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Proof step 66 from proof leninv-inf (previous step)

# nσ = ⌜n0⌝ + ⌜1⌝ , stutf(nσ), ∀ n. ¬(n ≠ 0 → (∃ m. ¬ n0 < m ∧ nσ[m] = n - 1)) ⊦ nσ[n0] + 1 = 0, ∃ m. ¬ n0 < m ∧ nσ[m] = nσ[n0] + 1 - 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 67:
# nσ = ⌜n0⌝ + ⌜1⌝ , stutf(nσ), ∀ n. ¬(n ≠ 0 → (∃ m. ¬ n0 < m ∧ nσ[m] = n - 1)) ⊦ ∃ m. ¬ n0 < m ∧ nσ[m] = nσ[n0]

Rule argument

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)