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Proof step 34 from proof keys-shift-left (previous step)

n0 < # zbrar, nused < # zbrar, n < # zbrar, sorted(zbrar, 0, nused + 1), n0 ≤ nused, n ≤ nused ⊦ zbrar[n0].key = zbrar[n].key, n0 < n, ∃ 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 35:
n < # zbrar, nused < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), n0 ≤ nused, n ≤ n0, 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: let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)