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

nσ[0] < nσ[m0], n < nσ[m0], nσ[0] < nσ[m0 + 1], ⌜m0⌝ + ⌜1⌝ < # nσ, n < nσ[m0 + 1], nσ[0] ≤ n, mon<(nσ), ⌜m0⌝ < # nσ, nσ[m] ≤ n, n < nσ[m + 1], m ≤ m0, nσ[0] < nσ[m + 1], nσ[m] < nσ[m0], nσ[m] < nσ[m0 + 1], nσ[m] < nσ[m + 1] ⊦ nσ[m0] = 0, nσ[m0 + 1] = 0, nσ[m + 1] = 0, ∃ m. nσ[m] ≤ n ∧ n < nσ[m + 1] ∧ m ≤ m0 + 1

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 4 terms: m

Additional information

Used simplifier rules: lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%l-02: ⊦ ¬ m + n < m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: m