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Proof step 5 from proof nodes-ginval-rem-01 (previous step)

dom gstore1 ∪ ns = dom gstore ⊦ ∀ adr. (adr ∈ nodes(gstore, ginval \ dom gstore1 \ dom gstore) ↔ adr ∈ nodes(gstore, ginval)) ∧ (adr ∈ nodes(gstore, ginval \ dom gstore1 \ dom gstore) → nodes(gstore, ginval \ dom gstore1 \ dom gstore)[adr] = nodes(gstore, ginval)[adr])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
dom gstore1 ∪ ns = dom gstore ⊦ (adr ∈ gstore → (¬ adr.lnum ∈ ginval \ dom gstore1 \ dom gstore ↔ ¬ adr.lnum ∈ ginval)) ∧ ( adr ∈ gstore ∧ ¬ adr.lnum ∈ ginval \ dom gstore1 \ dom gstore → nodes(gstore, ginval \ dom gstore1 \ dom gstore)[adr] = nodes(gstore, ginval)[adr])

Rule argument

Additional information

Used simplifier rules: nodes-gstore-in: ⊦ adr ∈ nodes(gstore, ginval) ↔ ¬ ¬(adr ∈ gstore ∧ ¬ adr.lnum ∈ ginval);