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

⊦ st \ dom st = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ st1 = st2 ↔ (∀ a. (a ∈ st1 ↔ a ∈ st2) ∧ st1[a] = st2[a])

Rule argument

spec: store inst: name: Extension seq: ⊦ st1 = st2 ↔ (∀ a. (a ∈ st1 ↔ a ∈ st2) ∧ st1[a] = st2[a]) subst: [st2, st1] → [∅, st \ dom st] flags: rewrite

Additional information

Used simplifier rules: Diff-ext: ⊦ a ∈ st \ s ↔ a ∈ st ∧ ¬ a ∈ s;%Dom: ⊦ a ∈ dom st ↔ a ∈ st;%In-empty: ⊦ ¬ a ∈ ∅; from specification store%notmemlookup: ⊦ ¬ a ∈ st → st[a] = (∅)[a]; from specification store Used terms: ∅, st \ dom st