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Proof step 7 from proof restrict-gt3 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
key0 < key, key1 < key, key ∈ ri ⊦ (ri |> key0 |> key1)[key] = ri[key], key0 < key1

Rule argument

Additional information

Used simplifier rules: nll: ⊦ ¬ key0 < key ∧ key0 < key1 → key < key1; (forward) from specification oelem[key-order]