nqed.
nlemma eqex_to_eq : ∀e1,e2:exadecim.(eq_ex e1 e2 = true) → (e1 = e2).
- #e1; #e2; #H;
- nletin K ≝ (bool_destruct ?? (e1 = e2) H);
- nelim e1 in K:(%) ⊢ %;
- nelim e2;
+ #e1; #e2;
+ ncases e1;
+ ncases e2;
nnormalize;
##[ ##1,18,35,52,69,86,103,120,137,154,171,188,205,222,239,256: #H; napply (refl_eq ??)
- ##| ##*: #H; napply H
+ ##| ##*: #H; napply (bool_destruct ??? H)
##]
nqed.
nlemma eq_to_eqex : ∀e1,e2.e1 = e2 → eq_ex e1 e2 = true.
- #e1; #e2; #H;
- nletin K ≝ (exadecim_destruct ?? (eq_ex e1 e2 = true) H);
- nelim e1 in K:(%) ⊢ %;
- nelim e2;
+ #m1; #m2;
+ ncases m1;
+ ncases m2;
nnormalize;
##[ ##1,18,35,52,69,86,103,120,137,154,171,188,205,222,239,256: #H; napply (refl_eq ??)
- ##| ##*: #H; napply H
+ ##| ##*: #H; napply (exadecim_destruct ??? H)
##]
nqed.