proposition: Lemma ltR_min z : z < min x y <-> z < x /\ z < y.
proof: Proof. case: (min x y) / IFR_cases => _ [[lexy]|[ltyx]] ->. by split=> [ltzx|[]//]; split=> //; apply: ltR_le_trans ltzx lexy. by split=> [ltzy|[]//]; split=> //; apply: ltR_trans ltzy ltyx. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div order) mathcomp(ssralg ssrnum ssrint rat intdiv) Coq(Morphisms Setoid) fourcolor(real realsyntax)