update in static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_teqo.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_teqo.ma
index 276d8c18fff5be187b3559572b37cd97542fdfdd..0ffa64fb35a312b3859ecc6cab0ad72975b518b8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_teqo.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_teqo.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "static_2/syntax/teqo_teqx.ma".
+include "static_2/syntax/teqo_teqg.ma".
 include "basic_2/rt_computation/cpxs_lsubr.ma".
 include "basic_2/rt_computation/cpxs_cnx.ma".
 include "basic_2/rt_computation/lpxs_cpxs.ma".
@@ -22,7 +22,7 @@ include "basic_2/rt_computation/lpxs_cpxs.ma".
 (* Forward lemmas with sort-irrelevant outer equivalence for terms **********)
 
 lemma cpxs_fwd_sort (G) (L):
-      ∀X2,s1. ❪G,L❫ ⊢ ⋆s1 ⬈* X2 → ⋆s1 ⩳ X2.
+      ∀X2,s1. ❪G,L❫ ⊢ ⋆s1 ⬈* X2 → ⋆s1 ~ X2.
 #G #L #X2 #s1 #H
 elim (cpxs_inv_sort1 … H) -H #s2 #H destruct //
 qed-.
@@ -33,7 +33,7 @@ lemma cpxs_fwd_delta_drops (I) (G) (L) (K):
       ∀V1,i. ⇩[i] L ≘ K.ⓑ[I]V1 →
       ∀V2. ⇧[↑i] V1 ≘ V2 →
       ∀X2. ❪G,L❫ ⊢ #i ⬈* X2 →
-      ∨∨ #i ⩳ X2 | ❪G,L❫ ⊢ V2 ⬈* X2.
+      ∨∨ #i ~ X2 | ❪G,L❫ ⊢ V2 ⬈* X2.
 #I #G #L #K #V1 #i #HLK #V2 #HV12 #X2 #H
 elim (cpxs_inv_lref1_drops … H) -H /2 width=1 by or_introl/
 * #I0 #K0 #V0 #U0 #HLK0 #HVU0 #HU0
@@ -44,7 +44,7 @@ qed-.
 (* Basic_1: was just: pr3_iso_beta *)
 lemma cpxs_fwd_beta (p) (G) (L):
       ∀V,W,T,X2. ❪G,L❫ ⊢ ⓐV.ⓛ[p]W.T ⬈* X2 →
-      ∨∨ ⓐV.ⓛ[p]W.T ⩳ X2 | ❪G,L❫ ⊢ ⓓ[p]ⓝW.V.T ⬈* X2.
+      ∨∨ ⓐV.ⓛ[p]W.T ~ X2 | ❪G,L❫ ⊢ ⓓ[p]ⓝW.V.T ⬈* X2.
 #p #G #L #V #W #T #X2 #H elim (cpxs_inv_appl1 … H) -H *
 [ #V0 #T0 #_ #_ #H destruct /2 width=1 by teqo_pair, or_introl/
 | #b #W0 #T0 #HT0 #HU
@@ -59,7 +59,7 @@ qed-.
 lemma cpxs_fwd_theta (p) (G) (L):
            ∀V1,V,T,X2. ❪G,L❫ ⊢ ⓐV1.ⓓ[p]V.T ⬈* X2 →
            ∀V2. ⇧[1] V1 ≘ V2 →
-           ∨∨ ⓐV1.ⓓ[p]V.T ⩳ X2 | ❪G,L❫ ⊢ ⓓ[p]V.ⓐV2.T ⬈* X2.
+           ∨∨ ⓐV1.ⓓ[p]V.T ~ X2 | ❪G,L❫ ⊢ ⓓ[p]V.ⓐV2.T ⬈* X2.
 #p #G #L #V1 #V #T #X2 #H #V2 #HV12
 elim (cpxs_inv_appl1 … H) -H *
 [ -HV12 #V0 #T0 #_ #_ #H destruct /2 width=1 by teqo_pair, or_introl/
@@ -90,7 +90,7 @@ qed-.
 
 lemma cpxs_fwd_cast (G) (L):
       ∀W,T,X2. ❪G,L❫ ⊢ ⓝW.T ⬈* X2 →
-      ∨∨ ⓝW. T ⩳ X2 | ❪G,L❫ ⊢ T ⬈* X2 | ❪G,L❫ ⊢ W ⬈* X2.
+      ∨∨ ⓝW. T ~ X2 | ❪G,L❫ ⊢ T ⬈* X2 | ❪G,L❫ ⊢ W ⬈* X2.
 #G #L #W #T #X2 #H
 elim (cpxs_inv_cast1 … H) -H /2 width=1 by or3_intro1, or3_intro2/ *
 #W0 #T0 #_ #_ #H destruct /2 width=1 by teqo_pair, or3_intro0/
@@ -98,5 +98,5 @@ qed-.
 
 lemma cpxs_fwd_cnx (G) (L):
       ∀T1. ❪G,L❫ ⊢ ⬈𝐍 T1 →
-      ∀X2. ❪G,L❫ ⊢ T1 ⬈* X2 → T1 ⩳ X2.
-/3 width=5 by cpxs_inv_cnx1, teqx_teqo/ qed-.
+      ∀X2. ❪G,L❫ ⊢ T1 ⬈* X2 → T1 ~ X2.
+/3 width=5 by cpxs_inv_cnx1, teqg_teqo/ qed-.