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Proof step 3 from proof inter-subseteq-simp (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ as ⊆ as0 ↔ (∀ adr. adr ∈ as → adr ∈ as0)
Proof step 5:
as0 ∩ as ⊆ as1 ⊦ as1 ⊆ as, ∀ adr. adr ∈ as0 ∩ as → adr ∈ as1 ∩ as

Rule argument

spec: set-basic, inst: node-store name: Subset seq: ⊦ as ⊆ as0 ↔ (∀ adr. adr ∈ as → adr ∈ as0) subst: [as0, as] → [as1 ∩ as, as0 ∩ as] flags: <all paths>

Additional information

Used terms: as1 ∩ as, as0 ∩ as