; + ##| ##20: ncases t2; nnormalize; #H; ##[ ##20: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##21: nelim t2; nnormalize; #H; + ##| ##21: ncases t2; nnormalize; #H; ##[ ##21: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##22: nelim t2; nnormalize; #H; + ##| ##22: ncases t2; nnormalize; #H; ##[ ##22: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##23: nelim t2; nnormalize; #H; + ##| ##23: ncases t2; nnormalize; #H; ##[ ##23: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##24: nelim t2; nnormalize; #H; + ##| ##24: ncases t2; nnormalize; #H; ##[ ##24: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##25: nelim t2; nnormalize; #H; + ##| ##25: ncases t2; nnormalize; #H; ##[ ##25: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##26: nelim t2; nnormalize; #H; + ##| ##26: ncases t2; nnormalize; #H; ##[ ##26: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##27: nelim t2; nnormalize; #H; + ##| ##27: ncases t2; nnormalize; #H; ##[ ##27: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##28: nelim t2; nnormalize; #H; + ##| ##28: ncases t2; nnormalize; #H; ##[ ##28: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##29: nelim t2; nnormalize; #H; + ##| ##29: ncases t2; nnormalize; #H; ##[ ##29: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##30: nelim t2; nnormalize; #H; + ##| ##30: ncases t2; nnormalize; #H; ##[ ##30: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##31: nelim t2; nnormalize; #H; + ##| ##31: ncases t2; nnormalize; #H; ##[ ##31: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] - ##| ##32: nelim t2; nnormalize; #H; + ##| ##32: ncases t2; nnormalize; #H; ##[ ##32: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bool_destruct ??? H) ##] ##] nqed. nlemma eq_to_eqbitrig : ∀t1,t2.t1 = t2 → eq_bitrig t1 t2 = true. - #t1; #t2; #H; - nletin K ≝ (bitrigesim_destruct ?? (eq_bitrig t1 t2 = true) H); - nelim t1 in K:(%) ⊢ %; - ##[ ##1: nelim t2; nnormalize; #H; + #t1; #t2; + ncases t1; + ##[ ##1: ncases t2; nnormalize; #H; ##[ ##1: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##2: nelim t2; nnormalize; #H; + ##| ##2: ncases t2; nnormalize; #H; ##[ ##2: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##3: nelim t2; nnormalize; #H; + ##| ##3: ncases t2; nnormalize; #H; ##[ ##3: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##4: nelim t2; nnormalize; #H; + ##| ##4: ncases t2; nnormalize; #H; ##[ ##4: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##5: nelim t2; nnormalize; #H; + ##| ##5: ncases t2; nnormalize; #H; ##[ ##5: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##6: nelim t2; nnormalize; #H; + ##| ##6: ncases t2; nnormalize; #H; ##[ ##6: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##7: nelim t2; nnormalize; #H; + ##| ##7: ncases t2; nnormalize; #H; ##[ ##7: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##8: nelim t2; nnormalize; #H; + ##| ##8: ncases t2; nnormalize; #H; ##[ ##8: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##9: nelim t2; nnormalize; #H; + ##| ##9: ncases t2; nnormalize; #H; ##[ ##9: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##10: nelim t2; nnormalize; #H; + ##| ##10: ncases t2; nnormalize; #H; ##[ ##10: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##11: nelim t2; nnormalize; #H; + ##| ##11: ncases t2; nnormalize; #H; ##[ ##11: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##12: nelim t2; nnormalize; #H; + ##| ##12: ncases t2; nnormalize; #H; ##[ ##12: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##13: nelim t2; nnormalize; #H; + ##| ##13: ncases t2; nnormalize; #H; ##[ ##13: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##14: nelim t2; nnormalize; #H; + ##| ##14: ncases t2; nnormalize; #H; ##[ ##14: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##15: nelim t2; nnormalize; #H; + ##| ##15: ncases t2; nnormalize; #H; ##[ ##15: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##16: nelim t2; nnormalize; #H; + ##| ##16: ncases t2; nnormalize; #H; ##[ ##16: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##17: nelim t2; nnormalize; #H; + ##| ##17: ncases t2; nnormalize; #H; ##[ ##17: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##18: nelim t2; nnormalize; #H; + ##| ##18: ncases t2; nnormalize; #H; ##[ ##18: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##19: nelim t2; nnormalize; #H; + ##| ##19: ncases t2; nnormalize; #H; ##[ ##19: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##20: nelim t2; nnormalize; #H; + ##| ##20: ncases t2; nnormalize; #H; ##[ ##20: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##21: nelim t2; nnormalize; #H; + ##| ##21: ncases t2; nnormalize; #H; ##[ ##21: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##22: nelim t2; nnormalize; #H; + ##| ##22: ncases t2; nnormalize; #H; ##[ ##22: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##23: nelim t2; nnormalize; #H; + ##| ##23: ncases t2; nnormalize; #H; ##[ ##23: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##24: nelim t2; nnormalize; #H; + ##| ##24: ncases t2; nnormalize; #H; ##[ ##24: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##25: nelim t2; nnormalize; #H; + ##| ##25: ncases t2; nnormalize; #H; ##[ ##25: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##26: nelim t2; nnormalize; #H; + ##| ##26: ncases t2; nnormalize; #H; ##[ ##26: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##27: nelim t2; nnormalize; #H; + ##| ##27: ncases t2; nnormalize; #H; ##[ ##27: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##28: nelim t2; nnormalize; #H; + ##| ##28: ncases t2; nnormalize; #H; ##[ ##28: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##29: nelim t2; nnormalize; #H; + ##| ##29: ncases t2; nnormalize; #H; ##[ ##29: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##30: nelim t2; nnormalize; #H; + ##| ##30: ncases t2; nnormalize; #H; ##[ ##30: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##31: nelim t2; nnormalize; #H; + ##| ##31: ncases t2; nnormalize; #H; ##[ ##31: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] - ##| ##32: nelim t2; nnormalize; #H; + ##| ##32: ncases t2; nnormalize; #H; ##[ ##32: napply (refl_eq ??) - ##| ##*: napply H + ##| ##*: napply (bitrigesim_destruct ??? H) ##] ##] nqed.