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Proof step 13 from proof sorted-all (previous step)

n + m3 + 1 < # zbrar, n < # zbrar, m < m0, m < m3, m0 ≤ m3, ∀ m, m0. m < m0 ∧ ¬ m3 + 1 < m0 → zbrar[n + m].key < zbrar[n + m0].key ⊦ zbrar[(n + 1) + m].key < zbrar[(n + 1) + m0].key, sorted(zbrar, n + 1, m3 + 1) ∧ zbrar[n].key < zbrar[n + 1].key

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 6 terms: 1 + m, m0 + 1

Additional information

Used simplifier rules: ⊦ m + n < m + n0 ↔ n < n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m0 ∧ n ≤ n0 → ¬ m0 + n0 < m + n; (s) Used terms: 1 + m, m0 + 1