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Proof step 100 from proof inv-ls-succ (previous step)

max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1) = ⌜n0⌝ , leninv(nσ) = ∞, stutf(nσ), n0 ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 101:
⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m)
Proof step 102:
(⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1) ∧ (∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = n + 1 → ¬ n0 < m), leninv(nσ) = ∞, stutf(nσ), n0 ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n ⊦

Rule argument

spec: inst: name: maxinf-fin seq: ⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m) subst: [n, np] → [n0, λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1] flags: rewrite, current

Additional information

Used terms: n0, λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1