DEFINITION lift_weight()
TYPE =
∀t:T.∀h:nat.∀d:nat.(eq nat (weight (lift h d t)) (weight t))
BODY =
assume t: T
assume h: nat
assume d: nat
assume m: nat
suppose : le d m
by (refl_equal . .)
we proved eq nat O O
we proved ∀m:nat.(le d m)→(eq nat O O)
by (lift_weight_map . . . . previous)
we proved eq nat (weight_map λ:nat.O (lift h d t)) (weight_map λ:nat.O t)
that is equivalent to eq nat (weight (lift h d t)) (weight t)
we proved ∀t:T.∀h:nat.∀d:nat.(eq nat (weight (lift h d t)) (weight t))