Step
*
1
of Lemma
last_induction
1. [T] : Type
2. [Q] : (T List) ⟶ ℙ
3. Q[[]]
4. ∀ys:T List. ∀y:T. (Q[ys]
⇒ Q[ys @ [y]])
5. n : ℕ
6. zs : T List
7. ∀z1:T List. (||z1|| < ||zs||
⇒ Q[z1])
8. ↑null(zs)
⊢ Q[zs]
BY
{ (DVar `zs' THEN All Reduce THEN Auto) }
Latex:
Latex:
1. [T] : Type
2. [Q] : (T List) {}\mrightarrow{} \mBbbP{}
3. Q[[]]
4. \mforall{}ys:T List. \mforall{}y:T. (Q[ys] {}\mRightarrow{} Q[ys @ [y]])
5. n : \mBbbN{}
6. zs : T List
7. \mforall{}z1:T List. (||z1|| < ||zs|| {}\mRightarrow{} Q[z1])
8. \muparrow{}null(zs)
\mvdash{} Q[zs]
By
Latex:
(DVar `zs' THEN All Reduce THEN Auto)
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