proposition: Lemma ExistsUnique2 : (forall A (P : A -> A -> Prop), (exists !x, exists !y, P x y) -> (exists !x, exists y, P x y) /\ (exists !x, exists y, P y x)) -> False.
proof: Proof. move/(_ _ _ qlm); rewrite /Q/=; case=> H1 H2. case: H1; case; case; case; case=> //= _. - move=>G1; move:(G1 false)=>/=G2. by suff: true = false by []; last by apply: G2; exists true. - move=>G1; move:(G1 true)=>/=G2. by suff: false = true by []; last by apply: G2; exists true. - move=>G1; move:(G1 true)=>/=G2. by suff: false = true by []; last by apply: G2; exists true. Qed.
imports: mathcomp(ssreflect ssrnat prime ssrbool eqtype)