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Proof step 10 from proof range-le (previous step)

2 + m < nused, 2 + m < # zbrar, nused ≤ # zbrar ⊦ ((ri |≤ key) |> zbrar[m].key) |≤ zbrar[m + 1].key = (ri |> zbrar[m].key) |≤ zbrar[m + 1].key, key < zbrar[m + 1].key

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: node-index-restrict name: restrict-norm seq: ⊦ (ri |≤ key1) |> key0 = (ri |> key0) |≤ key1 subst: [key0, key1, ri] → [zbrar[m].key, key, ri] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ key0 < key1 → ri |≤ key0 |≤ key1 = ri |≤ key1; (s) Used terms: zbrar[m].key, key, ri