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Proof step 16 from proof leninv-inf (previous step)

# nσ = ∞, nσ[m0] = n - 1, nσ[m] + 1 < n, m0 < m1, stutf(nσ) ⊦ nσ[m1] = n - 1, ∃ m0. m < m0 ∧ nσ[m] < nσ[m0]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
# nσ = ∞, nσ[m0] = m2, n = m2 + 1, m0 < m1, nσ[m] + 1 < n, stutf(nσ) ⊦ nσ[m1] = m2, n = 0, ∃ m0. m < m0 ∧ nσ[m] < nσ[m0]

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m2]

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, m2