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Proof step 4 from proof down-store-write (previous step)

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

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: n = m

Additional information

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