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Proof step 13 from proof inv-inverts-leq (previous step)

leninv(nσ) = ∞, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ∞, ∞.n < n, ⌜n⌝ < # nσ, stutf(nσ), (∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = nσ[n]) ∨ (∀ n0. ¬ ⌜n0⌝ < # nσ ∨ nσ[n0] ≠ nσ[n]) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ max∞(np) = ∞ ↔ (∀ n. ∃ n0. n < n0 ∧ np(n0)) ∨ (∀ n. ¬ np(n))
Proof step 15:
leninv(nσ) = ∞, ⌜n⌝ < # nσ, ∞.n < n, stutf(nσ), (∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = nσ[n]) ∨ (∀ n0. ¬ ⌜n0⌝ < # nσ ∨ nσ[n0] ≠ nσ[n]), (∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = nσ[n]) ∨ (∀ n0. ¬(⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n])) ⊦

Rule argument

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

Additional information

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