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Proof step 5 from proof min-put-01 (previous step)

st[a, d].keys.min = a ⊦ st[a, d0].min = a, st[a, d] = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
(st.keys ++ a).min = a ⊦ st[a, d0].min = a

Rule argument

Additional information

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