inductive fpb (G1) (L1) (T1): relation3 genv lenv term ≝
| fpb_fqu: ∀G2,L2,T2. ❪G1,L1,T1❫ ⬂ ❪G2,L2,T2❫ → fpb G1 L1 T1 G2 L2 T2
-| fpb_cpx: â\88\80T2. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88 T2 â\86\92 (T1 â\89\9b T2 → ⊥) → fpb G1 L1 T1 G1 L1 T2
-| fpb_lpx: â\88\80L2. â\9dªG1,L1â\9d« â\8a¢ â¬\88 L2 â\86\92 (L1 â\89\9b[T1] L2 → ⊥) → fpb G1 L1 T1 G1 L2 T1
+| fpb_cpx: â\88\80T2. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88 T2 â\86\92 (T1 â\89\85 T2 → ⊥) → fpb G1 L1 T1 G1 L1 T2
+| fpb_lpx: â\88\80L2. â\9dªG1,L1â\9d« â\8a¢ â¬\88 L2 â\86\92 (L1 â\89\85[T1] L2 → ⊥) → fpb G1 L1 T1 G1 L2 T1
.
interpretation
(* Basic_2A1: includes: cpr_fpb *)
lemma cpm_fpb (h) (n) (G) (L):
- â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h,n] T2 â\86\92 (T1 â\89\9b T2 → ⊥) → ❪G,L,T1❫ ≻ ❪G,L,T2❫.
+ â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h,n] T2 â\86\92 (T1 â\89\85 T2 → ⊥) → ❪G,L,T1❫ ≻ ❪G,L,T2❫.
/3 width=3 by fpb_cpx, cpm_fwd_cpx/ qed.
lemma lpr_fpb (h) (G) (T):
- â\88\80L1,L2. â\9dªG,L1â\9d« â\8a¢ â\9e¡[h,0] L2 â\86\92 (L1 â\89\9b[T] L2 → ⊥) → ❪G,L1,T❫ ≻ ❪G,L2,T❫.
+ â\88\80L1,L2. â\9dªG,L1â\9d« â\8a¢ â\9e¡[h,0] L2 â\86\92 (L1 â\89\85[T] L2 → ⊥) → ❪G,L1,T❫ ≻ ❪G,L2,T❫.
/3 width=2 by fpb_lpx, lpr_fwd_lpx/ qed.