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Proof step 7 from proof ginval-down (previous step)

⊦ n ∈ gstore ↓, (n ∈ gstore ↓ \ ginval ↔ n ∈ gstore \ ginval) ∧ (n ∈ gstore ↓ \ ginval → (gstore ↓ \ ginval)[n] = gstore ↓[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ n ∈ gstore, (n ∈ gstore ↓ \ ginval ↔ n ∈ gstore \ ginval) ∧ (n ∈ gstore ↓ \ ginval → (gstore ↓ \ ginval)[n] = gstore ↓[n])

Rule argument

Additional information

Used simplifier rules: down-store-in: ⊦ n ∈ gstore ↓ ↔ n ∈ gstore;