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Proof step 6 from proof keep-range (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 7:
zbr.key = zbrar[m].key, n = 0, n < nused, m < # zbrar, n < # zbrar, nused ≤ # zbrar ⊦ key-range(zbrar[m, zbr], n, nused, ri) = key-range(zbrar, n, nused, ri)
Proof step 15:
zbr.key = zbrar[m].key, n < nused, m < # zbrar, n < # zbrar, nused ≤ # zbrar ⊦ key-range(zbrar[m, zbr], n, nused, ri) = key-range(zbrar, n, nused, ri), n + 1 < nused

Rule argument

pos: right 2

Proof step 6 from proof keep-range (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information