proposition: Lemma bigminID a P F : \big[min/x]_(i <- r | P i) F i = min (\big[min/x]_(i <- r | P i && a i) F i) (\big[min/x]_(i <- r | P i && ~~ a i) F i).
proof: Proof. by rewrite (bigID_idem _ _ a) //= minxx. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)