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Proof step 13 from proof monls-ls (previous step)

¬ nσ[m1 + m] ≤ nσ[m], ⌜m1⌝ + ⌜1⌝ + ⌜m⌝ < # nσ, nσ[(m1 + 1) + m] ≤ nσ[m], ∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1], ⌜m1⌝ + ⌜m⌝ < # nσ ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
nσ[(m1 + 1) + m] < nσ[m1 + m], nσ[m] < nσ[m1 + m], ⌜m1⌝ + ⌜m⌝ < # nσ, nσ[(m1 + 1) + m] ≤ nσ[m], ⌜m1⌝ + ⌜1⌝ + ⌜m⌝ < # nσ, ∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1] ⊦

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; from specification nat-basic1%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat