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Proof step 16 from proof butmin-put-01 (previous step)

a = (st.keys ++ a).min ⊦ a = st[a, d].min, a ∈ st, ¬ a ∈ st[a, (∅)[a]] -- st[a, (∅)[a]].min ∧ d = (∅)[a]

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: min-def seq: ⊦ st ≠ ∅ → st.min = st.keys.min subst: [st] → [st[a, d]] flags: <all paths>

Additional information

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