proposition: Lemma leq_gen_scale_saturated : forall (f:E1)(x y u:E), leq_gen f x y -> is_leq_gen_scale f u -> inc y u -> inc x u.
proof: Proof. ir. cp H. uh H. nin H. ee. assert (is_leq_gen_scale f (U x0)). uhg; sh x0; xd. nin (leq_gen_scale_or H0 H4). assert (scale_subset u x0). apply leq_gen_scale_subset with f. am. am. am. uh H6; ee. apply H8 with y. am. am. ap H5. uh H3; ee; am. Qed.
imports: Arith order