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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fqus.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fqus.ma
index 147114a11..0744bd0fc 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fqus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fqus.ma
@@ -67,8 +67,8 @@ lemma fqus_cpx_trans: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2,
 qed-.
 
 lemma fqu_cpx_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)
@@ -99,8 +99,8 @@ lemma fqu_cpx_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] 
 qed-.
 
 lemma fquq_cpx_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_cpx_trans_ntdeq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fquq, ex3_intro/
@@ -109,8 +109,8 @@ lemma fquq_cpx_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[
 qed-.
 
 lemma fqup_cpx_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_cpx_trans_ntdeq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fqup, ex3_intro/
@@ -121,8 +121,8 @@ lemma fqup_cpx_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b]
 qed-.
 
 lemma fqus_cpx_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_cpx_trans_ntdeq … H12 … HTU2 H) -T2
   /3 width=4 by fqup_fqus, ex3_intro/