proposition: Lemma setIf_1 f x: intersectionf (singleton x) f = f x.
proof: Proof. set_extens t => tx; first exact :(setIf_hi tx (set1_1 x)). apply: setIf_i; [ fprops | by move=> j; move/set1_P => ->]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)