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Proof step 6 from proof min-def (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 7:
⊦ a ∈ s → ¬ a < s.min

Rule argument

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

Additional information

Used simplifier rules: Keys: ⊦ a ∈ st.keys ↔ a ∈ st; Used terms: st.min, st.keys