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Proof step 2 from proof bmin-bls (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: oset inst: name: min-delmin seq: ⊦ 1 < # s → s.min < (s -- s.min).min subst: [s] → [s] flags: rewrite, current

Additional information

Used simplifier rules: min-one-01: ⊦ # s = 1 → ∅ ++ s.min = s;%one-02: ⊦ m ≠ 0 → (¬ 1 < m ↔ m = 1); from specification nat-basic1 Used terms: s