-lemma cpms_tdneq_fwd_fpbg (h) (o) (n): ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 →
- (T1 ≛[h,o] T2 → ⊥) → ⦃G,L,T1⦄ >[h,o] ⦃G,L,T2⦄.
-/3 width=2 by cpms_fwd_cpxs, cpxs_tdneq_fpbg/ qed-.
-
-lemma fpbg_cpms_trans (h) (o) (n): ∀G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ >[h,o] ⦃G2, L2, T⦄ →
- ∀T2. ⦃G2, L2⦄ ⊢ T ➡*[n,h] T2 → ⦃G1, L1, T1⦄ >[h,o] ⦃G2, L2, T2⦄.
+lemma cpms_tneqx_fwd_fpbg (h) (n):
+ ∀G,L,T1,T2. ❪G,L❫ ⊢ T1 ➡*[n,h] T2 →
+ (T1 ≛ T2 → ⊥) → ❪G,L,T1❫ >[h] ❪G,L,T2❫.
+/3 width=2 by cpms_fwd_cpxs, cpxs_tneqx_fpbg/ qed-.
+
+lemma fpbg_cpms_trans (h) (n):
+ ∀G1,G2,L1,L2,T1,T. ❪G1,L1,T1❫ >[h] ❪G2,L2,T❫ →
+ ∀T2. ❪G2,L2❫ ⊢ T ➡*[n,h] T2 → ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.