proposition: Lemma diagonal_is_identity x: diagonal x = identity_g x.
proof: Proof. set_extens t. move /diagonal_i_P => [pt Pt eql]; rewrite -pt -eql;apply /funI_P; ex_tac. by move /funI_P => [z zx ->]; apply/diagonal_pi_P. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)