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Proof step 19 from proof monls-exists-maxleq (previous step)

nσ[0] < nσ[2 + m2], nσ[m2 + 1] < nσ[m], nσ[m2 + 1] < nσ[2 + m2], nσ[0] + 1 < nσ[m], nσ[0] < nσ[m2 + 1], mon<(nσ), nσ[0] < nσ[m], ⌜m⌝ < # nσ, m2 < m, nσ[0] + 1 < nσ[2 + m2] ⊦ m = 0, nσ[2 + m2] = 0, nσ[m2 + 1] = 0, nσ[m] = 0, nσ[m2] < nσ[m2 + 1] ∧ nσ[m2 + 1] ≤ nσ[m2 + 1] ∧ m2 ≤ m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
nσ[0] < nσ[m2], nσ[m2 + 1] ≤ nσ[m2], nσ[0] + 1 < nσ[2 + m2], m2 < m, ⌜m⌝ < # nσ, nσ[0] < nσ[m], mon<(nσ), nσ[0] < nσ[m2 + 1], nσ[0] + 1 < nσ[m], nσ[m2 + 1] < nσ[2 + m2], nσ[m2 + 1] < nσ[m], nσ[0] < nσ[2 + m2] ⊦ nσ[m] = 0, nσ[m2 + 1] = 0, nσ[2 + m2] = 0, m = 0, nσ[m2] = 0

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%lels-03: ⊦ m < n → m ≤ n; from specification nat%ler: ⊦ m ≤ m; from specification nat