-axiom tdeq_canc_sn: ∀h,o. left_cancellable … (tdeq h o).
-
-lemma tdeq_cpx_trans: ∀h,o,U1,T1. U1 ≡[h, o] T1 → ∀G,L,T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 →
- ∃∃U2. ⦃G, L⦄ ⊢ U1 ⬈[h] U2 & U2 ≡[h, o] T2.
-#h #o #U1 #T1 #HUT1 #G #L #T2 #HT12
-elim (cpx_tdeq_conf_lexs … o … HT12 … U1 … L … L) /3 width=3 by tdeq_sym, ex2_intro/
-qed-.
-
-lemma tdeq_cpxs_trans: ∀h,o,U1,T1. U1 ≡[h, o] T1 → ∀G,L,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 →
- ∃∃U2. ⦃G, L⦄ ⊢ U1 ⬈*[h] U2 & U2 ≡[h, o] T2.
-#h #o #U1 #T1 #HUT1 #G #L #T2 #HT12 @(cpxs_ind … HT12) -T2 /2 width=3 by ex2_intro/
+lemma tdeq_cpxs_trans: ∀h,U1,T1. U1 ≛ T1 → ∀G,L,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 →
+ ∃∃U2. ⦃G, L⦄ ⊢ U1 ⬈*[h] U2 & U2 ≛ T2.
+#h #U1 #T1 #HUT1 #G #L #T2 #HT12 @(cpxs_ind … HT12) -T2 /2 width=3 by ex2_intro/