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Proof step 7 from proof at-range (previous step)

n = 0, n < # zbrar, n < nused, key ∈ key-range(zbrar, n, nused, ri), nused ≤ # zbrar ⊦ key-range(zbrar, n, nused, ri)[key] = ri[key], n ≠ 0 ∧ n + 1 < nused

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
key ∈ key-range(zbrar, 0, nused, ri), nused ≤ # zbrar ⊦ # zbrar = 0, key-range(zbrar, 0, nused, ri)[key] = ri[key], nused = 0

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < m ↔ m ≠ 0; (s)