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Proof step 5 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 6:
n ∈ gstore ⊦ (n ∈ gstore ↓ \ ginval → ¬ n ∈ ginval) ∧ (n ∈ gstore ↓ \ ginval → (gstore ↓ \ ginval)[n] = gstore[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 ∈ gstore \ ns ↔ n ∈ gstore ∧ ¬ n ∈ ns; (ws)