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Proof step 2 from proof min-ins-04 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ a < s.min ∧ s ≠ ∅ → (s ++ a).min = a

Rule argument

spec: oset inst: name: min-insert seq: ⊦ a < s.min ∧ s ≠ ∅ → (s ++ a).min = a subst: [a, s] → [a, s] flags: rewrite, current

Additional information

Used simplifier rules: seq: ⊦ ¬ b < a → (¬ a < b ↔ a = b); from specification oelem%nen: ⊦ ¬ b < a ∧ a = c → ¬ b < c; (forward) from specification oelem%eq: ⊦ a ∈ s → s ++ a = s; from specification set-basic Used terms: a, s