update in static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpxs_teqo_vector.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_teqo_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_teqo_vector.ma
index 5bc7ef7800e37f8d24f2a0ec2572f4ed8d775df1..f12edb09ff070376d0e07b1b34aa3df3754b3d84 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_teqo_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_teqo_vector.ma
@@ -21,7 +21,7 @@ include "basic_2/rt_computation/cpxs_teqo.ma".
 (* Vector form of forward lemmas with outer equivalence for terms ***********)
 
 lemma cpxs_fwd_sort_vector (G) (L):
-      ∀s,Vs,X2. ❪G,L❫ ⊢ ⒶVs.⋆s ⬈* X2 → ⒶVs.⋆s ⩳ X2.
+      ∀s,Vs,X2. ❪G,L❫ ⊢ ⒶVs.⋆s ⬈* X2 → ⒶVs.⋆s ~ X2.
 #G #L #s #Vs elim Vs -Vs /2 width=4 by cpxs_fwd_sort/
 #V #Vs #IHVs #X2 #H
 elim (cpxs_inv_appl1 … H) -H *
@@ -40,7 +40,7 @@ lemma cpxs_fwd_delta_drops_vector (I) (G) (L) (K):
       ∀V1,i. ⇩[i] L ≘ K.ⓑ[I]V1 →
       ∀V2. ⇧[↑i] V1 ≘ V2 →
       ∀Vs,X2. ❪G,L❫ ⊢ ⒶVs.#i ⬈* X2 →
-      ∨∨ ⒶVs.#i ⩳ X2 | ❪G,L❫ ⊢ ⒶVs.V2 ⬈* X2.
+      ∨∨ ⒶVs.#i ~ X2 | ❪G,L❫ ⊢ ⒶVs.V2 ⬈* X2.
 #I #G #L #K #V1 #i #HLK #V2 #HV12 #Vs
 elim Vs -Vs /2 width=5 by cpxs_fwd_delta_drops/
 #V #Vs #IHVs #X2 #H -K -V1
@@ -66,7 +66,7 @@ qed-.
 (* Basic_1: was just: pr3_iso_appls_beta *)
 lemma cpxs_fwd_beta_vector (p) (G) (L):
       ∀Vs,V,W,T,X2. ❪G,L❫ ⊢ ⒶVs.ⓐV.ⓛ[p]W.T ⬈* X2 →
-      ∨∨ ⒶVs.ⓐV.ⓛ[p]W. T ⩳ X2 | ❪G,L❫ ⊢ ⒶVs.ⓓ[p]ⓝW.V.T ⬈* X2.
+      ∨∨ ⒶVs.ⓐV.ⓛ[p]W. T ~ X2 | ❪G,L❫ ⊢ ⒶVs.ⓓ[p]ⓝW.V.T ⬈* X2.
 #p #G #L #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_beta/
 #V0 #Vs #IHVs #V #W #T #X2 #H
 elim (cpxs_inv_appl1 … H) -H *
@@ -92,7 +92,7 @@ qed-.
 lemma cpxs_fwd_theta_vector (G) (L):
       ∀V1b,V2b. ⇧[1] V1b ≘ V2b →
       ∀p,V,T,X2. ❪G,L❫ ⊢ ⒶV1b.ⓓ[p]V.T ⬈* X2 →
-      ∨∨ ⒶV1b.ⓓ[p]V.T ⩳ X2 | ❪G,L❫ ⊢ ⓓ[p]V.ⒶV2b.T ⬈* X2.
+      ∨∨ ⒶV1b.ⓓ[p]V.T ~ X2 | ❪G,L❫ ⊢ ⓓ[p]V.ⒶV2b.T ⬈* X2.
 #G #L #V1b #V2b * -V1b -V2b /3 width=1 by or_intror/
 #V1b #V2b #V1a #V2a #HV12a #HV12b #p
 generalize in match HV12a; -HV12a
@@ -141,7 +141,7 @@ qed-.
 (* Basic_1: was just: pr3_iso_appls_cast *)
 lemma cpxs_fwd_cast_vector (G) (L):
       ∀Vs,W,T,X2. ❪G,L❫ ⊢ ⒶVs.ⓝW.T ⬈* X2 →
-      ∨∨ ⒶVs. ⓝW. T ⩳ X2
+      ∨∨ ⒶVs. ⓝW. T ~ X2
        | ❪G,L❫ ⊢ ⒶVs.T ⬈* X2
        | ❪G,L❫ ⊢ ⒶVs.W ⬈* X2.
 #G #L #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_cast/
@@ -173,7 +173,7 @@ qed-.
 (* Basic_1: was just: nf2_iso_appls_lref *)
 lemma cpxs_fwd_cnx_vector (G) (L):
       ∀T. 𝐒❪T❫ → ❪G,L❫ ⊢ ⬈𝐍 T →
-      ∀Vs,X2. ❪G,L❫ ⊢ ⒶVs.T ⬈* X2 → ⒶVs.T ⩳ X2.
+      ∀Vs,X2. ❪G,L❫ ⊢ ⒶVs.T ⬈* X2 → ⒶVs.T ~ X2.
 #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 #X2 #H
 elim (cpxs_inv_appl1 … H) -H *