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Proof step 8 from proof inj-put-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

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