proposition: Lemma bigA1 (T : choiceType) (pS : pSystem) (F : T -> pS) (s : T) : mprv ((\and_(s <- [fset s]) F s) <--> F s).
proof: Proof. rewrite fset1Es. rule axAI. rewrite big_cons big_nil. by rewrite -> axAEl. apply: bigAI => ?. by rewrite inE => /eqP ->. Qed.
imports: mathcomp(all_ssreflect) CompDecModal.libs(edone base fset induced_sym) Setoid Morphisms Relation_Definitions