inductive fpb (h) (o) (G1) (L1) (T1): relation3 genv lenv term ≝
| fpb_fqu : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → fpb h o G1 L1 T1 G2 L2 T2
-| fpb_cpx : â\88\80T2. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88[h] T2 â\86\92 (T1 â\89¡[h, o] T2 → ⊥) → fpb h o G1 L1 T1 G1 L1 T2
-| fpb_lfpx: â\88\80L2. â¦\83G1, L1â¦\84 â\8a¢ â¬\88[h, T1] L2 â\86\92 (L1 â\89¡[h, o, T1] L2 → ⊥) → fpb h o G1 L1 T1 G1 L2 T1
+| fpb_cpx : â\88\80T2. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88[h] T2 â\86\92 (T1 â\89\9b[h, o] T2 → ⊥) → fpb h o G1 L1 T1 G1 L1 T2
+| fpb_lfpx: â\88\80L2. â¦\83G1, L1â¦\84 â\8a¢ â¬\88[h, T1] L2 â\86\92 (L1 â\89\9b[h, o, T1] L2 → ⊥) → fpb h o G1 L1 T1 G1 L2 T1
.
interpretation
(* Basic properties *********************************************************)
(* Basic_2A1: includes: cpr_fpb *)
-lemma cpm_fpb: â\88\80n,h,o,G,L,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡[n, h] T2 â\86\92 (T1 â\89¡[h, o] T2 → ⊥) →
+lemma cpm_fpb: â\88\80n,h,o,G,L,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡[n, h] T2 â\86\92 (T1 â\89\9b[h, o] T2 → ⊥) →
⦃G, L, T1⦄ ≻[h, o] ⦃G, L, T2⦄.
/3 width=2 by fpb_cpx, cpm_fwd_cpx/ qed.
(* Basic_2A1: includes: lpr_fpb *)
-lemma lfpr_fpb: â\88\80h,o,G,L1,L2,T. â¦\83G, L1â¦\84 â\8a¢ â\9e¡[h, T] L2 â\86\92 (L1 â\89¡[h, o, T] L2 → ⊥) →
+lemma lfpr_fpb: â\88\80h,o,G,L1,L2,T. â¦\83G, L1â¦\84 â\8a¢ â\9e¡[h, T] L2 â\86\92 (L1 â\89\9b[h, o, T] L2 → ⊥) →
⦃G, L1, T⦄ ≻[h, o] ⦃G, L2, T⦄.
/3 width=1 by fpb_lfpx, lfpr_fwd_lfpx/ qed.