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Proof step 2 from proof insert (previous step)

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;%Keys: ⊦ a ∈ st.keys ↔ a ∈ st;%Min-min: ⊦ a ∈ st → ¬ a < st.min;%inf: ⊦ a ∈ st → a ∈ st.keys;% ⊦ s ++ a = s ↔ a ∈ s; (s)