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