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Proof step 8 from proof min-put (previous step)

⊦ (st.keys ++ a).min = st.min, a = (st.keys ++ a).min, a < st.keys.min ∧ st.keys ≠ ∅

User applied rule cut formula

And obtained the following new goals

Proof step 9:
st.keys ≠ ∅ ⊦ (st.keys ++ a).min = st.min, a = (st.keys ++ a).min, a < st.keys.min ∧ st.keys ≠ ∅

Rule argument

fma: st.keys ≠ ∅

Additional information

Used simplifier rules: min-one: ⊦ (∅ ++ a).min = a; from specification oset Used formulas: st.keys ≠ ∅