inductive fpb (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
| fpb_fquq: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ → fpb h g G1 L1 T1 G2 L2 T2
| fpb_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] T2 → fpb h g G1 L1 T1 G1 L1 T2
-| fpb_lpx : ∀L2. ⦃G1, L1⦄ ⊢ ➡[h, g, T1, 0] L2 → fpb h g G1 L1 T1 G1 L2 T1
+| fpb_llpx: ∀L2. ⦃G1, L1⦄ ⊢ ➡[h, g, T1, 0] L2 → fpb h g G1 L1 T1 G1 L2 T1
.
interpretation
lemma cpr_fpb: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L, T1⦄ ≽[h, g] ⦃G, L, T2⦄.
/3 width=1 by fpb_cpx, cpr_cpx/ qed.
-lemma lpr_fpb: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡[T, 0] L2 → ⦃G, L1, T⦄ ≽[h, g] ⦃G, L2, T⦄.
-/3 width=1 by fpb_lpx, llpr_llpx/ qed.
+lemma llpr_fpb: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡[T, 0] L2 → ⦃G, L1, T⦄ ≽[h, g] ⦃G, L2, T⦄.
+/3 width=1 by fpb_llpx, llpr_llpx/ qed.