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Proof step 19 from proof butmin-rewput (previous step)

st.min ∈ st ⊦ st = ∅, st.min = st[a, d].min, a = st[a, d].min, st.min = a

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
st.keys.min ∈ st ⊦ st.keys.min = a, a = st[a, d].min, st.keys.min = st[a, d].min, st = ∅

Rule argument

Additional information

Used simplifier rules: min-def: ⊦ st ≠ ∅ → st.min = st.keys.min;%Min-min: ⊦ a ∈ st → ¬ a < st.min;%inf: ⊦ a ∈ st → a ∈ st.keys;%Min-in: ⊦ st ≠ ∅ → st.min ∈ st;%Keys: ⊦ a ∈ st.keys ↔ a ∈ st;%irreflexivity: ⊦ ¬ a < a; from specification oelem