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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

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