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