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Proof step 2 from proof inter-subseteq-simp (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
as0 ∩ as ⊆ as1 ⊦ as0 ∩ as ⊆ as1 ∩ as, as1 ⊆ as

Rule argument

Additional information

Used simplifier rules: subseteq-inter-same: ⊦ as ⊆ as0 ∩ as ↔ as ⊆ as0;%int-c: ⊦ as ∩ as0 = as0 ∩ as; from specification set-union[node-store]%int-a: ⊦ (as ∩ as0) ∩ as1 = as ∩ as0 ∩ as1; from specification set-union[node-store]%sub-ntrans: ⊦ as ⊆ as0 ∧ ¬ as ⊆ as1 → ¬ as0 ⊆ as1; (forward) from specification set-basic[node-store]