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Proof step 118 from proof inv-ls-succ (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 119:
⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m)
Proof step 120:
leninv(nσ) = ∞, nσ[n0] = n + 1, (⌜n1⌝ < # nσ ∧ nσ[n1] = n) ∧ (∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = n → ¬ n1 < m), n0 ≤ n1, stutf(nσ), ⌜n0⌝ < # nσ, ∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = n + 1 → ¬ n0 < m ⊦

Rule argument

spec: inst: name: maxinf-fin seq: ⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m) subst: [n, np] → [n1, λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n] flags: rewrite, current

Additional information

Used terms: n1, λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n