proposition: Lemma eq_bigmin_cond (A : pred I) F : #|A| > 0 -> {i0 | i0 \in A & \min_(i in A) F i = F i0}.
proof: Proof. case: (pickP A) => [i0 Ai0 _ | ]; last by move/eq_card0->. by exists [arg min_(i < i0 in A) F i]; [case: arg_minnP | apply: bigmin_eq_arg]. Qed.
imports: HB(structures) mathcomp(all_ssreflect)