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Proof step 54 from proof inv-ls-succ (previous step)

max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1) = ∞, ∞.n ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n, n < nσ[m], ⌜m⌝ < # nσ, stutf(nσ), ∀ m2. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m2 - 1 ∧ (# nσ ≠ ∞ ∨ ¬(∀ m1. m0 < m1 → nσ[m1] = m2 - 1))) → ¬ nσ[m] + 1 < m2, # nσ ≠ ∞ ∨ ¬(m < m0 → nσ[m0] = nσ[m]) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 55:
⊦ max∞(np) = ∞ ↔ (∀ n. ∃ n0. n < n0 ∧ np(n0)) ∨ (∀ n. ¬ np(n))
Proof step 56:
(∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = n + 1) ∨ (∀ n0. ¬(⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1)), ∞.n ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n, n < nσ[m], ⌜m⌝ < # nσ, stutf(nσ), ∀ m2. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m2 - 1 ∧ (# nσ ≠ ∞ ∨ ¬(∀ m1. m0 < m1 → nσ[m1] = m2 - 1))) → ¬ nσ[m] + 1 < m2, # nσ ≠ ∞ ∨ ¬(m < m0 → nσ[m0] = nσ[m]) ⊦

Rule argument

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

Additional information

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