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Proof step 131 from proof inv-ls-succ (previous step)

leninv(nσ) = ⌜n1⌝ , max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1) = ⌜n0⌝ , stutf(nσ), 1 + n < n1, n0 ≤ ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n1)[n], (∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = n) ∨ (∀ n2. ¬ ⌜n2⌝ < # nσ ∨ nσ[n2] ≠ n) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 132:
⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m)
Proof step 133:
leninv(nσ) = ⌜n1⌝ , (⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1) ∧ (∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = n + 1 → ¬ n0 < m), stutf(nσ), 1 + n < n1, n0 ≤ ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n1)[n], (∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = n) ∨ (∀ n2. ¬ ⌜n2⌝ < # nσ ∨ nσ[n2] ≠ n) ⊦

Rule argument

spec: inst: name: maxinf-fin seq: ⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m) subst: [n, np] → [n0, λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1] flags: rewrite, current

Additional information

Used terms: n0, λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1