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Proof step 3 from proof min-def (previous step)

st.min ∈ st ⊦ st.min = st.keys.min, st = ∅

User applied rule insert lemma

And obtained the following new goals

Proof step 4:
⊦ a ∈ st → ¬ a < st.min
Proof step 5:
st.min ∈ st, st.keys.min ∈ st → ¬ st.keys.min < st.min ⊦ st.min = st.keys.min, st = ∅

Rule argument

spec: <toplevel> name: Min-min seq: ⊦ a ∈ st → ¬ a < st.min subst: [a, st] → [st.keys.min, st]

Additional information

Used terms: st.keys.min, st