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Proof step 38 from proof inv-get-inverse-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
# nσ = ⌜n⌝ , max∞(λ n0. n0 < n ∧ nσ[n0] = nσ[n - 1]) = ∞, 1 + m + ∞.n < n, stutf(nσ), ∀ n0. n0 < n → nσ[n0] < nσ[n - 1] ⊦ nσ[∞.n + m + 1] = nσ[n - 1] + 1

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf% ⊦ ⌜n1⌝ + ⌜n⌝ + ⌜m⌝ < ⌜n0⌝ ↔ n1 + n + m < n0; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)