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Proof step 108 from proof leninv-succ (previous step)

# nσ = ⌜m1⌝ + ⌜1⌝ , nσ[m0] = m - 1, nσ[m1] + 1 < m, stutf(nσ), m0 ≤ m1 ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 109:
# nσ = ⌜m1⌝ + ⌜1⌝ , nσ[m0] = m2, m = m2 + 1, nσ[m1] + 1 < m, stutf(nσ), m0 ≤ m1 ⊦ m = 0

Rule argument

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