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Proof step 7 from proof butmin-ins (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
s.min < a, s.min ∈ s, s.max ∈ s ⊦ s = ∅, (s ++ a) -- s.min = (s -- s.min) ++ a, # s = 0

Rule argument

Additional information

Used simplifier rules: ls-le: ⊦ a < b → (¬ b < a ↔ true); from specification oelem