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Proof step 1 from proof del-01 (conclusion)

⊦ a ∈ st.keys → (st -- a).keys = st.keys -- a

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
a ∈ st ⊦ (st -- a).keys = st.keys -- a, a < st.min

Rule argument

Additional information

Used simplifier rules: Keys: ⊦ a ∈ st.keys ↔ a ∈ st;%Min-min: ⊦ a ∈ st → ¬ a < st.min;%inf: ⊦ a ∈ st → a ∈ st.keys;