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Proof step 4 from proof inj-put-01 (previous step)

∀ a0. (a0 ∈ st[a, d][b, d0] ↔ a0 ∈ st[b, d0]) ∧ st[a, d][b, d0][a0] = st[b, d0][a0] ⊦ a = b, a ∈ st ∧ st[a] = d

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information