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Proof step 4 from proof ginval-down (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 5:
n ∈ gstore ↓ ⊦ (n ∈ gstore ↓ \ ginval ↔ n ∈ gstore \ ginval) ∧ (n ∈ gstore ↓ \ ginval → (gstore ↓ \ ginval)[n] = gstore ↓[n])
Proof step 7:
⊦ n ∈ gstore ↓, (n ∈ gstore ↓ \ ginval ↔ n ∈ gstore \ ginval) ∧ (n ∈ gstore ↓ \ ginval → (gstore ↓ \ ginval)[n] = gstore ↓[n])

Rule argument

fma: n ∈ gstore ↓

Additional information

Used formulas: n ∈ gstore ↓