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Proof step 7 from proof min-insert (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ a ∈ s → ¬ a < s.min

Rule argument

spec: oset inst: name: Min-min seq: ⊦ a ∈ s → ¬ a < s.min subst: [s, a] → [s ++ a, a] flags: rewrite, current

Additional information

Used simplifier rules: add: ⊦ ¬ a ∈ s ++ b ↔ a ≠ b ∧ ¬ a ∈ s; from specification set-basic Used terms: s ++ a, a