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Proof step 2 from proof min-put-ls (previous step)

st.keys.min < a, st.keys.min ∈ st ⊦ st = ∅, st[a, d].min = st.keys.min

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ st ≠ ∅ → st.min = st.keys.min
Proof step 4:
st[a, d] ≠ ∅, st.keys.min < a, st.keys.min ∈ st ⊦ st = ∅, st[a, d].keys.min = st.keys.min

Rule argument

spec: ostore inst: name: min-def seq: ⊦ st ≠ ∅ → st.min = st.keys.min subst: [st] → [st[a, d]] flags: rewrite, current

Additional information

Used simplifier rules: neq: ⊦ st[a, d] ≠ ∅; from specification store Used terms: st[a, d]