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Proof step 7 from proof range-rem-in (previous step)

ri-cons(ri, nodes(gstore, ginval)), key ∈ ri, adr ∈ ri -- key ⊦ adr ≠ ri[key] ∧ adr ∈ ri

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
ri-cons(ri, nodes(gstore, ginval)), ri[key] ∈ ri -- key, key ∈ ri ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ key ∈ ri ∧ ri[key] = adr → adr ∈ ri; (s)% ⊦ ¬ adr ∈ ri → ¬ adr ∈ ri -- key; (s)