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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_drops.ma
index 0c319c2ea..78f28e9b1 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_drops.ma
@@ -21,8 +21,8 @@ include "basic_2/rt_transition/cpx.ma".
 
 (* Basic_2A1: was: cpx_delta *)
 lemma cpx_delta_drops: ∀h,I,G,L,K,V,V2,W2,i.
-                       ⬇*[i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ⬈[h] V2 →
-                       ⬆*[⫯i] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ⬈[h] W2.
+                       ⬇*[i] L ≘ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ⬈[h] V2 →
+                       ⬆*[⫯i] V2 ≘ W2 → ⦃G, L⦄ ⊢ #i ⬈[h] W2.
 #h * #G #L #K #V #V2 #W2 #i #HLK *
 /3 width=7 by cpg_ell_drops, cpg_delta_drops, ex_intro/
 qed.
@@ -33,8 +33,8 @@ qed.
 lemma cpx_inv_atom1_drops: ∀h,I,G,L,T2. ⦃G, L⦄ ⊢ ⓪{I} ⬈[h] T2 →
                            ∨∨ T2 = ⓪{I}
                             | ∃∃s. T2 = ⋆(next h s) & I = Sort s
-                            | ∃∃J,K,V,V2,i. ⬇*[i] L ≡ K.ⓑ{J}V & ⦃G, K⦄ ⊢ V ⬈[h] V2 &
-                                            ⬆*[⫯i] V2 ≡ T2 & I = LRef i.
+                            | ∃∃J,K,V,V2,i. ⬇*[i] L ≘ K.ⓑ{J}V & ⦃G, K⦄ ⊢ V ⬈[h] V2 &
+                                            ⬆*[⫯i] V2 ≘ T2 & I = LRef i.
 #h #I #G #L #T2 * #c #H elim (cpg_inv_atom1_drops … H) -H *
 /4 width=9 by or3_intro0, or3_intro1, or3_intro2, ex4_5_intro, ex2_intro, ex_intro/
 qed-.
@@ -42,8 +42,8 @@ qed-.
 (* Basic_2A1: was: cpx_inv_lref1 *)
 lemma cpx_inv_lref1_drops: ∀h,G,L,T2,i. ⦃G, L⦄ ⊢ #i ⬈[h] T2 →
                            T2 = #i ∨
-                           ∃∃J,K,V,V2. ⬇*[i] L ≡ K. ⓑ{J}V & ⦃G, K⦄ ⊢ V ⬈[h] V2 &
-                                       ⬆*[⫯i] V2 ≡ T2.
+                           ∃∃J,K,V,V2. ⬇*[i] L ≘ K. ⓑ{J}V & ⦃G, K⦄ ⊢ V ⬈[h] V2 &
+                                       ⬆*[⫯i] V2 ≘ T2.
 #h #G #L #T1 #i * #c #H elim (cpg_inv_lref1_drops … H) -H *
 /4 width=7 by ex3_4_intro, ex_intro, or_introl, or_intror/
 qed-.