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Proof step 185 from proof inv-get-inverse-between (previous step)

mon≤(nσ) ∧ m0 ≤ n1 ∧ ⌜n1⌝ < # nσ → nσ[m0] ≤ nσ[n1], nσ[n] = nσ[n1] + 1, # nσ = ⌜m0⌝ + ⌜1⌝ , nσ[n] ≤ nσ[m0], n1 + m + 1 < m0, n ≤ m0, n1 + m + 1 < n, nσ[n1] < nσ[m0], stutf(nσ), n1 ≤ m0, ∀ m. ¬ m0 < m ∧ nσ[m] = nσ[n1] → ¬ n1 < m, ∀ m. ¬ m0 < m ∧ nσ[m] = nσ[n] → ¬ n < m ⊦ n = 0, nσ[n1 + m + 1] = nσ[n], nσ[m0] = 0, m0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 186:
nσ[n] = nσ[n1] + 1, # nσ = ⌜m0⌝ + ⌜1⌝ , nσ[n] ≤ nσ[m0], n1 + m + 1 < m0, n ≤ m0, n1 + m + 1 < n, nσ[n1] < nσ[m0], stutf(nσ), n1 < m0, ∀ m. ¬ m0 < m ∧ nσ[m] = nσ[n1] → ¬ n1 < m, ∀ m. ¬ m0 < m ∧ nσ[m] = nσ[n] → ¬ n < m ⊦ n = 0, nσ[n1 + m + 1] = nσ[n], nσ[m0] = 0, m0 = 0, n1 = m0

Rule argument

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (¬ mon≤(nσ) ↔ false);%lels-02: ⊦ m ≠ n → (m ≤ n ↔ m < n); from specification nat%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%inf-inseq-reduce: ⊦ n∞ = ⌜m⌝ + ⌜n0⌝ → (⌜n⌝ < n∞ ↔ n < m + n0); from specification nat-inf%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%anti: ⊦ m ≤ n → (n ≤ m ↔ m = n); from specification nat