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Proof step 2 from proof bmin-one-03 (previous step)

# s = 1, s.butmin.min ∈ s.butmin, s.butmin.max ∈ s.butmin ⊦ s.butmin = ∅, # s.butmin = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ s ≠ ∅ → s.butmin = s -- s.min

Rule argument

spec: oset inst: name: Butmin seq: ⊦ s ≠ ∅ → s.butmin = s -- s.min subst: [s] → [s] flags: rewrite, current

Additional information

Used simplifier rules: min-one-01: ⊦ # s = 1 → ∅ ++ s.min = s;%del-e-02: ⊦ s -- a = ∅ ↔ s = ∅ ∨ s = ∅ ++ a; from specification set-union%Size-empty: ⊦ # ∅ = 0; from specification set-basic Used terms: s