+++ /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/notation/relations/statictype_5.ma".
-include "basic_2/grammar/genv.ma".
-include "basic_2/substitution/drop.ma".
-include "basic_2/static/sh.ma".
-
-(* STATIC TYPE ASSIGNMENT ON TERMS ******************************************)
-
-(* activate genv *)
-inductive sta (h:sh): relation4 genv lenv term term ≝
-| sta_sort: ∀G,L,k. sta h G L (⋆k) (⋆(next h k))
-| sta_ldef: ∀G,L,K,V,W,U,i. ⇩[i] L ≡ K.ⓓV → sta h G K V W →
- ⇧[0, i + 1] W ≡ U → sta h G L (#i) U
-| sta_ldec: ∀G,L,K,W,V,U,i. ⇩[i] L ≡ K.ⓛW → sta h G K W V →
- ⇧[0, i + 1] W ≡ U → sta h G L (#i) U
-| sta_bind: ∀a,I,G,L,V,T,U. sta h G (L.ⓑ{I}V) T U →
- sta h G L (ⓑ{a,I}V.T) (ⓑ{a,I}V.U)
-| sta_appl: ∀G,L,V,T,U. sta h G L T U → sta h G L (ⓐV.T) (ⓐV.U)
-| sta_cast: ∀G,L,W,T,U. sta h G L T U → sta h G L (ⓝW.T) U
-.
-
-interpretation "static type assignment (term)"
- 'StaticType h G L T U = (sta h G L T U).
-
-(* Basic inversion lemmas ************************************************)
-
-fact sta_inv_sort1_aux: ∀h,G,L,T,U. ⦃G, L⦄ ⊢ T •[h] U → ∀k0. T = ⋆k0 →
- U = ⋆(next h k0).
-#h #G #L #T #U * -G -L -T -U
-[ #G #L #k #k0 #H destruct //
-| #G #L #K #V #W #U #i #_ #_ #_ #k0 #H destruct
-| #G #L #K #W #V #U #i #_ #_ #_ #k0 #H destruct
-| #a #I #G #L #V #T #U #_ #k0 #H destruct
-| #G #L #V #T #U #_ #k0 #H destruct
-| #G #L #W #T #U #_ #k0 #H destruct
-qed-.
-
-(* Basic_1: was: sty0_gen_sort *)
-lemma sta_inv_sort1: ∀h,G,L,U,k. ⦃G, L⦄ ⊢ ⋆k •[h] U → U = ⋆(next h k).
-/2 width=5 by sta_inv_sort1_aux/ qed-.
-
-fact sta_inv_lref1_aux: ∀h,G,L,T,U. ⦃G, L⦄ ⊢ T •[h] U → ∀j. T = #j →
- (∃∃K,V,W. ⇩[j] L ≡ K.ⓓV & ⦃G, K⦄ ⊢ V •[h] W &
- ⇧[0, j+1] W ≡ U
- ) ∨
- (∃∃K,W,V. ⇩[j] L ≡ K.ⓛW & ⦃G, K⦄ ⊢ W •[h] V &
- ⇧[0, j+1] W ≡ U
- ).
-#h #G #L #T #U * -G -L -T -U
-[ #G #L #k #j #H destruct
-| #G #L #K #V #W #U #i #HLK #HVW #HWU #j #H destruct /3 width=6 by or_introl, ex3_3_intro/
-| #G #L #K #W #V #U #i #HLK #HWV #HWU #j #H destruct /3 width=6 by or_intror, ex3_3_intro/
-| #a #I #G #L #V #T #U #_ #j #H destruct
-| #G #L #V #T #U #_ #j #H destruct
-| #G #L #W #T #U #_ #j #H destruct
-]
-qed-.
-
-(* Basic_1: was sty0_gen_lref *)
-lemma sta_inv_lref1: ∀h,G,L,U,i. ⦃G, L⦄ ⊢ #i •[h] U →
- (∃∃K,V,W. ⇩[i] L ≡ K.ⓓV & ⦃G, K⦄ ⊢ V •[h] W &
- ⇧[0, i+1] W ≡ U
- ) ∨
- (∃∃K,W,V. ⇩[i] L ≡ K.ⓛW & ⦃G, K⦄ ⊢ W •[h] V &
- ⇧[0, i+1] W ≡ U
- ).
-/2 width=3 by sta_inv_lref1_aux/ qed-.
-
-fact sta_inv_gref1_aux: ∀h,G,L,T,U. ⦃G, L⦄ ⊢ T •[h] U → ∀p0. T = §p0 → ⊥.
-#h #G #L #T #U * -G -L -T -U
-[ #G #L #k #p0 #H destruct
-| #G #L #K #V #W #U #i #_ #_ #_ #p0 #H destruct
-| #G #L #K #W #V #U #i #_ #_ #_ #p0 #H destruct
-| #a #I #G #L #V #T #U #_ #p0 #H destruct
-| #G #L #V #T #U #_ #p0 #H destruct
-| #G #L #W #T #U #_ #p0 #H destruct
-qed-.
-
-lemma sta_inv_gref1: ∀h,G,L,U,p. ⦃G, L⦄ ⊢ §p •[h] U → ⊥.
-/2 width=8 by sta_inv_gref1_aux/ qed-.
-
-fact sta_inv_bind1_aux: ∀h,G,L,T,U. ⦃G, L⦄ ⊢ T •[h] U → ∀b,J,X,Y. T = ⓑ{b,J}Y.X →
- ∃∃Z. ⦃G, L.ⓑ{J}Y⦄ ⊢ X •[h] Z & U = ⓑ{b,J}Y.Z.
-#h #G #L #T #U * -G -L -T -U
-[ #G #L #k #b #J #X #Y #H destruct
-| #G #L #K #V #W #U #i #_ #_ #_ #b #J #X #Y #H destruct
-| #G #L #K #W #V #U #i #_ #_ #_ #b #J #X #Y #H destruct
-| #a #I #G #L #V #T #U #HTU #b #J #X #Y #H destruct /2 width=3 by ex2_intro/
-| #G #L #V #T #U #_ #b #J #X #Y #H destruct
-| #G #L #W #T #U #_ #b #J #X #Y #H destruct
-]
-qed-.
-
-(* Basic_1: was: sty0_gen_bind *)
-lemma sta_inv_bind1: ∀h,b,J,G,L,Y,X,U. ⦃G, L⦄ ⊢ ⓑ{b,J}Y.X •[h] U →
- ∃∃Z. ⦃G, L.ⓑ{J}Y⦄ ⊢ X •[h] Z & U = ⓑ{b,J}Y.Z.
-/2 width=3 by sta_inv_bind1_aux/ qed-.
-
-fact sta_inv_appl1_aux: ∀h,G,L,T,U. ⦃G, L⦄ ⊢ T •[h] U → ∀X,Y. T = ⓐY.X →
- ∃∃Z. ⦃G, L⦄ ⊢ X •[h] Z & U = ⓐY.Z.
-#h #G #L #T #U * -G -L -T -U
-[ #G #L #k #X #Y #H destruct
-| #G #L #K #V #W #U #i #_ #_ #_ #X #Y #H destruct
-| #G #L #K #W #V #U #i #_ #_ #_ #X #Y #H destruct
-| #a #I #G #L #V #T #U #_ #X #Y #H destruct
-| #G #L #V #T #U #HTU #X #Y #H destruct /2 width=3 by ex2_intro/
-| #G #L #W #T #U #_ #X #Y #H destruct
-]
-qed-.
-
-(* Basic_1: was: sty0_gen_appl *)
-lemma sta_inv_appl1: ∀h,G,L,Y,X,U. ⦃G, L⦄ ⊢ ⓐY.X •[h] U →
- ∃∃Z. ⦃G, L⦄ ⊢ X •[h] Z & U = ⓐY.Z.
-/2 width=3 by sta_inv_appl1_aux/ qed-.
-
-fact sta_inv_cast1_aux: ∀h,G,L,T,U. ⦃G, L⦄ ⊢ T •[h] U → ∀X,Y. T = ⓝY.X →
- ⦃G, L⦄ ⊢ X •[h] U.
-#h #G #L #T #U * -G -L -T -U
-[ #G #L #k #X #Y #H destruct
-| #G #L #K #V #W #U #i #_ #_ #_ #X #Y #H destruct
-| #G #L #K #W #V #U #i #_ #_ #_ #X #Y #H destruct
-| #a #I #G #L #V #T #U #_ #X #Y #H destruct
-| #G #L #V #T #U #_ #X #Y #H destruct
-| #G #L #W #T #U #HTU #X #Y #H destruct //
-]
-qed-.
-
-(* Basic_1: was: sty0_gen_cast *)
-lemma sta_inv_cast1: ∀h,G,L,X,Y,U. ⦃G, L⦄ ⊢ ⓝY.X •[h] U → ⦃G, L⦄ ⊢ X •[h] U.
-/2 width=4 by sta_inv_cast1_aux/ qed-.
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