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Proof step 59 from proof leninv-inf (previous step)

# nσ = ⌜n1⌝ + ⌜1⌝ , nσ[m] = n - 1, nσ[n1] + 1 < n, stutf(nσ), m ≤ n1, ∀ n. ∃ n0. n < n0 ∧ (∃ m. ¬ n1 < m ∧ nσ[m] = n0 - 1) ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 60:
# nσ = ⌜n1⌝ + ⌜1⌝ , nσ[m] = m0, n = m0 + 1, nσ[n1] + 1 < n, stutf(nσ), m ≤ n1, ∀ n. ∃ n0. n < n0 ∧ (∃ m. ¬ n1 < m ∧ nσ[m] = n0 - 1) ⊦ n = 0

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m1]

Additional information

Used simplifier rules: n0 < n ⊦ ¬ m + (* n) < (* n0); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m1