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Proof step 150 from proof inv-ls-succ (previous step)

nσ[n0] = n + 1, leninv(nσ) = ⌜n1⌝ , max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) = ⌜n2⌝ , n + 1 < n1, 1 + n < n1, ⌜n0⌝ < # nσ, stutf(nσ), n0 ≤ n2, ∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = n + 1 → ¬ n0 < m ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 151:
⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m)
Proof step 152:
nσ[n2] = n, nσ[n0] = n + 1, leninv(nσ) = ⌜n1⌝ , ⌜n0⌝ < # nσ, 1 + n < n1, n + 1 < n1, ⌜n2⌝ < # nσ, stutf(nσ), n0 ≤ n2, ∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = n + 1 → ¬ n0 < m, ∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = n → ¬ n2 < m ⊦

Rule argument

spec: <toplevel> name: maxinf-fin seq: ⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m) subst: [n, np] → [n2, λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n] flags: <all paths>

Additional information

Used terms: n2, λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n