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Proof step 5 from proof notin-add-diff-dom-nodes (previous step)

⊦ adr0 ∈ (as ++ adr) \ dom nodes(st) ↔ adr0 = adr ∨ adr0 ∈ as \ dom nodes(st), adr ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ adr ∈ as \ as0 ↔ adr ∈ as ∧ ¬ adr ∈ as0
Proof step 7:
⊦ adr0 ∈ as ++ adr ∧ ¬ adr0 ∈ dom nodes(st) ↔ adr0 = adr ∨ adr0 ∈ as \ dom nodes(st), adr ∈ st

Rule argument

spec: set-union, inst: address-store name: Difference seq: ⊦ adr ∈ as \ as0 ↔ adr ∈ as ∧ ¬ adr ∈ as0 subst: [as0, as, adr] → [dom nodes(st), as ++ adr, adr0] flags: <all paths>

Additional information

Used terms: dom nodes(st), as ++ adr, adr0