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Proof step 98 from proof leninv-succ (previous step)

# nσ = ⌜m1⌝ + ⌜1⌝ , stutf(nσ), m ≤ m1, (nσ[m1] + 1 ≠ 0 → (∃ m2. ¬ m1 < m2 ∧ nσ[m2] = nσ[m1] + 1 - 1)) → ¬ nσ[m] + 1 < nσ[m1] + 1, ∀ m0. (m0 ≠ 0 → (∃ m2. ¬ m1 < m2 ∧ nσ[m2] = m0 - 1)) → ¬ nσ[m] + 1 < m0 ⊦ nσ[m1] = nσ[m]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 99:
# nσ = ⌜m1⌝ + ⌜1⌝ , stutf(nσ), m ≤ m1, ∀ m0. (m0 ≠ 0 → (∃ m2. ¬ m1 < m2 ∧ nσ[m2] = m0 - 1)) → ¬ nσ[m] + 1 < m0, (∃ m0. ¬ m1 < m0 ∧ nσ[m0] = nσ[m1]) → ¬ nσ[m] < nσ[m1] ⊦ nσ[m1] = nσ[m]

Rule argument

Additional information

Used simplifier rules: l: ⊦ m + n < m + n0 ↔ n < n0; from specification nat-basic2%add-base: ⊦ n + 0 = n; from specification nat-basic2%add-01: ⊦ n ≤ m → m + n0 - n = (m - n) + n0; from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2