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Proof step 4 from proof mk-in (previous step)

st.min ∈ st ⊦ # st.keys = 0, st = ∅, st.keys = ∅, st.keys.min ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ a ∈ st ↔ a ∈ st.keys

Rule argument

spec: ostore inst: name: inkeys seq: ⊦ a ∈ st ↔ a ∈ st.keys subst: [st, a] → [st, st.keys.min] flags: rewrite, current

Additional information

Used simplifier rules: min-inn: ⊦ ¬ s.min ∈ s ↔ s = ∅; from specification oset Used terms: st, st.keys.min