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