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

n < nused, key ∈ key-range(zbrar, n, nused, ri), nused ≤ # zbrar ⊦ key-range(zbrar, n, nused, ri)[key] = ri[key]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n < nused, n < # zbrar, key ∈ key-range(zbrar, n, nused, ri), nused ≤ # zbrar ⊦ key-range(zbrar, n, nused, ri)[key] = ri[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