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Proof step 6 from proof in-keyrange-in-ri (previous step)

n < nused, n < # zbrar, key ∈ (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)), nused ≤ # zbrar ⊦ key ∈ ri

User applied rule case distinction

And obtained the following new goals

Proof step 7:
n = 0, n < # zbrar, n < nused, key ∈ (nused = 1 ⊃ ri;ri |≤ zbrar[0].key), nused ≤ # zbrar ⊦ key ∈ ri
Proof step 9:
n < # zbrar, n < nused, key ∈ (n + 1 = nused ⊃ ri |> zbrar[n - 1].key;(ri |> zbrar[n - 1].key) |≤ zbrar[n].key), nused ≤ # zbrar ⊦ n = 0, key ∈ ri

Rule argument

pos: left 3

Proof step 6 from proof in-keyrange-in-ri (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information