proposition: Lemma setX1_P x a y: inc y (product1 x a) <-> [/\ fgraph y, domain y = singleton a & inc (Vg y a) x].
proof: Proof. apply: (iff_trans (setXf_P _ _ _)); split; move=> [pa pb pc];split => //. apply: pc; fprops. by move => i /set1_P ->. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)