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Proof step 1 from proof size-del-02 (conclusion)

⊦ a ∈ st → ¬ # st.keys ≤ # (st -- a).keys

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

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