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Proof step 12 from proof butmin-rewput (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ a ≠ st[a, d].min → st[a, d].min = st.min

Rule argument

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

Additional information

Used simplifier rules: min-def: ⊦ st ≠ ∅ → st.min = st.keys.min; Used terms: d, a, st