-intros 10.elim H2
- [apply SA_Top
- [rewrite > H5 in H3;
- apply (WFE_Typ_subst ? ? ? ? ? ? ? H3 (JS_to_WFT1 ? ? ? H))
- |rewrite > H5 in H4;apply (WFT_env_incl ? ? H4);apply incl_fv_env]
- |apply SA_Refl_TVar
- [rewrite > H5 in H3;apply (WFE_Typ_subst ? ? ? ? ? ? ? H3);
- apply (JS_to_WFT1 ? ? ? H)
- |rewrite > H5 in H4;rewrite < fv_env_extends;apply H4]
- |elim (decidable_eq_nat X n)
- [apply (SA_Trans_TVar ? ? ? P)
- [rewrite < H7;elim l1;simplify
- [constructor 1|constructor 2;assumption]
- |rewrite > append_cons;apply H1;
- lapply (WFE_bound_bound true n t1 U ? ? H3)
- [apply (JS_to_WFE ? ? ? H4)
- |rewrite < Hletin;rewrite < append_cons;apply (H5 ? H6)
- |rewrite < H7;rewrite > H6;elim l1;simplify
- [constructor 1|constructor 2;assumption]]]
- |apply (SA_Trans_TVar ? ? ? t1)
- [rewrite > H6 in H3;apply (lookup_env_extends ? ? ? ? ? ? ? ? ? ? H3);
- unfold;intro;apply H7;symmetry;assumption
- |apply (H5 ? H6)]]
- |apply (SA_Arrow ? ? ? ? ? (H4 ? H7) (H6 ? H7))
- |apply (SA_All ? ? ? ? ? (H4 ? H7));intros;
- apply (H6 ? ? (mk_bound true X1 t2::l1))
- [rewrite > H7;rewrite > fv_env_extends;apply H8
- |simplify;rewrite < H7;reflexivity]]
+intros 10.elim H2; destruct;
+ [letin x \def fv_env. letin y ≝incl. autobatch depth=4 size=8.
+ | autobatch depth=4 size=7;
+ | elim (decidable_eq_nat X n)
+ [apply (SA_Trans_TVar ? ? ? P); destruct;
+ [ autobatch
+ | lapply (WFE_bound_bound true X t1 U ? ? H3); autobatch]
+ | apply (SA_Trans_TVar ? ? ? t1); autobatch]
+ | autobatch
+ | apply SA_All;
+ [ autobatch
+ | intros; apply (H6 ? ? (mk_bound true X1 t2::l1)); autobatch]]