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Proof step 3 from proof ginval-extract-nodes (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ (adr ∈ gstore \ ginval ∧ ¬ adr.lnum ∈ ginval → adr ∈ gstore) ∧ (adr ∈ gstore ∧ ¬ adr.lnum ∈ ginval → nodes(gstore, ginval)[adr] = nodes(gstore \ ginval, ginval)[adr])

Rule argument

Additional information

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