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Proof step 50 from proof payload-shift-left (previous step)

zbrar[n] = mkzentry(key, adr), zbrar[n0] = mkzentry(key0, adr0), n0 < # zbrar, nused < # zbrar, n < # zbrar, n0 < nused, n0 + 1 < # zbrar, n0 < n, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ key0 ≠ key ∧ (∃ n1. ¬ nused < n1 ∧ zbrar[n1].entry? ∧ zbrar[n1].key = key0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
zbrar[n] = mkzentry(key, adr), zbrar[n0] = mkzentry(key0, adr0), n0 < # zbrar, nused < # zbrar, n < # zbrar, n0 < nused, n0 + 1 < # zbrar, n0 < n, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ key0 ≠ key ∧ (∃ n1. ¬ nused < n1 ∧ zbrar[n1].entry? ∧ zbrar[n1].key = key0)

Rule argument

Additional information

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