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Proof step 6 from proof stutf-slowincrease (previous step)

nσ[m] + n0 + 1 < nσ[m + n0 + 1], ⌜m⌝ + ⌜n0⌝ + ⌜1⌝ < # nσ, stutf(nσ), ¬ nσ[m] + n0 < nσ[m + n0] ∨ ¬ ⌜m⌝ + ⌜n0⌝ < # nσ ∨ ¬ stutf(nσ) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
nσ[m] + n0 + 1 < nσ[m + n0 + 1], ⌜m⌝ + ⌜n0⌝ + ⌜1⌝ < # nσ, ⌜m⌝ + ⌜n0⌝ < # nσ, stutf(nσ), nσ[m + n0] ≤ nσ[m] + n0 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)% ⊦ ⌜n⌝ + ⌜m⌝ < ⌜n0⌝ ↔ n + m < n0; (s)% ⊦ ⌜n⌝ + n∞1 < ⌜n⌝ + n∞2 ↔ n∞1 < n∞2; (s)%lsle-trans: ⊦ n∞ < n∞1 ∧ ¬ n∞2 < n∞1 → n∞ < n∞2; (forward) from specification nat-inf