proposition: Lemma bigABBA (T: eqType) (xs: seq T) (F: T -> form) p : prv ((\and_(s <- xs) [p](F s)) ---> [p](\and_(s <- xs) F s)).
proof: Proof. elim: xs => [|t xs IH]. - drop. rewrite big_nil. apply: rNec. exact: axI. - rewrite !big_cons. rewrite -> IH, axABBA. exact: axI. Qed.
imports: Relations Lia Setoid Morphisms mathcomp(all_ssreflect) CompDecModal.libs(edone bcase fset base modular_hilbert sltype rewrite_inequality fset_tac)