proposition: Lemma inl_sumP S x: inc x (inl_sum S) <-> [/\ pairp x, inc (Q x) (isI S) & inc (P x) (Vg (isE S) (Q x))].
proof: Proof. split; first by case/disjointU_P; rewrite is_domain_E. by move => [ha hb hc]; apply /disjointU_P; rewrite is_domain_E. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)