DEFINITION K_ind()
TYPE =
∀P:K→Prop
.(∀b:B.(P (Bind b)))→(∀f:F.(P (Flat f)))→∀k:K.(P k)
BODY =
assume P: K→Prop
suppose H: ∀b:B.(P (Bind b))
suppose H1: ∀f:F.(P (Flat f))
assume k: K
by cases on k we prove P k
case Bind b:B ⇒
the thesis becomes P (Bind b)
by (H .)
P (Bind b)
case Flat f:F ⇒
the thesis becomes P (Flat f)
by (H1 .)
P (Flat f)
we proved P k
we proved
∀P:K→Prop
.(∀b:B.(P (Bind b)))→(∀f:F.(P (Flat f)))→∀k:K.(P k)