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Proof step 2 from proof insert-inter-notin-dom-nodes (previous step)

⊦ (as ++ adr) ∩ dom nodes(st) = as ∩ dom nodes(st), adr ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0)
Proof step 4:
⊦ adr ∈ st, ∀ adr0. adr0 ∈ (as ++ adr) ∩ dom nodes(st) ↔ adr0 ∈ as ∩ dom nodes(st)

Rule argument

spec: set-basic, inst: address-store name: Extension seq: ⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0) subst: [as0, as] → [as ∩ dom nodes(st), (as ++ adr) ∩ dom nodes(st)] flags: <all paths>

Additional information

Used terms: as ∩ dom nodes(st), (as ++ adr) ∩ dom nodes(st)