nnormalize;
#H;
##[ ##1,5,9: napply (λx:P.x)
- ##| ##2,3: napply (False_ind ??);
+ ##| ##2,3: napply (False_ind (λ_.?) ?);
nchange with (match AST_BASE_TYPE_BYTE8 with [ AST_BASE_TYPE_BYTE8 ⇒ False | _ ⇒ True]);
nrewrite > H;
nnormalize;
napply I
- ##| ##4,6: napply (False_ind ??);
+ ##| ##4,6: napply (False_ind (λ_.?) ?);
nchange with (match AST_BASE_TYPE_WORD16 with [ AST_BASE_TYPE_WORD16 ⇒ False | _ ⇒ True]);
nrewrite > H;
nnormalize;
napply I
- ##| ##7,8: napply (False_ind ??);
+ ##| ##7,8: napply (False_ind (λ_.?) ?);
nchange with (match AST_BASE_TYPE_WORD32 with [ AST_BASE_TYPE_WORD32 ⇒ False | _ ⇒ True]);
nrewrite > H;
nnormalize;
##| ##2: #t; #n; #b; nnormalize; #H
##| ##3: #l; #b; nnormalize; #H
##]
- napply (False_ind ??);
+ napply (False_ind (λ_.?) ?);
nchange with (match AST_TYPE_BASE b with [ AST_TYPE_BASE _ ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##2: ncases b2;
##| ##1: #b; #t; #n; nnormalize; #H
##| ##3: #l; #t; #n; nnormalize; #H
##]
- napply (False_ind ??);
+ napply (False_ind (λ_.?) ?);
nchange with (match AST_TYPE_ARRAY t n with [ AST_TYPE_ARRAY _ _ ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##| ##3: ncases b2;
##| ##1: #b; #l; nnormalize; #H
##| ##2: #t; #n; #l; nnormalize; #H
##]
- napply (False_ind ??);
+ napply (False_ind (λ_.?) ?);
nchange with (match AST_TYPE_STRUCT l with [ AST_TYPE_STRUCT _ ⇒ False | _ ⇒ True ]);
nrewrite > H; nnormalize; napply I
##]
nqed.
-(* eq_ast lemmas missing *)
+nlemma symmetric_eqasttype_aux1
+ : ∀nl1,nl2.
+ (eq_ast_type (AST_TYPE_STRUCT nl1) (AST_TYPE_STRUCT nl2)) = (eq_ast_type (AST_TYPE_STRUCT nl2) (AST_TYPE_STRUCT nl1)) →
+ (bfold_right_neList2 ? (λx,y.eq_ast_type x y) nl1 nl2) = (bfold_right_neList2 ? (λx,y.eq_ast_type x y) nl2 nl1).
+ #nl1; #nl2; #H;
+ napply H.
+nqed.
+
+nlemma symmetric_eqasttype : symmetricT ast_type bool eq_ast_type.
+ #t1; napply (ast_type_index ????? t1);
+ ##[ ##1: #b1; #t2; ncases t2;
+ ##[ ##1: #b2; nchange with ((eq_ast_base_type b1 b2) = (eq_ast_base_type b2 b1));
+ nrewrite > (symmetric_eqastbasetype b1 b2);
+ napply (refl_eq ??)
+ ##| ##2: #st2; #n2; nnormalize; napply (refl_eq ??)
+ ##| ##3: #nl2; nnormalize; napply (refl_eq ??)
+ ##]
+ ##| ##2: #st1; #n1; #H; #t2; ncases t2;
+ ##[ ##2: #st2; #n2; nchange with (((eq_ast_type st1 st2)⊗(eq_nat n1 n2)) = ((eq_ast_type st2 st1)⊗(eq_nat n2 n1)));
+ nrewrite > (symmetric_eqnat n1 n2);
+ nrewrite > (H st2);
+ napply (refl_eq ??)
+ ##| ##1: #b2; nnormalize; napply (refl_eq ??)
+ ##| ##3: #nl2; nnormalize; napply (refl_eq ??)
+ ##]
+ ##| ##3: #hh1; #H; #t2; ncases t2;
+ ##[ ##3: #nl2; ncases nl2;
+ ##[ ##1: #hh2; nchange with ((eq_ast_type hh1 hh2) = (eq_ast_type hh2 hh1));
+ nrewrite > (H hh2);
+ napply (refl_eq ??)
+ ##| ##2: #hh2; #ll2; nnormalize; napply (refl_eq ??)
+ ##]
+ ##| ##1: #b2; nnormalize; napply (refl_eq ??)
+ ##| ##2: #st2; #n2; nnormalize; napply (refl_eq ??)
+ ##]
+ ##| ##4: #hh1; #ll1; #H; #H1; #t2; ncases t2;
+ ##[ ##3: #nl2; ncases nl2;
+ ##[ ##1: #hh2; nnormalize; napply (refl_eq ??)
+ ##| ##2: #hh2; #ll2; nnormalize;
+ nrewrite > (H hh2);
+ nrewrite > (symmetric_eqasttype_aux1 ll1 ll2 (H1 (AST_TYPE_STRUCT ll2)));
+ napply (refl_eq ??)
+ ##]
+ ##| ##1: #b2; nnormalize; napply (refl_eq ??)
+ ##| ##2: #st2; #n2; nnormalize; napply (refl_eq ??)
+ ##]
+ ##]
+nqed.
+
+...
+
nlemma isbastbasetype_to_isastbasetype : ∀ast.isb_ast_base_type ast = true → is_ast_base_type ast.
#ast;