proposition: Lemma EXR_ind s t u : mprv (u ---> EX (t :/\: (s :\/: u))) -> mprv (u ---> EX (ER s t)).
proof: Proof. move => IH. rewrite -> IH. apply: rEXn. apply: rER_ind. exact: axAEl. rewrite <- IH. rule axAcase. drop. exact: axI. Qed.
imports: mathcomp(all_ssreflect) CompDecModal.libs(edone base fset induced_sym) Setoid Morphisms Relation_Definitions