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Proof step 3 from proof at-range (previous step)

n < nused, n < # zbrar, key ∈ key-range(zbrar, n, nused, ri), nused ≤ # zbrar ⊦ key-range(zbrar, n, nused, ri)[key] = ri[key]

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:
n < # zbrar, n < nused, key ∈ key-range(zbrar, n, nused, ri), nused ≤ # zbrar ⊦ key-range(zbrar, n, nused, ri)[key] = ri[key], n ≠ 0 ∧ n + 1 < nused ∧ nused ≤ # zbrar
Proof step 12:
n < # zbrar, n < nused, n + 1 < nused, key ∈ (ri |> zbrar[n - 1].key) |≤ zbrar[n].key, nused ≤ # zbrar ⊦ ((ri |> zbrar[n - 1].key) |≤ zbrar[n].key)[key] = ri[key], n = 0

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] flags: <all paths>

Additional information

Used terms: ri, nused, n, zbrar