(* Basic eliminators ********************************************************)
lemma fsb_ind_alt: ∀h,g. ∀R: relation3 …. (
- â\88\80G1,L1,T1. â¦\83G1, L1â¦\84 â\8a¢ ⦥[h,g] T1 → (
+ â\88\80G1,L1,T1. ⦥[h,g] â¦\83G1, L1, T1â¦\84 → (
∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2
) → R G1 L1 T1
) →
- â\88\80G,L,T. â¦\83G, Lâ¦\84 â\8a¢ ⦥[h, g] T → R G L T.
+ â\88\80G,L,T. ⦥[h, g] â¦\83G, L, Tâ¦\84 → R G L T.
#h #g #R #IH #G #L #T #H elim H -G -L -T
/4 width=1 by fsb_intro/
qed-.
(* Basic inversion lemmas ***************************************************)
-lemma fsb_inv_csx: â\88\80h,g,G,L,T. â¦\83G, Lâ¦\84 â\8a¢ ⦥[h, g] T → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
+lemma fsb_inv_csx: â\88\80h,g,G,L,T. ⦥[h, g] â¦\83G, L, Tâ¦\84 → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
#h #g #G #L #T #H elim H -G -L -T /5 width=1 by csx_intro, fpb_cpx/
qed-.