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Proof step 28 from proof keys-shift-left (previous step)

n0 < # zbrar, nused < # zbrar, n < # zbrar, n0 < nused, n0 + 1 < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ ∃ n1. ¬ nused < n1 ∧ zbrar[n1].key = (n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).key, ¬ nused < n0 ∧ zbrar[n0].key = (n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
n0 < # zbrar, nused < # zbrar, n < # zbrar, n0 < nused, n0 + 1 < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ zbrar[n0].key = (n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).key, ∃ n1. ¬ nused < n1 ∧ zbrar[n1].key = zbrar[n0 + 1].key

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → ¬ n < m; (s)