-lemma cnx_tdeq_trans: ∀h,o,G,L,T1. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃T1⦄ →
- ∀T2. T1 ≡[h, o] T2 → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃T2⦄.
-#h #o #G #L #T1 #HT1 #T2 #HT12 #T #HT2
-elim (tdeq_cpx_trans … HT12 … HT2) -HT2 #T0 #HT10 #HT0
-lapply (HT1 … HT10) -HT1 -HT10 /2 width=5 by tdeq_repl/ (**) (* full auto fails *)
+lemma cnx_teqx_trans (G) (L):
+ ∀T1. ❪G,L❫ ⊢ ⬈𝐍 T1 → ∀T2. T1 ≅ T2 → ❪G,L❫ ⊢ ⬈𝐍 T2.
+#G #L #T1 #HT1 #T2 #HT12 #T #HT2
+lapply (teqx_cpx_trans … HT12 … HT2) -HT2 #H
+lapply (HT1 … H) -HT1 -H /2 width=5 by teqx_canc_sn/ (**) (* full auto fails *)