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Proof step 3 from proof range-load-save (previous step)

# zbrar = BRANCH_SIZE, n < nused, n < BRANCH_SIZE, nused ≤ BRANCH_SIZE ⊦ key-range(load(save(zbrar, 0, nused), 0, nused), 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 < nused ∧ 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))
Proof step 5:
# zbrar = BRANCH_SIZE, n < BRANCH_SIZE, n < nused, nused ≤ BRANCH_SIZE, nused ≤ # load(save(zbrar, 0, nused), 0, nused) ⊦ (n = 0 ⊃ (nused = 1 ⊃ ri;ri |≤ load(save(zbrar, 0, nused), 0, nused)[0].key) ;(n + 1 = nused ⊃ ri |> load(save(zbrar, 0, nused), 0, nused)[n - 1].key ;(ri |> load(save(zbrar, 0, nused), 0, nused)[n - 1].key) |≤ load(save(zbrar, 0, nused), 0, nused)[n].key ) ) = key-range(zbrar, n, nused, ri)

Rule argument

spec: <toplevel> name: range seq: ⊦ n < nused ∧ 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 ) ) subst: [ri, nused, n, zbrar] → [ri, nused, n, load(save(zbrar, 0, nused), 0, nused)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # load(brar, m, nused) = BRANCH_SIZE; (s) Used terms: ri, nused, n, load(save(zbrar, 0, nused), 0, nused)