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Proof step 3 from proof mk-in (previous step)

st.min ∈ st ⊦ st = ∅, st.keys.min ∈ st

User applied rule cut formula

And obtained the following new goals

Proof step 4:
st.min ∈ st ⊦ st.keys = ∅, st = ∅, st.keys.min ∈ st

Rule argument

fma: st.keys = ∅

Additional information

Used simplifier rules: empty-01: ⊦ st ≠ ∅ → (st.keys = ∅ ↔ false); Used formulas: st.keys = ∅