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Proof step 35 from proof inv-inverts-last (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ max∞(np) = ∞ ↔ (∀ n. ∃ n0. n < n0 ∧ np(n0)) ∨ (∀ n. ¬ np(n))
Proof step 37:
# nσ = ⌜n⌝ + ⌜1⌝ , leninv(nσ) = ⌜n1⌝ , nσ[n] < n1, stutf(nσ), (∀ n0. ∃ n1. n0 < n1 ∧ ¬ n < n1 ∧ nσ[n1] = nσ[n]) ∨ (∀ n0. ¬(¬ n < n0 ∧ nσ[n0] = nσ[n])) ⊦ ∞.n = n

Rule argument

spec: <toplevel> name: maxinf-inf seq: ⊦ max∞(np) = ∞ ↔ (∀ n. ∃ n0. n < n0 ∧ np(n0)) ∨ (∀ n. ¬ np(n)) subst: [np] → [λ n0. ¬ n < n0 ∧ nσ[n0] = nσ[n]] flags: <all paths>

Additional information

Used terms: λ n0. ¬ n < n0 ∧ nσ[n0] = nσ[n]