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Proof step 8 from proof restrict-gt1 (previous step)

key0 < key1, key1 < key, key0 < key, key ∈ ri ⊦ (ri |> key0 |> key1)[key] = ri[key]

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: at-gt seq: ⊦ key1 < key0 ∧ key0 ∈ ri → (ri |> key1)[key0] = ri[key0] subst: [key0, key1, ri] → [key, key1, ri |> key0] flags: <all paths>

Additional information

Used simplifier rules: in-gt: ⊦ key0 ∈ ri |> key1 ↔ key0 ∈ ri ∧ key1 < key0;%at-gt: ⊦ key1 < key0 ∧ key0 ∈ ri → (ri |> key1)[key0] = ri[key0]; Used terms: key, key1, ri |> key0