DEFINITION lt_le_e()
TYPE =
∀n:nat.∀d:nat.∀P:Prop.((lt n d)→P)→((le d n)→P)→P
BODY =
assume n: nat
assume d: nat
assume P: Prop
suppose H: (lt n d)→P
suppose H0: (le d n)→P
(H1)
by (le_or_lt . .)
or (le d n) (lt n d)
end of H1
we proceed by induction on H1 to prove P
case or_introl ⇒
the thesis becomes the hypothesis H0
case or_intror ⇒
the thesis becomes the hypothesis H
we proved P
we proved ∀n:nat.∀d:nat.∀P:Prop.((lt n d)→P)→((le d n)→P)→P