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Proof step 7 from proof empty-01 (previous step)

st.keys = ∅, st.min ∈ st ⊦ st = ∅, ¬ a ∈ st ∧ st[a] = (∅)[a]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2)
Proof step 9:
st.min ∈ st, ∀ a. a ∈ st.keys ↔ a ∈ ∅ ⊦ st = ∅, ¬ a ∈ st ∧ st[a] = (∅)[a]

Rule argument

spec: set-basic name: Extension seq: ⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2) subst: [s2, s1] → [∅, st.keys] flags: <all paths>

Additional information

Used terms: ∅, st.keys