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Proof step 4 from proof ins-same (previous step)

st[a, (∅)[a]] = st ⊦ a ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ st1 = st2 ↔ (∀ a. (a ∈ st1 ↔ a ∈ st2) ∧ st1[a] = st2[a])
Proof step 6:
∀ a0. (a0 ∈ st[a, (∅)[a]] ↔ a0 ∈ st) ∧ st[a, (∅)[a]][a0] = st[a0] ⊦ a ∈ st

Rule argument

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

Additional information

Used terms: st, st[a, (∅)[a]]