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Proof step 138 from proof inv-get-inverse-between (previous step)

nσ[n1 + 1] = nσ[n1] + 1, # nσ = ∞, nσ[n] = nσ[n1] + 1, n1 < m1, n1 + m + 1 < m1, n ≤ m1, stutf(nσ), nσ[n1] < nσ[m1], n1 + m + 1 < n, nσ[n] ≤ nσ[m1], nσ[n1 + 1] ≤ nσ[n1 + m + 1], ∀ m. nσ[m] = nσ[n] → ¬ n < m, ∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1, ∀ m. nσ[m] = nσ[n1] → ¬ n1 < m ⊦ nσ[n1 + 1] = nσ[n1], nσ[n] = nσ[m1] + 1, nσ[m1] = 0, nσ[n1 + m + 1] = nσ[n], n = 0, m1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 139:
nσ[n1 + 1] = nσ[n], # nσ = ∞, nσ[n] = nσ[n1] + 1, nσ[n] < nσ[n1 + m + 1], n1 < m1, n1 + m + 1 < m1, n ≤ m1, stutf(nσ), nσ[n1] < nσ[m1], n1 + m + 1 < n, nσ[n] ≤ nσ[m1], ∀ m. nσ[m] = nσ[n] → ¬ n < m, ∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1, ∀ m. nσ[m] = nσ[n1] → ¬ n1 < m ⊦ nσ[n1 + m + 1] = 0, nσ[n] = nσ[n1], nσ[n] = nσ[m1] + 1, nσ[m1] = 0, nσ[n1 + m + 1] = nσ[n], n = 0, m1 = 0

Rule argument

Additional information

Used simplifier rules: lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic1%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lels-02: ⊦ m ≠ n → (m ≤ n ↔ m < n); from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2