lemma lt_le_transitive: ∀A:excess.∀x,y,z:A.x < y → y ≤ z → x < z.
intros (A x y z LT LE); cases LT (LEx APx); split; [apply (le_transitive ???? LEx LE)]
lemma lt_le_transitive: ∀A:excess.∀x,y,z:A.x < y → y ≤ z → x < z.
intros (A x y z LT LE); cases LT (LEx APx); split; [apply (le_transitive ???? LEx LE)]