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Proof step 1 from proof inter-subseteq-simp (conclusion)

⊦ as0 ∩ as ⊆ as1 ∩ as ↔ as0 ∩ as ⊆ as1

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Rule argument

fma: as0 ∩ as ⊆ as1 ∩ as

Additional information

Used simplifier rules: sub-ntrans: ⊦ as ⊆ as0 ∧ ¬ as ⊆ as1 → ¬ as0 ⊆ as1; (forward) from specification set-basic[node-store]% ⊦ as ∩ as0 ⊆ as; (s)%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] Used formulas: as0 ∩ as ⊆ as1 ∩ as