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Proof step 31 from proof inv-get-lslen (previous step)

# nσ = ⌜m⌝ + ⌜1⌝ , m < ∞.n, stutf(nσ), n ≤ nσ[m], stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n), ∀ n0. m < n0 ∨ nσ[n0] ≠ n ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
# nσ = ⌜m⌝ + ⌜1⌝ , m0 < ∞.n, m < ∞.n, stutf(nσ), m0 ≤ m, nσ[m0] ≤ nσ[m], ∀ n0. m < n0 ∨ nσ[n0] ≠ nσ[m0] ⊦

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ n < n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ n∞ = ⌜m⌝ + ⌜n0⌝ → (⌜n⌝ < n∞ ↔ n < m + n0); (s)%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