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Proof step 1 from proof insert (conclusion)

⊦ a ∈ st → st[a, d].keys = st.keys

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: insert-03: ⊦ st[a, d].keys = st.keys ++ a;%inkeys-01: ⊦ a ∈ st → (¬ a ∈ st.keys ↔ false);%eq-03: ⊦ s ++ a = s ↔ a ∈ s; from specification set-basic