proposition: Lemma dirim_set1_P f x y: inc y (im_of_singleton f x) <-> inc (J x y) f.
proof: Proof. apply: (iff_trans (dirim_P f _ y)). split; [ by move => [z /set1_P ->] | move => pf; ex_tac; fprops ]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)