proposition: Lemma candu2P a b x: inc x (canonical_du2 a b) <-> (pairp x /\ ((inc (P x) a /\ Q x = C0) \/ (inc (P x) b /\ Q x = C1))).
proof: Proof. rewrite candu2_rw; split. case /setU2_P; move /indexed_P => [pa pb]; fprops. by move => [pa [] [h1 h2]]; apply/setU2_P; [left | right ]; apply /indexed_P. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)