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Proof step 4 from proof restrict-2 (previous step)

⊦ (adr ∈ (iast | as0) | as1 ↔ adr ∈ iast | (as0 ∩ as1)) ∧ ((iast | as0) | as1)[adr] = (iast | (as0 ∩ as1))[adr]

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Rule argument

fma: adr ∈ (iast | as0) | as1

Additional information

Used simplifier rules: ⊦ ¬ adr ∈ iast → iast[adr] = (∅)[adr]; (s)% ⊦ adr ∈ iast | as ↔ adr ∈ iast ∧ adr ∈ as; (ws)% ⊦ adr ∈ as ∩ as0 ↔ adr ∈ as ∧ adr ∈ as0; (ws)%int-a: ⊦ (as ∩ as0) ∩ as1 = as ∩ as0 ∩ as1; from specification set-union[node-store]%int-c: ⊦ as ∩ as0 = as0 ∩ as; from specification set-union[node-store]%ne-01: ⊦ adr ∈ as → as ≠ ∅; (forward) from specification set-basic[node-store] Used formulas: adr ∈ (iast | as0) | as1