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Proof step 13 from proof min-put (previous step)

st.keys.min ∈ st.keys ⊦ # st.keys = 0, st.keys = ∅, st.keys.min = st.min, a = st.keys.min, a < st.keys.min

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
st.keys.min < a, st.min < st.keys.min, st.min < a, st.keys.min ∈ st ⊦ # st.keys = 0, st.keys.min = st.min, a = st.keys.min

Rule argument

Additional information

Used simplifier rules: notempty: ⊦ a ∈ st.keys → st.keys ≠ ∅;%Keys: ⊦ a ∈ st.keys ↔ a ∈ st;%Min-min: ⊦ a ∈ st → ¬ a < st.min;%inf: ⊦ a ∈ st → a ∈ st.keys;%transitivity: ⊦ a < b ∧ b < c → a < c; (forward) from specification oelem% ⊦ a ≠ b → (a < b ↔ ¬ b < a); (ss)