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Proof step 7 from proof monls-exists-maxleq (previous step)

mon<(nσ), ⌜m1⌝ + ⌜1⌝ < # nσ, nσ[0] < nσ[m1 + 1] ⊦ nσ[m1 + 1] = 0, nσ[m1] < nσ[m1 + 1] ∧ nσ[m1 + 1] ≤ nσ[m1 + 1] ∧ m1 ≤ m1 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
nσ[0] < nσ[m1], nσ[m1 + 1] ≤ nσ[m1], nσ[0] < nσ[m1 + 1], ⌜m1⌝ + ⌜1⌝ < # nσ, mon<(nσ) ⊦ nσ[m1 + 1] = 0, nσ[m1] = 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%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%lep: ⊦ m ≤ m + n; from specification nat%ler: ⊦ m ≤ m; from specification nat