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Proof step 1 from proof union-left-empty (conclusion)

⊦ st ∪ ∅ = st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ st1 = st2 ↔ (∀ a. (a ∈ st1 ↔ a ∈ st2) ∧ st1[a] = st2[a])
Proof step 3:
⊦ ∀ a. (a ∈ st ∪ ∅ ↔ a ∈ st) ∧ (st ∪ ∅)[a] = st[a]

Rule argument

spec: store name: Extension seq: ⊦ st1 = st2 ↔ (∀ a. (a ∈ st1 ↔ a ∈ st2) ∧ st1[a] = st2[a]) subst: [st2, st1] → [st, st ∪ ∅] flags: <all paths>

Additional information

Used terms: st, st ∪ ∅