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Proof step 3 from proof down-store-write (previous step)

⊦ ∀ n. (n ∈ gstore[m, gblock] ↓ ↔ n ∈ gstore ↓[m, gblock ↓]) ∧ (n ∈ gstore[m, gblock] ↓ → gstore[m, gblock] ↓[n] = gstore ↓[m, gblock ↓][n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ (n ∈ gstore[m, gblock] ↔ n ∈ gstore ↓[m, gblock ↓]) ∧ (n ∈ gstore[m, gblock] → gstore[m, gblock][n] ↓ = gstore ↓[m, gblock ↓][n])

Rule argument

Additional information

Used simplifier rules: down-store-in: ⊦ n ∈ gstore ↓ ↔ n ∈ gstore;%down-store-at: ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓;