- ∀l.G=l@(mk_bound true X U::G1) → l@(mk_bound true X P::G1) ⊢ M ⊴ N.
-intros 10.elim H2
- [letin x \def fv_env. letin y ≝incl.
- (* autobatch depth=4 size=8 by SA_Top, WFE_Typ_subst, H3, JS_to_WFT1, H, H4, WFT_env_incl, incl_fv_env]*)
- apply SA_Top
- [autobatch by WFE_Typ_subst, H3, JS_to_WFT1, H.
- (*
- rewrite > H5 in H3;
- apply (WFE_Typ_subst ? ? ? ? ? ? ? H3 (JS_to_WFT1 ? ? ? H)) *)
- |autobatch by H4, WFT_env_incl, incl_fv_env]
- (* rewrite > H5 in H4;apply (WFT_env_incl ? ? H4);apply incl_fv_env] *)
- |autobatch depth=4 by SA_Refl_TVar, WFE_Typ_subst, H3, JS_to_WFT1, H, H4.
- (*
- apply SA_Refl_TVar;
- [autobatch by WFE_Typ_subst, H3, JS_to_WFT1, H.
- (*
- rewrite > H5 in H3;apply (WFE_Typ_subst ? ? ? ? ? ? ? H3);
- apply (JS_to_WFT1 ? ? ? H) *)
- |autobatch by H4. (* 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]
- |applyS H1.
- lapply (WFE_bound_bound true n t1 U ? ? H3);
- [autobatch. (* apply (JS_to_WFE ? ? ? H4) *)
- |autobatch. (* rewrite < Hletin;rewrite < append_cons;apply (H5 ? H6) *)
- |destruct.elim l1;autobatch.
- ]]
- |(* autobatch depth=4 size=7 by SA_Trans_TVar, lookup_env_extends, H3, sym_neq, H5, H6, H7. *)
- apply (SA_Trans_TVar ? ? ? t1);
- [autobatch by lookup_env_extends, H3, sym_neq, H7.
- (* rewrite > H6 in H3; apply (lookup_env_extends ? ? ? ? ? ? ? ? ? ? H3);
- unfold;intro;apply H7;symmetry;assumption *)
- |apply (H5 ? H6)]]
- |autobatch; (* apply (SA_Arrow ? ? ? ? ? (H4 ? H7) (H6 ? H7)) *)
- |apply (SA_All ? ? ? ? ? (H4 ? H7));intros;autobatch]
- (*
- apply (H6 ? ? (mk_bound true X1 t2::l1))
- [rewrite > H7;rewrite > fv_env_extends;apply H8
- |simplify;rewrite < H7;reflexivity]] *)
+ ∀l.G=l@ !X ⊴ U::G1 → l@ !X ⊴ P::G1 ⊢ M ⊴ N.
+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 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]]