(* Basic_2A1: uses: fpbg_fleq_trans *)
lemma fpbg_feqx_trans:
∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ > ❪G,L,T❫ →
- â\88\80G2,L2,T2. â\9dªG,L,Tâ\9d« â\89\9b ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
+ â\88\80G2,L2,T2. â\9dªG,L,Tâ\9d« â\89\85 ❪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):
- â\88\80n1,T1,T. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h,n1] T â\86\92 (T1 â\89\9b T → ⊥) →
+ â\88\80n1,T1,T. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h,n1] T â\86\92 (T1 â\89\85 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.