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Proof step 2 from proof range-empty (previous step)

⊦ # range ∅ = 0, range ∅ = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0)

Rule argument

spec: set-basic, inst: node-store name: Extension seq: ⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0) subst: [as0, as] → [∅, range ∅] flags: <all paths>

Additional information

Used simplifier rules: range: ⊦ adr ∈ range ri ↔ adr ∈ ri;%data-in-empty: ⊦ ¬ adr ∈ ∅;% ⊦ ¬ adr ∈ ∅; (s) Used terms: ∅, range ∅