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Proof step 14 from proof min-put (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ st ≠ ∅ → st.min = st.keys.min

Rule argument

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

Additional information

Used simplifier rules: empty: ⊦ ∅.keys = ∅;% ⊦ # ∅ = 0; (s) Used terms: st