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Proof step 2 from proof stutf-maxinf-is-fin (previous step)

stutf(nσ) ⊦ max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m) = ∞ ↔ # nσ = ∞ ∧ (∃ n. ∀ n0. ¬ n0 < n → nσ[n0] = m) ∨ (∀ n. ⌜n⌝ < # nσ → nσ[n] < m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ max∞(np) = ∞ ↔ (∀ n. ∃ n0. n < n0 ∧ np(n0)) ∨ (∀ n. ¬ np(n))
Proof step 4:
stutf(nσ) ⊦ (∀ n. ∃ n0. n < n0 ∧ ⌜n0⌝ < # nσ ∧ nσ[n0] = m) ∨ (∀ n. ¬(⌜n⌝ < # nσ ∧ nσ[n] = m)) ↔ # nσ = ∞ ∧ (∃ n. ∀ n0. ¬ n0 < n → nσ[n0] = m) ∨ (∀ n. ⌜n⌝ < # nσ → 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 n. ⌜n⌝ < # nσ ∧ nσ[n] = m] flags: rewrite, current

Additional information

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