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Proof step 22 from proof inv-get-lslen (previous step)

n1 = m + 1 ∧ n1 ≠ 0, # nσ = ⌜n1⌝ , max∞(λ n0. n0 < n1 ∧ nσ[n0] = n) = ∞, n ≤ nσ[m], stutf(nσ), n1 ≤ ∞.n ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
# nσ = ⌜m⌝ + ⌜1⌝ , max∞(λ n0. ¬ m < n0 ∧ nσ[n0] = n) = ∞, n ≤ nσ[m], stutf(nσ), m < ∞.n ⊦ ∞.n = 0

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%succ-01: ⊦ m + 1 ≤ n ↔ m < n; from specification nat%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%add-fin: ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; from specification nat-inf