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Proof step 66 from proof inv-inverts-leq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 67:
⊦ max∞(np) = ∞ ↔ (∀ n. ∃ n0. n < n0 ∧ np(n0)) ∨ (∀ n. ¬ np(n))
Proof step 68:
(∀ n0. ∃ n1. n0 < n1 ∧ ¬ m < n1 ∧ nσ[n1] = nσ[n]) ∨ (∀ n0. ¬(¬ m < n0 ∧ nσ[n0] = nσ[n])), # nσ = ⌜m⌝ + ⌜1⌝ , n ≤ m, ∞.n ≤ m, nσ[n] ≤ nσ[m], ∞.n < n, stutf(nσ), ∞.n < m ⊦

Rule argument

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

Additional information

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