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Proof step 9 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 10:
⊦ 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: ⊦ (∅ ++ a).min = a; (s) Used formulas: st.keys ≠ ∅