+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-notation "hvbox( h ⊢ break term 46 L1 : ⊑ break term 46 L2 )"
- non associative with precedence 45
- for @{ 'CrSubEqN $h $L1 $L2 }.
-
-notation "hvbox( h ⊢ break term 46 L1 : : ⊑ break term 46 L2 )"
- non associative with precedence 45
- for @{ 'CrSubEqNAlt $h $L1 $L2 }.
-
-include "basic_2/dynamic/nta.ma".
-
-(* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE TYPE ASSIGNMENT ******************)
-
-(* Note: may not be transitive *)
-inductive lsubn (h:sh): relation lenv ≝
-| lsubn_atom: lsubn h (⋆) (⋆)
-| lsubn_pair: ∀I,L1,L2,W. lsubn h L1 L2 → lsubn h (L1. ⓑ{I} W) (L2. ⓑ{I} W)
-| lsubn_abbr: ∀L1,L2,V,W. ⦃h, L1⦄ ⊢ V : W → ⦃h, L2⦄ ⊢ V : W →
- lsubn h L1 L2 → lsubn h (L1. ⓓV) (L2. ⓛW)
-.
-
-interpretation
- "local environment refinement (native type assigment)"
- 'CrSubEqN h L1 L2 = (lsubn h L1 L2).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact lsubn_inv_atom1_aux: ∀h,L1,L2. h ⊢ L1 :⊑ L2 → L1 = ⋆ → L2 = ⋆.
-#h #L1 #L2 * -L1 -L2
-[ //
-| #I #L1 #L2 #V #_ #H destruct
-| #L1 #L2 #V #W #_ #_ #_ #H destruct
-]
-qed.
-
-lemma lsubn_inv_atom1: ∀h,L2. h ⊢ ⋆ :⊑ L2 → L2 = ⋆.
-/2 width=4/ qed-.
-
-fact lsubn_inv_pair1_aux: ∀h,L1,L2. h ⊢ L1 :⊑ L2 → ∀I,K1,V. L1 = K1. ⓑ{I} V →
- (∃∃K2. h ⊢ K1 :⊑ K2 & L2 = K2. ⓑ{I} V) ∨
- ∃∃K2,W. ⦃h, K1⦄ ⊢ V : W & ⦃h, K2⦄ ⊢ V : W &
- h ⊢ K1 :⊑ K2 & L2 = K2. ⓛW & I = Abbr.
-#h #L1 #L2 * -L1 -L2
-[ #I #K1 #V #H destruct
-| #J #L1 #L2 #V #HL12 #I #K1 #W #H destruct /3 width=3/
-| #L1 #L2 #V #W #H1VW #H2VW #HL12 #I #K1 #V1 #H destruct /3 width=7/
-]
-qed.
-
-lemma lsubn_inv_pair1: ∀h,I,K1,L2,V. h ⊢ K1. ⓑ{I} V :⊑ L2 →
- (∃∃K2. h ⊢ K1 :⊑ K2 & L2 = K2. ⓑ{I} V) ∨
- ∃∃K2,W. ⦃h, K1⦄ ⊢ V : W & ⦃h, K2⦄ ⊢ V : W &
- h ⊢ K1 :⊑ K2 & L2 = K2. ⓛW & I = Abbr.
-/2 width=3/ qed-.
-
-fact lsubn_inv_atom2_aux: ∀h,L1,L2. h ⊢ L1 :⊑ L2 → L2 = ⋆ → L1 = ⋆.
-#h #L1 #L2 * -L1 -L2
-[ //
-| #I #L1 #L2 #V #_ #H destruct
-| #L1 #L2 #V #W #_ #_ #_ #H destruct
-]
-qed.
-
-lemma lsubc_inv_atom2: ∀h,L1. h ⊢ L1 :⊑ ⋆ → L1 = ⋆.
-/2 width=4/ qed-.
-
-fact lsubn_inv_pair2_aux: ∀h,L1,L2. h ⊢ L1 :⊑ L2 → ∀I,K2,W. L2 = K2. ⓑ{I} W →
- (∃∃K1. h ⊢ K1 :⊑ K2 & L1 = K1. ⓑ{I} W) ∨
- ∃∃K1,V. ⦃h, K1⦄ ⊢ V : W & ⦃h, K2⦄ ⊢ V : W &
- h ⊢ K1 :⊑ K2 & L1 = K1. ⓓV & I = Abst.
-#h #L1 #L2 * -L1 -L2
-[ #I #K2 #W #H destruct
-| #J #L1 #L2 #V #HL12 #I #K2 #W #H destruct /3 width=3/
-| #L1 #L2 #V #W #H1VW #H2VW #HL12 #I #K2 #W2 #H destruct /3 width=7/
-]
-qed.
-
-(* Basic_1: was: csubt_gen_bind *)
-lemma lsubn_inv_pair2: ∀h,I,L1,K2,W. h ⊢ L1 :⊑ K2. ⓑ{I} W →
- (∃∃K1. h ⊢ K1 :⊑ K2 & L1 = K1. ⓑ{I} W) ∨
- ∃∃K1,V. ⦃h, K1⦄ ⊢ V : W & ⦃h, K2⦄ ⊢ V : W &
- h ⊢ K1 :⊑ K2 & L1 = K1. ⓓV & I = Abst.
-/2 width=3/ qed-.
-
-(* Basic_forward lemmas *****************************************************)
-
-lemma lsubn_fwd_lsubs1: ∀h,L1,L2. h ⊢ L1 :⊑ L2 → L1 ≼[0, |L1|] L2.
-#h #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
-qed-.
-
-lemma lsubn_fwd_lsubs2: ∀h,L1,L2. h ⊢ L1 :⊑ L2 → L1 ≼[0, |L2|] L2.
-#h #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
-qed-.
-
-(* Basic properties *********************************************************)
-
-(* Basic_1: was: csubt_refl *)
-lemma lsubn_refl: ∀h,L. h ⊢ L :⊑ L.
-#h #L elim L -L // /2 width=1/
-qed.
-
-(* Basic_1: removed theorems 6:
- csubt_gen_flat csubt_drop_flat csubt_clear_conf
- csubt_getl_abbr csubt_getl_abst csubt_ty3_ld
-*)