- some renaming according to the written version of basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / snv.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv.ma
index 88d4db42136f98153d6ef97e8bb992680198746d..6eb3dff2439cc317ff62a5b7ddc3fde9d2c8ab11 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv.ma
@@ -22,8 +22,8 @@ inductive snv (h) (g): relation3 genv lenv term ≝
 | snv_sort: ∀G,L,k. snv h g G L (⋆k)
 | snv_lref: ∀I,G,L,K,V,i. ⬇[i] L ≡ K.ⓑ{I}V → snv h g G K V → snv h g G L (#i)
 | snv_bind: ∀a,I,G,L,V,T. snv h g G L V → snv h g G (L.ⓑ{I}V) T → snv h g G L (ⓑ{a,I}V.T)
-| snv_appl: ∀a,G,L,V,W0,T,U0,l. snv h g G L V → snv h g G L T →
-            ⦃G, L⦄ ⊢ V •*➡*[h, g, 1] W0 → ⦃G, L⦄ ⊢ T •*➡*[h, g, l] ⓛ{a}W0.U0 → snv h g G L (ⓐV.T)
+| snv_appl: ∀a,G,L,V,W0,T,U0,d. snv h g G L V → snv h g G L T →
+            ⦃G, L⦄ ⊢ V •*➡*[h, g, 1] W0 → ⦃G, L⦄ ⊢ T •*➡*[h, g, d] ⓛ{a}W0.U0 → snv h g G L (ⓐV.T)
 | snv_cast: ∀G,L,U,T,U0. snv h g G L U → snv h g G L T →
             ⦃G, L⦄ ⊢ U •*➡*[h, g, 0] U0 → ⦃G, L⦄ ⊢ T •*➡*[h, g, 1] U0 → snv h g G L (ⓝU.T)
 .
@@ -39,7 +39,7 @@ fact snv_inv_lref_aux: ∀h,g,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, g] → ∀i. X = #i
 [ #G #L #k #i #H destruct
 | #I #G #L #K #V #i0 #HLK #HV #i #H destruct /2 width=5 by ex2_3_intro/
 | #a #I #G #L #V #T #_ #_ #i #H destruct
-| #a #G #L #V #W0 #T #U0 #l #_ #_ #_ #_ #i #H destruct
+| #a #G #L #V #W0 #T #U0 #d #_ #_ #_ #_ #i #H destruct
 | #G #L #U #T #U0 #_ #_ #_ #_ #i #H destruct
 ]
 qed-.
@@ -53,7 +53,7 @@ fact snv_inv_gref_aux: ∀h,g,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, g] → ∀p. X = §p
 [ #G #L #k #p #H destruct
 | #I #G #L #K #V #i #_ #_ #p #H destruct
 | #a #I #G #L #V #T #_ #_ #p #H destruct
-| #a #G #L #V #W0 #T #U0 #l #_ #_ #_ #_ #p #H destruct
+| #a #G #L #V #W0 #T #U0 #d #_ #_ #_ #_ #p #H destruct
 | #G #L #U #T #U0 #_ #_ #_ #_ #p #H destruct
 ]
 qed-.
@@ -67,7 +67,7 @@ fact snv_inv_bind_aux: ∀h,g,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, g] → ∀a,I,V,T. X
 [ #G #L #k #b #Z #X1 #X2 #H destruct
 | #I #G #L #K #V #i #_ #_ #b #Z #X1 #X2 #H destruct
 | #a #I #G #L #V #T #HV #HT #b #Z #X1 #X2 #H destruct /2 width=1 by conj/
-| #a #G #L #V #W0 #T #U0 #l #_ #_ #_ #_ #b #Z #X1 #X2 #H destruct
+| #a #G #L #V #W0 #T #U0 #d #_ #_ #_ #_ #b #Z #X1 #X2 #H destruct
 | #G #L #U #T #U0 #_ #_ #_ #_ #b #Z #X1 #X2 #H destruct
 ]
 qed-.
@@ -77,20 +77,20 @@ lemma snv_inv_bind: ∀h,g,a,I,G,L,V,T. ⦃G, L⦄ ⊢ ⓑ{a,I}V.T ¡[h, g] →
 /2 width=4 by snv_inv_bind_aux/ qed-.
 
 fact snv_inv_appl_aux: ∀h,g,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, g] → ∀V,T. X = ⓐV.T →
-                       ∃∃a,W0,U0,l. ⦃G, L⦄ ⊢ V ¡[h, g] & ⦃G, L⦄ ⊢ T ¡[h, g] &
-                                    ⦃G, L⦄ ⊢ V •*➡*[h, g, 1] W0 & ⦃G, L⦄ ⊢ T •*➡*[h, g, l] ⓛ{a}W0.U0.
+                       ∃∃a,W0,U0,d. ⦃G, L⦄ ⊢ V ¡[h, g] & ⦃G, L⦄ ⊢ T ¡[h, g] &
+                                    ⦃G, L⦄ ⊢ V •*➡*[h, g, 1] W0 & ⦃G, L⦄ ⊢ T •*➡*[h, g, d] ⓛ{a}W0.U0.
 #h #g #G #L #X * -L -X
 [ #G #L #k #X1 #X2 #H destruct
 | #I #G #L #K #V #i #_ #_ #X1 #X2 #H destruct
 | #a #I #G #L #V #T #_ #_ #X1 #X2 #H destruct
-| #a #G #L #V #W0 #T #U0 #l #HV #HT #HVW0 #HTU0 #X1 #X2 #H destruct /2 width=6 by ex4_4_intro/
+| #a #G #L #V #W0 #T #U0 #d #HV #HT #HVW0 #HTU0 #X1 #X2 #H destruct /2 width=6 by ex4_4_intro/
 | #G #L #U #T #U0 #_ #_ #_ #_ #X1 #X2 #H destruct
 ]
 qed-.
 
 lemma snv_inv_appl: ∀h,g,G,L,V,T. ⦃G, L⦄ ⊢ ⓐV.T ¡[h, g] →
-                    ∃∃a,W0,U0,l. ⦃G, L⦄ ⊢ V ¡[h, g] & ⦃G, L⦄ ⊢ T ¡[h, g] &
-                                 ⦃G, L⦄ ⊢ V •*➡*[h, g, 1] W0 & ⦃G, L⦄ ⊢ T •*➡*[h, g, l] ⓛ{a}W0.U0.
+                    ∃∃a,W0,U0,d. ⦃G, L⦄ ⊢ V ¡[h, g] & ⦃G, L⦄ ⊢ T ¡[h, g] &
+                                 ⦃G, L⦄ ⊢ V •*➡*[h, g, 1] W0 & ⦃G, L⦄ ⊢ T •*➡*[h, g, d] ⓛ{a}W0.U0.
 /2 width=3 by snv_inv_appl_aux/ qed-.
 
 fact snv_inv_cast_aux: ∀h,g,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, g] → ∀U,T. X = ⓝU.T →
@@ -100,7 +100,7 @@ fact snv_inv_cast_aux: ∀h,g,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, g] → ∀U,T. X = 
 [ #G #L #k #X1 #X2 #H destruct
 | #I #G #L #K #V #i #_ #_ #X1 #X2 #H destruct
 | #a #I #G #L #V #T #_ #_ #X1 #X2 #H destruct
-| #a #G #L #V #W0 #T #U0 #l #_ #_ #_ #_ #X1 #X2 #H destruct
+| #a #G #L #V #W0 #T #U0 #d #_ #_ #_ #_ #X1 #X2 #H destruct
 | #G #L #U #T #U0 #HV #HT #HU0 #HTU0 #X1 #X2 #H destruct /2 width=3 by ex4_intro/
 ]
 qed-.