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Proof step 5 from proof put-gt (previous step)

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