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Proof step 1 from proof indef-01 (conclusion)

⊦ a ∈ st ↔ st = (st -- a)[a, st[a]]

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 ∈ st ↔ (∀ a0. (a0 ∈ st ↔ a0 ∈ (st -- a)[a, st[a]]) ∧ st[a0] = (st -- a)[a, st[a]][a0])

Rule argument

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

Additional information

Used terms: (st -- a)[a, st[a]], st