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

ri-cons(ri, nodes(gstore, ginval)), key ∈ ri ⊦ ∀ adr. adr ∈ range(ri -- key) ↔ adr ∈ range ri -- ri[key]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
ri-cons(ri, nodes(gstore, ginval)), key ∈ ri ⊦ adr ∈ ri -- key ↔ adr ≠ ri[key] ∧ adr ∈ ri

Rule argument

Additional information

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