proposition: Lemma inf_pr2 r x y z: order r -> gle r z x -> gle r z y -> (forall t, gle r t x -> gle r t y -> gle r t z) -> inf r x y = z.
proof: Proof. move=> or zx zy h. move: (glb_set2 or zx zy h) => aux. symmetry;apply: infimum_pr2 => //. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)