G1 ⊢ P ⊴ U → (∀G2,T.G2@G1 ⊢ U ⊴ T → G2@G1 ⊢ P ⊴ T) → G ⊢ M ⊴ N →
∀l.G=l@(mk_bound true X U::G1) → l@(mk_bound true X P::G1) ⊢ M ⊴ N.
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]
+ [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]
- |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
+ |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)]]
- |apply (SA_Arrow ? ? ? ? ? (H4 ? H7) (H6 ? H7))
- |apply (SA_All ? ? ? ? ? (H4 ? H7));intros;
+ |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]]
+ |simplify;rewrite < H7;reflexivity]] *)
qed.
lemma JS_trans_prova: ∀T,G1.WFType G1 T →
∀G,R,U.incl ? (fv_env G1) (fv_env G) → G ⊢ R ⊴ T → G ⊢ T ⊴ U → G ⊢ R ⊴ U.
intros 3;elim H;clear H; try autobatch;
- [rewrite > (JSubtype_Top ? ? H3);autobatch
+ [
+ rewrite > (JSubtype_Top ? ? H3);autobatch
|generalize in match H7;generalize in match H4;generalize in match H2;
generalize in match H5;clear H7 H4 H2 H5;
generalize in match (refl_eq ? (Arrow t t1));