proposition: Lemma axAUeq s t : mprv (AU s t <--> t :\/: s :/\: AX (AU s t)).
proof: Proof. rule axAI. - apply: rAU_ind; first exact: axOIl. rewrite /Or. do 3 Intro. ApplyH axAI. apply: rRot => /=. Rev. drop. apply: rNorm. Intro. ApplyH (ax_case t); Intro; first by ApplyH axAUI. ApplyH axAUf; [ApplyH axAEl|ApplyH axAEr]; Apply* 1. - rule axOE; first exact: axAUI. rule axAcase. exact: axAUf. Qed.
imports: mathcomp(all_ssreflect) CompDecModal.libs(edone base fset induced_sym) Setoid Morphisms Relation_Definitions