-lemma csx_tdeq_trans: ∀h,o,G,L,T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
- ∀T2. T1 ≡[h, o] T2 → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
-#h #o #G #L #T1 #H @(csx_ind … H) -T1 #T #_ #IH #T2 #HT2
-@csx_intro #T1 #HT21 #HnT21 elim (tdeq_cpx_trans … HT2 … HT21) -HT21
-/4 width=5 by tdeq_repl/
+lemma csx_teqg_trans (S) (G) (L):
+ reflexive … S → symmetric … S →
+ ∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 →
+ ∀T2. T1 ≛[S] T2 → ❪G,L❫ ⊢ ⬈*𝐒 T2.
+#S #G #L #H1S #H2S #T1 #H @(csx_ind … H) -T1 #T #_ #IH #T2 #HT2
+@csx_intro #T1 #HT21 #HnT21
+lapply (teqg_cpx_trans … HT2 … HT21) // -HT21 #HT1
+/5 width=4 by teqg_teqx, teqg_canc_sn, teqg_refl/