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Proof step 3 from proof min-put (previous step)

⊦ st[a, d].min = st.min, a = st[a, d].min

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ st ≠ ∅ → st.min = st.keys.min
Proof step 5:
⊦ st[a, d].keys.min = st.min, st[a, d] = ∅, a = st[a, d].keys.min

Rule argument

spec: <toplevel> name: min-def seq: ⊦ st ≠ ∅ → st.min = st.keys.min subst: [st] → [st[a, d]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ st[a, d] ≠ ∅; (s) Used terms: st[a, d]