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Proof step 1 from proof ins-same (conclusion)

⊦ st[a, st[a]] = st ↔ a ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ st[a] = d ∧ a ∈ st → st[a, d] = st
Proof step 3:
⊦ st[a, st[a]] = st ↔ a ∈ st, st[a] = st[a] ∧ a ∈ st

Rule argument

spec: <toplevel> name: ins seq: ⊦ st[a] = d ∧ a ∈ st → st[a, d] = st subst: [d, a, st] → [st[a], a, st] flags: <all paths>

Additional information

Used terms: st[a], a, st