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Proof step 1 from proof range-put (conclusion)

n < nused, nused ≤ # zbrar, n ≠ 0 → zbrar[n - 1].key < key, nused ≠ 0 → key ≤ zbrar[n].key ⊦ key-range(zbrar, n, nused, ri[key, adr]) = key-range(zbrar, n, nused, ri)[key, adr]

System applied rule normalize

And obtained the following new goals

Proof step 2:
n < nused, nused ≤ # zbrar, nused ≠ 0 → key ≤ zbrar[n].key, n ≠ 0 → zbrar[n - 1].key < key ⊦ key-range(zbrar, n, nused, ri[key, adr]) = key-range(zbrar, n, nused, ri)[key, adr]

Proof step 1 from proof range-put (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information