(* Advanced eliminators *****************************************************)
-lemma csx_ind_fpb: ∀h,o. ∀R:relation3 genv lenv term.
+lemma csx_ind_fpb: ∀h,o. ∀Q:relation3 genv lenv term.
(∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
- (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
- R G1 L1 T1
+ (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+ Q G1 L1 T1
) →
- ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → R G L T.
+ ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → Q G L T.
/4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_alt/ qed-.
-lemma csx_ind_fpbg: ∀h,o. ∀R:relation3 genv lenv term.
+lemma csx_ind_fpbg: ∀h,o. ∀Q:relation3 genv lenv term.
(∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
- (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
- R G1 L1 T1
+ (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+ Q G1 L1 T1
) →
- ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → R G L T.
+ ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → Q G L T.
/4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_fpbg/ qed-.