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Proof step 8 from proof inter-subseteq-simp (previous step)

adr ∈ as0, adr ∈ as, ∀ adr. adr ∈ as0 ∩ as → adr ∈ as1 ⊦ # as0 = 0, # as = 0, as = ∅, as0 = ∅, adr ∈ as1, as1 ⊆ as

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: adr

Additional information

Used simplifier rules: ⊦ 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] Used terms: adr