[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 10 from proof min-put (previous step)

⊦ # st.keys = 0, st.keys = ∅, a = (st.keys ++ a).min, (st.keys ++ a).min = st.min, a < st.keys.min

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ a ∈ s ∧ ¬ b < a → (s ++ b).min = s.min
Proof step 12:
st.keys.min ∈ st.keys ∧ ¬ a < st.keys.min ⊦ # st.keys = 0, st.keys = ∅, a = st.keys.min, st.keys.min = st.min, a < st.keys.min

Rule argument

spec: oset inst: name: min-ins-01 seq: ⊦ a ∈ s ∧ ¬ b < a → (s ++ b).min = s.min subst: [a, s, b] → [st.keys.min, st.keys, a] flags: rewrite

Additional information

Used simplifier rules: min-inn: ⊦ ¬ s.min ∈ s ↔ s = ∅; from specification oset Used terms: st.keys.min, st.keys, a