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Proof step 3 from proof restrict-norm (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
key0 < key, key ∈ ri ⊦ ((ri |≤ key1) |> key0)[key] = ((ri |> key0) |≤ key1)[key], key1 < key

Rule argument

Additional information

Used simplifier rules: in-gt: ⊦ key0 ∈ ri |> key1 ↔ key0 ∈ ri ∧ key1 < key0;%in-le: ⊦ key0 ∈ ri |≤ key1 ↔ key0 ∈ ri ∧ ¬ key1 < key0;