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Proof step 2 from proof keys-mod-0 (previous step)

zbrar[n].key = key, n < nused, sorted(zbrar, 0, nused), nused ≤ # zbrar ⊦ keys(zbrar[n, mkzentry(key, adr)], 0, nused) = keys(zbrar, 0, nused) ++ key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n < nused, n < # zbrar, sorted(zbrar, 0, nused), nused ≤ # zbrar ⊦ keys(zbrar[n, mkzentry(zbrar[n].key, adr)], 0, nused) = keys(zbrar, 0, nused) ++ zbrar[n].key

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