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Proof step 4 from proof min-put-ls (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
st.keys.min < a, st.keys.min ∈ st ⊦ st = ∅, (st.keys ++ a).min = st.keys.min

Rule argument

Additional information

Used simplifier rules: insert-03: ⊦ st[a, d].keys = st.keys ++ a;%neq: ⊦ st[a, d] ≠ ∅; from specification store