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Proof step 4 from proof min-insert (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
(s ++ a).min < a, a < s.min, (s ++ a).min < s.min, s.min ∈ s, s.max ∈ s ⊦ # s = 0, (s ++ a).min = a, s = ∅

Rule argument

Additional information

Used simplifier rules: transitivity: ⊦ a < b ∧ b < c → a < c; (forward) from specification oelem