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Proof step 8 from proof monls-exists-maxls (previous step)

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

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: m