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Proof step 3 from proof mk-in (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
st.min ∈ st ⊦ # st.keys = 0, st = ∅, st.keys = ∅, st.keys.min ∈ st

Rule argument

Additional information

Used simplifier rules: size-zero: ⊦ # s ≠ 0 → s ≠ ∅; (forward) from specification set-basic%size-zero-01: ⊦ s ≠ ∅ → # s ≠ 0; (forward) from specification set-basic