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Proof step 11 from proof disj-write (previous step)

n0 < # asar, n < # asar, n < m, n0 < m, m ≤ # asar, ∀ n0, n1. n0 < m ∧ n1 < m ∧ n0 ≠ n1 → asar[n0] ∩ asar[n1] = ∅, ∀ n0, n1. n0 < m ∧ n1 < m ∧ n0 ≠ n1 → asar[n, as][n0] ∩ asar[n, as][n1] = ∅ ⊦ #(asar[n0] ∩ as) = 0, n0 = n, asar[n0] ∩ as = ∅

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 7 terms: n0, n

Additional information

Used simplifier rules: ⊦ m ≠ n → asar[n, a0][m] = asar[m]; (s)% ⊦ m < # asar → asar[m, a0][m] = a0; (s) Used terms: n0, n