proposition: Lemma worders_qle_prop E x y: worders_qle E x y -> forall a b, inc a x -> inc b y -> a <=O b.
proof: Proof. move:(worders_eq_equivalence E) => ee. move =>[ha hb [a1 [b1 [ a1x b1y cp1]]]] a b ax bx. move: (related_in_quo ha ax a1x) (related_in_quo hb bx b1y) => qa qb. by apply /(worders_eq_compat_le qa qb). Qed.
imports: mathcomp(ssreflect ssrbool eqtype ssrfun)