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

n < nused, n < # zbrar, nused ≤ # zbrar ⊦ key-range(zbrar, n, nused, ∅) = ∅

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))

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] → [∅, nused, n, zbrar] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ∅ |≤ key = ∅; (s)% ⊦ ∅ |> key = ∅; (s) Used terms: ∅, nused, n, zbrar