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Proof step 1 from proof inj-put-01 (conclusion)

⊦ a ≠ b → (st[a, d][b, d0] = st[b, d0] ↔ a ∈ st ∧ st[a] = d)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
st[a, d][b, d0] = st[b, d0] ⊦ a = b, a ∈ st ∧ st[a] = d

Rule argument

Additional information

Used simplifier rules: ins-same-01: ⊦ a ∈ st → st[a, st[a]] = st;