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Proof step 2 from proof notin-add-diff-dom-nodes (previous step)

⊦ (as ++ adr) \ dom nodes(st) = (as \ dom nodes(st)) ++ adr, 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)) ++ adr

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)) ++ adr, (as ++ adr) \ dom nodes(st)] flags: <all paths>

Additional information

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