X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcpxs_fqus.ma;h=27fd06b7b0d1d06c786e21439d0916801349c569;hb=6167cca50de37eba76a062537b24f7caef5b34f2;hp=9ecbc31c60794963d26550bc1ca5d4060093709a;hpb=6d49221c1fefe6a2c5bddb3db24d3698414a700f;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
index 9ecbc31c6..27fd06b7b 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
@@ -55,8 +55,8 @@ qed-.
 
 (* Note: a proof based on fqu_cpx_trans_ntdeq might exist *)
 lemma fqu_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
-                            ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≡[h, o] U2 → ⊥) →
-                            ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐[b] ⦃G2, L2, U2⦄.
+                            ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≛[h, o] U2 → ⊥) →
+                            ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≛[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐[b] ⦃G2, L2, U2⦄.
 #h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 [ #I #G #L #V1 #V2 #HV12 #_ elim (lifts_total V2 𝐔❴1❵)
   #U2 #HVU2 @(ex3_intro … U2)
@@ -87,8 +87,8 @@ lemma fqu_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b]
 qed-.
 
 lemma fquq_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
-                             ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≡[h, o] U2 → ⊥) →
-                             ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐⸮[b] ⦃G2, L2, U2⦄.
+                             ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≛[h, o] U2 → ⊥) →
+                             ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≛[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐⸮[b] ⦃G2, L2, U2⦄.
 #h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 elim H12 -H12
 [ #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_ntdeq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fquq, ex3_intro/
@@ -97,8 +97,8 @@ lemma fquq_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮
 qed-.
 
 lemma fqup_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
-                             ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≡[h, o] U2 → ⊥) →
-                             ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐+[b] ⦃G2, L2, U2⦄.
+                             ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≛[h, o] U2 → ⊥) →
+                             ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≛[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐+[b] ⦃G2, L2, U2⦄.
 #h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1
 [ #G1 #L1 #T1 #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_ntdeq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fqup, ex3_intro/
@@ -109,8 +109,8 @@ lemma fqup_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b
 qed-.
 
 lemma fqus_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
-                             ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≡[h, o] U2 → ⊥) →
-                             ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐*[b] ⦃G2, L2, U2⦄.
+                             ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≛[h, o] U2 → ⊥) →
+                             ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≛[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐*[b] ⦃G2, L2, U2⦄.
 #h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fqus_inv_fqup … H12) -H12
 [ #H12 elim (fqup_cpxs_trans_ntdeq … H12 … HTU2 H) -T2
   /3 width=4 by fqup_fqus, ex3_intro/