-lemma cpxs_tdneq_fwd_step_sn: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) →
- ∃∃T,T0. ⦃G, L⦄ ⊢ T1 ⬈[h] T & T1 ≛[h, o] T → ⊥ & ⦃G, L⦄ ⊢ T ⬈*[h] T0 & T0 ≛[h, o] T2.
-#h #o #G #L #T1 #T2 #H @(cpxs_ind_dx … H) -T1
+lemma cpxs_tdneq_fwd_step_sn: ∀h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) →
+ ∃∃T,T0. ⦃G, L⦄ ⊢ T1 ⬈[h] T & T1 ≛ T → ⊥ & ⦃G, L⦄ ⊢ T ⬈*[h] T0 & T0 ≛ T2.
+#h #G #L #T1 #T2 #H @(cpxs_ind_dx … H) -T1