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Proof step 5 from proof min-put (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ (st.keys ++ a).min = st.min, a = (st.keys ++ a).min

Rule argument

Additional information

Used simplifier rules: insert-03: ⊦ st[a, d].keys = st.keys ++ a;% ⊦ st[a, d] ≠ ∅; (s)