DEFINITION land_ind()
TYPE =
∀A:Prop.∀B:Prop.∀P:Prop.(A→B→P)→(land A B)→P
BODY =
assume A: Prop
assume B: Prop
assume P: Prop
suppose H: A→B→P
suppose H1: land A B
by cases on H1 we prove P
case conj H2:A H3:B ⇒
the thesis becomes P
by (H H2 H3)
P
we proved P
we proved ∀A:Prop.∀B:Prop.∀P:Prop.(A→B→P)→(land A B)→P