X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Fcpxs_tstc_vector.ma;h=cea820cfbc4aa4e29585cce2529f33f0d7188848;hb=b5d702735754632652b2659c425dd67d7f92f24b;hp=61f43dda69d71b7917a55e69cfdcc193361f5118;hpb=f62eeb3c7824564ccbe4fff6e75ddee46ca39cc0;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc_vector.ma
index 61f43dda6..cea820cfb 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc_vector.ma
@@ -21,9 +21,9 @@ include "basic_2/computation/cpxs_tstc.ma".
 (* Vector form of forward lemmas involving same top term constructor ********)
 
 (* Basic_1: was just: nf2_iso_appls_lref *)
-lemma cpxs_fwd_cnx_vector: ∀h,g,L,T.  𝐒⦃T⦄ → ⦃h, L⦄ ⊢ 𝐍[g]⦃T⦄ →
-                           ∀Vs,U. ⦃h, L⦄ ⊢ ⒶVs.T ➡*[g] U → ⒶVs.T ≃ U.
-#h #g #L #T #H1T #H2T #Vs elim Vs -Vs [ @(cpxs_fwd_cnx … H2T) ] (**) (* /2 width=3 by cpxs_fwd_cnx/ does not work *)
+lemma cpxs_fwd_cnx_vector: ∀h,g,G,L,T.  𝐒⦃T⦄ → ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T⦄ →
+                           ∀Vs,U. ⦃G, L⦄ ⊢ ⒶVs.T ➡*[h, g] U → ⒶVs.T ≃ U.
+#h #g #G #L #T #H1T #H2T #Vs elim Vs -Vs [ @(cpxs_fwd_cnx … H2T) ] (**) (* /2 width=3 by cpxs_fwd_cnx/ does not work *)
 #V #Vs #IHVs #U #H
 elim (cpxs_inv_appl1 … H) -H *
 [ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1/
@@ -36,9 +36,9 @@ elim (cpxs_inv_appl1 … H) -H *
 ]
 qed-.
 
-lemma cpxs_fwd_sort_vector: ∀h,g,L,k,Vs,U. ⦃h, L⦄ ⊢ ⒶVs.⋆k ➡*[g] U →
-                            ⒶVs.⋆k ≃ U ∨ ⦃h, L⦄ ⊢ ⒶVs.⋆(next h k) ➡*[g] U.
-#h #g #L #k #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_sort/
+lemma cpxs_fwd_sort_vector: ∀h,g,G,L,k,Vs,U. ⦃G, L⦄ ⊢ ⒶVs.⋆k ➡*[h, g] U →
+                            ⒶVs.⋆k ≃ U ∨ ⦃G, L⦄ ⊢ ⒶVs.⋆(next h k) ➡*[h, g] U.
+#h #g #G #L #k #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_sort/
 #V #Vs #IHVs #U #H
 elim (cpxs_inv_appl1 … H) -H *
 [ -IHVs #V1 #T1 #_ #_ #H destruct /2 width=1/
@@ -61,9 +61,9 @@ qed-.
 
 
 (* Basic_1: was just: pr3_iso_appls_beta *)
-lemma cpxs_fwd_beta_vector: ∀h,g,a,L,Vs,V,W,T,U. ⦃h, L⦄ ⊢ ⒶVs.ⓐV.ⓛ{a}W.T ➡*[g] U →
-                            ⒶVs. ⓐV. ⓛ{a}W. T ≃ U ∨ ⦃h, L⦄ ⊢ ⒶVs.ⓓ{a}ⓝW.V.T ➡*[g] U.
-#h #g #a #L #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_beta/
+lemma cpxs_fwd_beta_vector: ∀h,g,a,G,L,Vs,V,W,T,U. ⦃G, L⦄ ⊢ ⒶVs.ⓐV.ⓛ{a}W.T ➡*[h, g] U →
+                            ⒶVs. ⓐV. ⓛ{a}W. T ≃ U ∨ ⦃G, L⦄ ⊢ ⒶVs.ⓓ{a}ⓝW.V.T ➡*[h, g] U.
+#h #g #a #G #L #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_beta/
 #V0 #Vs #IHVs #V #W #T #U #H
 elim (cpxs_inv_appl1 … H) -H *
 [ -IHVs #V1 #T1 #_ #_ #H destruct /2 width=1/
@@ -84,11 +84,11 @@ elim (cpxs_inv_appl1 … H) -H *
 ]
 qed-.
 
-lemma cpxs_fwd_delta_vector: ∀h,g,I,L,K,V1,i. ⇩[0, i] L ≡ K.ⓑ{I}V1 →
+lemma cpxs_fwd_delta_vector: ∀h,g,I,G,L,K,V1,i. ⇩[0, i] L ≡ K.ⓑ{I}V1 →
                              ∀V2. ⇧[0, i + 1] V1 ≡ V2 →
-                             ∀Vs,U. ⦃h, L⦄ ⊢ ⒶVs.#i ➡*[g] U →
-                             ⒶVs.#i ≃ U ∨ ⦃h, L⦄ ⊢ ⒶVs.V2 ➡*[g] U.
-#h #g #I #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs /2 width=5 by cpxs_fwd_delta/
+                             ∀Vs,U. ⦃G, L⦄ ⊢ ⒶVs.#i ➡*[h, g] U →
+                             ⒶVs.#i ≃ U ∨ ⦃G, L⦄ ⊢ ⒶVs.V2 ➡*[h, g] U.
+#h #g #I #G #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs /2 width=5 by cpxs_fwd_delta/
 #V #Vs #IHVs #U #H -K -V1
 elim (cpxs_inv_appl1 … H) -H *
 [ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1/
@@ -110,10 +110,10 @@ elim (cpxs_inv_appl1 … H) -H *
 qed-.
 
 (* Basic_1: was just: pr3_iso_appls_abbr *)
-lemma cpxs_fwd_theta_vector: ∀h,g,L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
-                             ∀a,V,T,U. ⦃h, L⦄ ⊢ ⒶV1s.ⓓ{a}V.T ➡*[g] U →
-                             ⒶV1s. ⓓ{a}V. T ≃ U ∨ ⦃h, L⦄ ⊢ ⓓ{a}V.ⒶV2s.T ➡*[g] U.
-#h #g #L #V1s #V2s * -V1s -V2s /3 width=1/
+lemma cpxs_fwd_theta_vector: ∀h,g,G,L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
+                             ∀a,V,T,U. ⦃G, L⦄ ⊢ ⒶV1s.ⓓ{a}V.T ➡*[h, g] U →
+                             ⒶV1s. ⓓ{a}V. T ≃ U ∨ ⦃G, L⦄ ⊢ ⓓ{a}V.ⒶV2s.T ➡*[h, g] U.
+#h #g #G #L #V1s #V2s * -V1s -V2s /3 width=1/
 #V1s #V2s #V1a #V2a #HV12a #HV12s #a
 generalize in match HV12a; -HV12a
 generalize in match V2a; -V2a
@@ -159,11 +159,11 @@ elim (cpxs_inv_appl1 … H) -H *
 qed-.
 
 (* Basic_1: was just: pr3_iso_appls_cast *)
-lemma cpxs_fwd_cast_vector: ∀h,g,L,Vs,W,T,U. ⦃h, L⦄ ⊢ ⒶVs.ⓝW.T ➡*[g] U →
+lemma cpxs_fwd_cast_vector: ∀h,g,G,L,Vs,W,T,U. ⦃G, L⦄ ⊢ ⒶVs.ⓝW.T ➡*[h, g] U →
                             ∨∨ ⒶVs. ⓝW. T ≃ U
-                             | ⦃h, L⦄ ⊢ ⒶVs.T ➡*[g] U
-                             | ⦃h, L⦄ ⊢ ⒶVs.W ➡*[g] U.
-#h #g #L #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_cast/
+                             | ⦃G, L⦄ ⊢ ⒶVs.T ➡*[h, g] U
+                             | ⦃G, L⦄ ⊢ ⒶVs.W ➡*[h, g] U.
+#h #g #G #L #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_cast/
 #V #Vs #IHVs #W #T #U #H
 elim (cpxs_inv_appl1 … H) -H *
 [ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1/
@@ -185,7 +185,7 @@ elim (cpxs_inv_appl1 … H) -H *
     @(cpxs_strap1 … (ⓐV0.ⓓ{b}V2.T0)) [ /2 width=1/ ] -V -Vs -T /2 width=3/
   | @or3_intro2 -T (**) (* explicit constructor *)
     @(cpxs_trans … HU) -U
-    @(cpxs_strap1 … (ⓐV0.ⓓ{b}V2.T0)) [ /2 width=1/ ] -V -Vs -W /2 width=3/  
+    @(cpxs_strap1 … (ⓐV0.ⓓ{b}V2.T0)) [ /2 width=1/ ] -V -Vs -W /2 width=3/
   ]
 ]
 qed-.