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Proof step 5 from proof restrict-gt1 (previous step)

key0 < key1 ⊦ ∀ key. (key ∈ ri |> key0 |> key1 ↔ key ∈ ri |> key1) ∧ (key ∈ ri |> key0 |> key1 → (ri |> key0 |> key1)[key] = (ri |> key1)[key])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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];