DEFINITION llt_wf__q_ind()
TYPE =
∀P:A→Prop
.∀n:nat.(λP0:A→Prop.λn0:nat.∀a:A.(eq nat (lweight a) n0)→(P0 a) P n)
→∀a:A.(P a)
BODY =
we must prove
∀P:A→Prop
.∀n:nat.(λP0:A→Prop.λn0:nat.∀a:A.(eq nat (lweight a) n0)→(P0 a) P n)
→∀a:A.(P a)
or equivalently
∀P:A→Prop
.(∀n:nat.∀a:A.(eq nat (lweight a) n)→(P a))→∀a:A.(P a)
assume P: A→Prop
suppose H: ∀n:nat.∀a:A.(eq nat (lweight a) n)→(P a)
assume a: A
by (refl_equal . .)
we proved eq nat (lweight a) (lweight a)
by (H . . previous)
we proved P a
we proved
∀P:A→Prop
.(∀n:nat.∀a:A.(eq nat (lweight a) n)→(P a))→∀a:A.(P a)
that is equivalent to
∀P:A→Prop
.∀n:nat.(λP0:A→Prop.λn0:nat.∀a:A.(eq nat (lweight a) n0)→(P0 a) P n)
→∀a:A.(P a)