-(* Advanced eliminators on atomica arity assignment for terms ***************)
-
-fact aaa_ind_fpb_aux: ∀h,o. ∀R:relation3 genv lenv term.
- (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
- (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
- R G1 L1 T1
- ) →
- ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ∀A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
-#h #o #R #IH #G #L #T #H @(csx_ind_fpb … H) -G -L -T
+fact aaa_ind_fpb_aux (Q:relation3 …):
+ (∀G1,L1,T1,A.
+ ❪G1,L1❫ ⊢ T1 ⁝ A →
+ (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → Q G2 L2 T2) →
+ Q G1 L1 T1
+ ) →
+ ∀G,L,T. ❪G,L❫ ⊢ ⬈*𝐒 T → ∀A. ❪G,L❫ ⊢ T ⁝ A → Q G L T.
+#R #IH #G #L #T #H @(csx_ind_fpb … H) -G -L -T