-lemma fpbg_fdeq_trans: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ >[h, o] ⦃G, L, T⦄ →
- ∀G2,L2,T2. ⦃G, L, T⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
-/3 width=5 by fpbg_fpbq_trans, fpbq_fdeq/ qed-.
+lemma fpbg_feqx_trans:
+ ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ > ❪G,L,T❫ →
+ ∀G2,L2,T2. ❪G,L,T❫ ≛ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
+/3 width=5 by fpbg_fpbq_trans, fpbq_feqx/ qed-.
+
+(* Properties with t-bound rt-transition for terms **************************)
+
+lemma cpm_tneqx_cpm_fpbg (h) (G) (L):
+ ∀n1,T1,T. ❪G,L❫ ⊢ T1 ➡[h,n1] T → (T1 ≛ T → ⊥) →
+ ∀n2,T2. ❪G,L❫ ⊢ T ➡[h,n2] T2 → ❪G,L,T1❫ > ❪G,L,T2❫.
+/4 width=5 by fpbq_fpbs, cpm_fpbq, cpm_fpb, ex2_3_intro/ qed.