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Proof step 28 from proof lsleninv-1 (previous step)

# nσ = ⌜n⌝ , n = m1 + 1, nσ[m1] < nσ[m0], nσ[m0] < nσ[m], nσ[m1] + 1 < nσ[m], nσ[m1] < nσ[m], m < n, m0 < n, stutf(nσ), m0 ≤ m ⊦ n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
# nσ = ⌜m1⌝ + ⌜1⌝ , nσ[m1] < nσ[m], nσ[m1] < nσ[m0], nσ[m0] < nσ[m], nσ[m1] + 1 < nσ[m], stutf(nσ), m ≤ m1, m0 ≤ m, m0 ≤ m1 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m + 1 ≠ 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)