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Proof step 2 from proof butmin-ins (previous step)

s.min < a, s.min ∈ s, s.max ∈ s ⊦ s = ∅, (s ++ a).butmin = (s -- s.min) ++ a, # s = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ s ≠ ∅ → s.butmin = s -- s.min
Proof step 4:
s ++ a ≠ ∅, s.min < a, s.min ∈ s, s.max ∈ s ⊦ s = ∅, (s ++ a) -- (s ++ a).min = (s -- s.min) ++ a, # s = 0

Rule argument

spec: oset inst: name: Butmin seq: ⊦ s ≠ ∅ → s.butmin = s -- s.min subst: [s] → [s ++ a] flags: rewrite, current

Additional information

Used simplifier rules: ne: ⊦ ∅ ≠ s ++ a; from specification set-basic Used terms: s ++ a