reorganization of the "static" component:

[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 07bdd7cbf24f83e18f6bbd943ae24e35a4343ee0..11e8bea806ddaec55adba1d2af80e81b866d9d63 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv.ma
@@ -20,18 +20,18 @@ include "basic_2/equivalence/cpcs.ma".
 
 definition scast: ∀h. sd h → nat → relation4 genv lenv term term ≝
                   λh,g,l,G,L,V,W. ∀V0,W0,l0.
-                  l0 ≤ l → ⦃G, L⦄ ⊢ V •*[h, g, l0+1] V0 → ⦃G, L⦄ ⊢ W •*[h, g, l0] W0 → ⦃G, L⦄ ⊢ V0 ⬌* W0.
+                  l0 ≤ l → ⦃G, L⦄ ⊢ V •*[h, l0+1] V0 → ⦃G, L⦄ ⊢ W •*[h, l0] W0 → ⦃G, L⦄ ⊢ V0 ⬌* W0.
 
 (* activate genv *)
 inductive snv (h:sh) (g:sd h): relation3 genv lenv term ≝
 | snv_sort: ∀G,L,k. snv h g G L (⋆k)
-| snv_lref: ∀I,G,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V → snv h g G K V → snv h g G L (#i)
+| 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,W,W0,T,U,l. snv h g G L V → snv h g G L T →
-            ⦃G, L⦄ ⊢ V ▪[h, g] l+1 → ⦃G, L⦄ ⊢ V •[h, g] W → ⦃G, L⦄ ⊢ W ➡* W0 →
+            ⦃G, L⦄ ⊢ V ▪[h, g] l+1 → ⦃G, L⦄ ⊢ V •[h] W → ⦃G, L⦄ ⊢ W ➡* W0 →
             ⦃G, L⦄ ⊢ T •*➡*[h, g] ⓛ{a}W0.U → snv h g G L (ⓐV.T)
 | snv_cast: ∀G,L,W,T,U,l. snv h g G L W → snv h g G L T →
-            ⦃G, L⦄ ⊢ T ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T •[h, g] U → ⦃G, L⦄ ⊢ U ⬌* W → snv h g G L (ⓝW.T)
+            ⦃G, L⦄ ⊢ T ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T •[h] U → ⦃G, L⦄ ⊢ U ⬌* W → snv h g G L (ⓝW.T)
 .
 
 interpretation "stratified native validity (term)"
@@ -40,10 +40,10 @@ interpretation "stratified native validity (term)"
 (* Basic inversion lemmas ***************************************************)
 
 fact snv_inv_lref_aux: ∀h,g,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, g] → ∀i. X = #i →
-                       ∃∃I,K,V. ⇩[0, i] L ≡ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ¡[h, g].
+                       ∃∃I,K,V. ⇩[i] L ≡ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ¡[h, g].
 #h #g #G #L #X * -G -L -X
 [ #G #L #k #i #H destruct
-| #I #G #L #K #V #i0 #HLK #HV #i #H destruct /2 width=5/
+| #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 #W #W0 #T #U #l #_ #_ #_ #_ #_ #_ #i #H destruct
 | #G #L #W #T #U #l #_ #_ #_ #_ #_ #i #H destruct
@@ -51,7 +51,7 @@ fact snv_inv_lref_aux: ∀h,g,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, g] → ∀i. X = #i
 qed-.
 
 lemma snv_inv_lref: ∀h,g,G,L,i. ⦃G, L⦄ ⊢ #i ¡[h, g] →
-                    ∃∃I,K,V. ⇩[0, i] L ≡ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ¡[h, g].
+                    ∃∃I,K,V. ⇩[i] L ≡ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ¡[h, g].
 /2 width=3 by snv_inv_lref_aux/ qed-.
 
 fact snv_inv_gref_aux: ∀h,g,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, g] → ∀p. X = §p → ⊥.
@@ -72,48 +72,48 @@ fact snv_inv_bind_aux: ∀h,g,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, g] → ∀a,I,V,T. X
 #h #g #G #L #X * -G -L -X
 [ #G #L #k #a #I #V #T #H destruct
 | #I0 #G #L #K #V0 #i #_ #_ #a #I #V #T #H destruct
-| #b #I0 #G #L #V0 #T0 #HV0 #HT0 #a #I #V #T #H destruct /2 width=1/
+| #b #I0 #G #L #V0 #T0 #HV0 #HT0 #a #I #V #T #H destruct /2 width=1 by conj/
 | #b #G #L #V0 #W0 #W00 #T0 #U0 #l #_ #_ #_ #_#_ #_ #a #I #V #T #H destruct
 | #G #L #W0 #T0 #U0 #l #_ #_ #_ #_ #_ #a #I #V #T #H destruct
 ]
 qed-.
 
 lemma snv_inv_bind: ∀h,g,a,I,G,L,V,T. ⦃G, L⦄ ⊢ ⓑ{a,I}V.T ¡[h, g] →
-                        ⦃G, L⦄ ⊢ V ¡[h, g] ∧ ⦃G, L.ⓑ{I}V⦄ ⊢ T ¡[h, g].
+                    ⦃G, L⦄ ⊢ V ¡[h, g] ∧ ⦃G, L.ⓑ{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,W,W0,U,l. ⦃G, L⦄ ⊢ V ¡[h, g] & ⦃G, L⦄ ⊢ T ¡[h, g] &
-                                   ⦃G, L⦄ ⊢ V ▪[h, g] l+1 & ⦃G, L⦄ ⊢ V •[h, g] W & ⦃G, L⦄ ⊢ W ➡* W0 &
-                                   ⦃G, L⦄ ⊢ T •*➡*[h, g] ⓛ{a}W0.U.
+                                     ⦃G, L⦄ ⊢ V ▪[h, g] l+1 & ⦃G, L⦄ ⊢ V •[h] W & ⦃G, L⦄ ⊢ W ➡* W0 &
+                                     ⦃G, L⦄ ⊢ T •*➡*[h, g] ⓛ{a}W0.U.
 #h #g #G #L #X * -L -X
 [ #G #L #k #V #T #H destruct
 | #I #G #L #K #V0 #i #_ #_ #V #T #H destruct
 | #a #I #G #L #V0 #T0 #_ #_ #V #T #H destruct
-| #a #G #L #V0 #W0 #W00 #T0 #U0 #l #HV0 #HT0 #Hl #HVW0 #HW00 #HTU0 #V #T #H destruct /2 width=8/
+| #a #G #L #V0 #W0 #W00 #T0 #U0 #l #HV0 #HT0 #Hl #HVW0 #HW00 #HTU0 #V #T #H destruct /2 width=8 by ex6_5_intro/
 | #G #L #W0 #T0 #U0 #l #_ #_ #_ #_ #_ #V #T #H destruct
 ]
 qed-.
 
 lemma snv_inv_appl: ∀h,g,G,L,V,T. ⦃G, L⦄ ⊢ ⓐV.T ¡[h, g] →
                     ∃∃a,W,W0,U,l. ⦃G, L⦄ ⊢ V ¡[h, g] & ⦃G, L⦄ ⊢ T ¡[h, g] &
-                                ⦃G, L⦄ ⊢ V ▪[h, g] l+1 & ⦃G, L⦄ ⊢ V •[h, g] W & ⦃G, L⦄ ⊢ W ➡* W0 &
-                                ⦃G, L⦄ ⊢ T •*➡*[h, g] ⓛ{a}W0.U.
+                                  ⦃G, L⦄ ⊢ V ▪[h, g] l+1 & ⦃G, L⦄ ⊢ V •[h] W & ⦃G, L⦄ ⊢ W ➡* W0 &
+                                  ⦃G, L⦄ ⊢ T •*➡*[h, g] ⓛ{a}W0.U.
 /2 width=3 by snv_inv_appl_aux/ qed-.
 
 fact snv_inv_cast_aux: ∀h,g,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, g] → ∀W,T. X = ⓝW.T →
                        ∃∃U,l. ⦃G, L⦄ ⊢ W ¡[h, g] & ⦃G, L⦄ ⊢ T ¡[h, g] &
-                              ⦃G, L⦄ ⊢ T ▪[h, g] l+1 & ⦃G, L⦄ ⊢ T •[h, g] U & ⦃G, L⦄ ⊢ U ⬌* W.
+                              ⦃G, L⦄ ⊢ T ▪[h, g] l+1 & ⦃G, L⦄ ⊢ T •[h] U & ⦃G, L⦄ ⊢ U ⬌* W.
 #h #g #G #L #X * -G -L -X
 [ #G #L #k #W #T #H destruct
 | #I #G #L #K #V #i #_ #_ #W #T #H destruct
 | #a #I #G #L #V #T0 #_ #_ #W #T #H destruct
 | #a #G #L #V #W0 #W00 #T0 #U #l #_ #_ #_ #_ #_ #_ #W #T #H destruct
-| #G #L #W0 #T0 #U0 #l #HW0 #HT0 #Hl #HTU0 #HUW0 #W #T #H destruct /2 width=4/
+| #G #L #W0 #T0 #U0 #l #HW0 #HT0 #Hl #HTU0 #HUW0 #W #T #H destruct /2 width=4 by ex5_2_intro/
 ]
 qed-.
 
 lemma snv_inv_cast: ∀h,g,G,L,W,T. ⦃G, L⦄ ⊢ ⓝW.T ¡[h, g] →
                     ∃∃U,l. ⦃G, L⦄ ⊢ W ¡[h, g] & ⦃G, L⦄ ⊢ T ¡[h, g] &
-                           ⦃G, L⦄ ⊢ T ▪[h, g] l+1 & ⦃G, L⦄ ⊢ T •[h, g] U & ⦃G, L⦄ ⊢ U ⬌* W.
+                           ⦃G, L⦄ ⊢ T ▪[h, g] l+1 & ⦃G, L⦄ ⊢ T •[h] U & ⦃G, L⦄ ⊢ U ⬌* W.
 /2 width=3 by snv_inv_cast_aux/ qed-.