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Proof step 2 from proof ins3 (previous step)

⊦ st[a, d1][b, d0][a, d] = st[b, d0][a, d]

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])
Proof step 4:
⊦ ∀ a0. (a0 ∈ st[a, d1][b, d0][a, d] ↔ a0 ∈ st[b, d0][a, d]) ∧ st[a, d1][b, d0][a, d][a0] = st[b, d0][a, d][a0]

Rule argument

spec: inst: name: Extension seq: ⊦ st1 = st2 ↔ (∀ a. (a ∈ st1 ↔ a ∈ st2) ∧ st1[a] = st2[a]) subst: [st2, st1] → [st[b, d0][a, d], st[a, d1][b, d0][a, d]] flags: rewrite, current

Additional information

Used terms: st[b, d0][a, d], st[a, d1][b, d0][a, d]