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Proof step 6 from proof min-put (previous step)

⊦ (st.keys ++ a).min = st.min, a = (st.keys ++ a).min

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ a < s.min ∧ s ≠ ∅ → (s ++ a).min = a
Proof step 8:
⊦ (st.keys ++ a).min = st.min, a = (st.keys ++ a).min, a < st.keys.min ∧ st.keys ≠ ∅

Rule argument

spec: oset name: min-insert seq: ⊦ a < s.min ∧ s ≠ ∅ → (s ++ a).min = a subst: [a, s] → [a, st.keys] flags: <all paths>

Additional information

Used terms: a, st.keys