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Proof step 58 from proof leninv-inf (previous step)

nσ[m] = n - 1, # nσ = ⌜n1⌝ + ⌜1⌝ , m ≤ n1, nσ[n1] + 1 < n, stutf(nσ), ∀ 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 59:
n = m0 + 1 ∧ n ≠ 0, nσ[m] = m0, # nσ = ⌜n1⌝ + ⌜1⌝ , m ≤ n1, nσ[n1] + 1 < n, stutf(nσ), ∀ n. ∃ n0. n < n0 ∧ (∃ m. ¬ n1 < m ∧ nσ[m] = n0 - 1) ⊦

Rule argument

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

Additional information

Used simplifier rules: l-num-06: n0 < n ⊦ ¬ m + (* n) < (* n0); from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m1