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Proof step 179 from proof inv-get-inverse-between (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 180:
# nσ = ⌜m0⌝ + ⌜1⌝ , max∞(λ n0. ¬ m0 < n0 ∧ nσ[n0] = nσ[n1] + 1) = ⌜n⌝ , nσ[n1] < nσ[m0], n1 + m + 1 < n, stutf(nσ), n1 ≤ m0, ∀ m. ¬ m0 < m ∧ nσ[m] = nσ[n1] → ¬ n1 < m ⊦ nσ[n1 + m + 1] = nσ[n1] + 1, max∞(λ n0. ¬ m0 < n0 ∧ nσ[n0] = nσ[n1] + 1) = ∞

Rule argument

spec: nat-inf name: elim seq: ⊦ n∞ ≠ ∞ → (n = n∞.n ↔ n∞ = ⌜n⌝ ) subst: [n∞, n] → [max∞(λ n0. ¬ m0 < n0 ∧ nσ[n0] = nσ[n1] + 1), n]

Additional information

Used simplifier rules: ⊦ n∞ ≠ ∞ → (n = n∞.n ↔ n∞ = ⌜n⌝ ); (elim) Used terms: max∞(λ n0. ¬ m0 < n0 ∧ nσ[n0] = nσ[n1] + 1), n