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

⊦ ∀ n0. (n0 ∈ (gstore -- n)↓ ↔ n0 ∈ gstore ↓ -- n) ∧ (n0 ∈ (gstore -- n)↓ → (gstore -- n)↓[n0] = (gstore ↓ -- n)[n0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
n0 ∈ gstore ⊦ (gstore -- n)↓[n0] = gstore[n0] ↓, n0 = n

Rule argument

Additional information

Used simplifier rules: down-store-in: ⊦ n ∈ gstore ↓ ↔ n ∈ gstore;%down-store-at: ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓;% ⊦ n ≠ n0 → (gstore -- n0)[n] = gstore[n]; (s)% ⊦ n ∈ gstore -- n0 ↔ n ≠ n0 ∧ n ∈ gstore; (s)