+++ /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 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/substitution/ldrop.ma".
-include "basic_2/static/sh.ma".
-
-(* STATIC TYPE ASSIGNMENT ON TERMS ******************************************)
-
-inductive sta (h:sh): lenv → relation term ≝
-| sta_sort: ∀L,k. sta h L (⋆k) (⋆(next h k))
-| sta_ldef: ∀L,K,V,W,U,i. ⇩[0, i] L ≡ K. ⓓV → sta h K V W →
- ⇧[0, i + 1] W ≡ U → sta h L (#i) U
-| sta_ldec: ∀L,K,W,V,U,i. ⇩[0, i] L ≡ K. ⓛW → sta h K W V →
- ⇧[0, i + 1] W ≡ U → sta h L (#i) U
-| sta_bind: ∀I,L,V,T,U. sta h (L. ⓑ{I} V) T U →
- sta h L (ⓑ{I}V.T) (ⓑ{I}V.U)
-| sta_appl: ∀L,V,T,U. sta h L T U →
- sta h L (ⓐV.T) (ⓐV.U)
-| sta_cast: ∀L,W,T,U. sta h L T U → sta h L (ⓝW. T) U
-.
-
-interpretation "static type assignment (term)"
- 'StaticType h L T U = (sta h L T U).
-
-(* Basic inversion lemmas ************************************************)
-
-fact sta_inv_sort1_aux: ∀h,L,T,U. ⦃h, L⦄ ⊢ T • U → ∀k0. T = ⋆k0 →
- U = ⋆(next h k0).
-#h #L #T #U * -L -T -U
-[ #L #k #k0 #H destruct //
-| #L #K #V #W #U #i #_ #_ #_ #k0 #H destruct
-| #L #K #W #V #U #i #_ #_ #_ #k0 #H destruct
-| #I #L #V #T #U #_ #k0 #H destruct
-| #L #V #T #U #_ #k0 #H destruct
-| #L #W #T #U #_ #k0 #H destruct
-qed.
-
-(* Basic_1: was: sty0_gen_sort *)
-lemma sta_inv_sort1: ∀h,L,U,k. ⦃h, L⦄ ⊢ ⋆k • U → U = ⋆(next h k).
-/2 width=4/ qed-.
-
-fact sta_inv_lref1_aux: ∀h,L,T,U. ⦃h, L⦄ ⊢ T • U → ∀j. T = #j →
- (∃∃K,V,W. ⇩[0, j] L ≡ K. ⓓV & ⦃h, K⦄ ⊢ V • W &
- ⇧[0, j + 1] W ≡ U
- ) ∨
- (∃∃K,W,V. ⇩[0, j] L ≡ K. ⓛW & ⦃h, K⦄ ⊢ W • V &
- ⇧[0, j + 1] W ≡ U
- ).
-#h #L #T #U * -L -T -U
-[ #L #k #j #H destruct
-| #L #K #V #W #U #i #HLK #HVW #HWU #j #H destruct /3 width=6/
-| #L #K #W #V #U #i #HLK #HWV #HWU #j #H destruct /3 width=6/
-| #I #L #V #T #U #_ #j #H destruct
-| #L #V #T #U #_ #j #H destruct
-| #L #W #T #U #_ #j #H destruct
-]
-qed.
-
-(* Basic_1: was sty0_gen_lref *)
-lemma sta_inv_lref1: ∀h,L,U,i. ⦃h, L⦄ ⊢ #i • U →
- (∃∃K,V,W. ⇩[0, i] L ≡ K. ⓓV & ⦃h, K⦄ ⊢ V • W &
- ⇧[0, i + 1] W ≡ U
- ) ∨
- (∃∃K,W,V. ⇩[0, i] L ≡ K. ⓛW & ⦃h, K⦄ ⊢ W • V &
- ⇧[0, i + 1] W ≡ U
- ).
-/2 width=3/ qed-.
-
-fact sta_inv_bind1_aux: ∀h,L,T,U. ⦃h, L⦄ ⊢ T • U → ∀J,X,Y. T = ⓑ{J}Y.X →
- ∃∃Z. ⦃h, L.ⓑ{J}Y⦄ ⊢ X • Z & U = ⓑ{J}Y.Z.
-#h #L #T #U * -L -T -U
-[ #L #k #J #X #Y #H destruct
-| #L #K #V #W #U #i #_ #_ #_ #J #X #Y #H destruct
-| #L #K #W #V #U #i #_ #_ #_ #J #X #Y #H destruct
-| #I #L #V #T #U #HTU #J #X #Y #H destruct /2 width=3/
-| #L #V #T #U #_ #J #X #Y #H destruct
-| #L #W #T #U #_ #J #X #Y #H destruct
-]
-qed.
-
-(* Basic_1: was: sty0_gen_bind *)
-lemma sta_inv_bind1: ∀h,J,L,Y,X,U. ⦃h, L⦄ ⊢ ⓑ{J}Y.X • U →
- ∃∃Z. ⦃h, L.ⓑ{J}Y⦄ ⊢ X • Z & U = ⓑ{J}Y.Z.
-/2 width=3/ qed-.
-
-fact sta_inv_appl1_aux: ∀h,L,T,U. ⦃h, L⦄ ⊢ T • U → ∀X,Y. T = ⓐY.X →
- ∃∃Z. ⦃h, L⦄ ⊢ X • Z & U = ⓐY.Z.
-#h #L #T #U * -L -T -U
-[ #L #k #X #Y #H destruct
-| #L #K #V #W #U #i #_ #_ #_ #X #Y #H destruct
-| #L #K #W #V #U #i #_ #_ #_ #X #Y #H destruct
-| #I #L #V #T #U #_ #X #Y #H destruct
-| #L #V #T #U #HTU #X #Y #H destruct /2 width=3/
-| #L #W #T #U #_ #X #Y #H destruct
-]
-qed.
-
-(* Basic_1: was: sty0_gen_appl *)
-lemma sta_inv_appl1: ∀h,L,Y,X,U. ⦃h, L⦄ ⊢ ⓐY.X • U →
- ∃∃Z. ⦃h, L⦄ ⊢ X • Z & U = ⓐY.Z.
-/2 width=3/ qed-.
-
-fact sta_inv_cast1_aux: ∀h,L,T,U. ⦃h, L⦄ ⊢ T • U → ∀X,Y. T = ⓝY.X →
- ⦃h, L⦄ ⊢ X • U.
-#h #L #T #U * -L -T -U
-[ #L #k #X #Y #H destruct
-| #L #K #V #W #U #i #_ #_ #_ #X #Y #H destruct
-| #L #K #W #V #U #i #_ #_ #_ #X #Y #H destruct
-| #I #L #V #T #U #_ #X #Y #H destruct
-| #L #V #T #U #_ #X #Y #H destruct
-| #L #W #T #U #HTU #X #Y #H destruct //
-]
-qed.
-
-(* Basic_1: was: sty0_gen_cast *)
-lemma sta_inv_cast1: ∀h,L,X,Y,U. ⦃h, L⦄ ⊢ ⓝY.X • U → ⦃h, L⦄ ⊢ X • U.
-/2 width=4/ qed-.