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Proof step 6 from proof inter-subseteq-simp (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ as ⊆ as0 ↔ (∀ adr. adr ∈ as → adr ∈ as0)
Proof step 8:
adr ∈ as0, adr ∈ as, ∀ adr. adr ∈ as0 ∩ as → adr ∈ as1 ⊦ # as0 = 0, # as = 0, as = ∅, as0 = ∅, adr ∈ as1, as1 ⊆ as

Rule argument

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

Additional information

Used terms: as1, as0 ∩ as