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Proof step 3 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ n ≠ 0 ∧ n + 1 < nused ∧ nused ≤ # zbrar → key-range(zbrar, n, nused, ri) = (ri |> zbrar[n - 1].key) |≤ zbrar[n].key
Proof step 5:
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 ≠ 0 ∧ n + 1 < nused ∧ nused ≤ # zbrar[m, zbr]
Proof step 21:
zbr.key = zbrar[m].key, n < nused, m < # zbrar, n < # zbrar, n + 1 < nused, nused ≤ # zbrar, nused ≤ # zbrar[m, zbr] ⊦ n = 0, (ri |> zbrar[m, zbr][n - 1].key) |≤ zbrar[m, zbr][n].key = key-range(zbrar, n, nused, ri)

Rule argument

spec: <toplevel> name: range-inner seq: ⊦ n ≠ 0 ∧ n + 1 < nused ∧ nused ≤ # zbrar → key-range(zbrar, n, nused, ri) = (ri |> zbrar[n - 1].key) |≤ zbrar[n].key subst: [ri, nused, n, zbrar] → [ri, nused, n, zbrar[m, zbr]] flags: <all paths>

Additional information

Used terms: ri, nused, n, zbrar[m, zbr]