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Proof step 6 from proof restrict-norm (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
key0 < key, key ∈ ri ⊦ ri[key] = ((ri |> key0) |≤ key1)[key], key1 < key

Rule argument

Additional information

Used simplifier rules: at-le: ⊦ ¬ key1 < key0 ∧ key0 ∈ ri → (ri |≤ key1)[key0] = ri[key0];%in-le: ⊦ key0 ∈ ri |≤ key1 ↔ key0 ∈ ri ∧ ¬ key1 < key0;