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Proof step 32 from proof keys-shift-left (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
n0 + 1 < # zbrar, n0 < n, n < # zbrar, nused < # zbrar, n0 < # zbrar, n0 < nused, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ zbrar[n0].key = zbrar[n].key, ∃ n1. n1 < nused ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).key = zbrar[n0].key

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic