proposition: Lemma setIt_constant (I:Set) (f:I ->Set) (x:I): constantp f -> intersectiont f = f x.
proof: Proof. have neI: nonempty I by exists (Ro x); apply: R_inc. move => cf;apply: extensionality; first by apply:setIt_s1. by move => z j;apply: setIt_i => // k; rewrite (cf k x). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)