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Proof step 2 from proof at-payload (previous step)

zbrar[m + n] = mkzentry(key, adr), n < nused, m + nused ≤ # zbrar, ∀ n0. n0 < n ∧ zbrar[m + n0].entry? → zbrar[m + n0].key ≠ key ⊦ payload(zbrar, m, nused)[key] = adr

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
zbrar[m + n] = mkzentry(key, adr), n < nused, m + nused ≤ # zbrar, ∀ n0. n0 < n ∧ zbrar[m + n0].entry? → zbrar[m + n0].key ≠ key ⊦ payload(zbrar, m, nused)[key] = adr

Rule argument

Additional information

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