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Proof step 2 from proof mk-in (previous step)

⊦ st.keys.min ∈ st ↔ true, st = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
st.min ∈ st ⊦ st = ∅, st.keys.min ∈ st

Rule argument

Additional information

Used simplifier rules: Min-in: ⊦ st ≠ ∅ → st.min ∈ st;%Min-min: ⊦ a ∈ st → ¬ a < st.min;%inf: ⊦ a ∈ st → a ∈ st.keys;%Keys: ⊦ a ∈ st.keys ↔ a ∈ st;% ⊦ ¬ a < a; (s)