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Proof step 165 from proof inv-get-inverse-between (previous step)

# nσ = ⌜m0⌝ + ⌜1⌝ , max∞(λ n0. ¬ m0 < n0 ∧ nσ[n0] = n) = ⌜n1⌝ , n1 + m + 1 < max∞(λ n0. ¬ m0 < n0 ∧ nσ[n0] = n + 1).n, n < nσ[m0], stutf(nσ) ⊦ nσ[n1 + m + 1] = n + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 166:
⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m)
Proof step 167:
# nσ = ⌜m0⌝ + ⌜1⌝ , nσ[n1] = n, n < nσ[m0], n1 + m + 1 < max∞(λ n0. ¬ m0 < n0 ∧ nσ[n0] = n + 1).n, stutf(nσ), ∀ m. ¬ m0 < m ∧ nσ[m] = n → ¬ n1 < m ⊦ nσ[n1 + m + 1] = n + 1, m0 < n1

Rule argument

spec: <toplevel> name: maxinf-fin seq: ⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m) subst: [n, np] → [n1, λ n0. ¬ m0 < n0 ∧ nσ[n0] = n] flags: <all paths>

Additional information

Used terms: n1, λ n0. ¬ m0 < n0 ∧ nσ[n0] = n