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Proof step 5 from proof range-write-in (previous step)

ri-inj(ri), key ∈ ri ⊦ ∀ adr0. adr0 ∈ range ri[key, adr] ↔ adr0 ∈ (range ri -- ri[key]) ++ adr

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
ri-inj(ri), key ∈ ri ⊦ adr0 ∈ ri[key, adr] ↔ adr0 = adr ∨ adr0 ≠ ri[key] ∧ adr0 ∈ ri

Rule argument

Additional information

Used simplifier rules: ⊦ adr ∈ as -- adr0 ↔ adr ≠ adr0 ∧ adr ∈ as; (s)% ⊦ adr ∈ as ++ adr0 ↔ adr = adr0 ∨ adr ∈ as; (s)% ⊦ adr ∈ range ri ↔ adr ∈ ri; (s)