DEFINITION le_trans_plus_r()
TYPE =
∀x:nat.∀y:nat.∀z:nat.(le (plus x y) z)→(le y z)
BODY =
assume x: nat
assume y: nat
assume z: nat
suppose H: le (plus x y) z
by (le_plus_r . .)
we proved le y (plus x y)
by (le_trans . . . previous H)
we proved le y z
we proved ∀x:nat.∀y:nat.∀z:nat.(le (plus x y) z)→(le y z)