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Proof step 3 from proof range (previous step)

n < nused, n < # zbrar, nused ≤ # zbrar ⊦ key-range(zbrar, n, nused, ri) = (n = 0 ⊃ (nused = 1 ⊃ ri;ri |≤ zbrar[0].key);(n + 1 = nused ⊃ ri |> zbrar[n - 1].key;(ri |> zbrar[n - 1].key) |≤ zbrar[n].key))

User applied rule case distinction

And obtained the following new goals

Proof step 4:
n = 0, n < # zbrar, n < nused, nused ≤ # zbrar ⊦ key-range(zbrar, n, nused, ri) = (nused = 1 ⊃ ri;ri |≤ zbrar[0].key)
Proof step 8:
n < # zbrar, n < nused, nused ≤ # zbrar ⊦ key-range(zbrar, n, nused, ri) = (n + 1 = nused ⊃ ri |> zbrar[n - 1].key;(ri |> zbrar[n - 1].key) |≤ zbrar[n].key), n = 0

Rule argument

pos: right 1

Proof step 3 from proof range (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information