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