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Theorem minmax-04

⊦ s ≠ ∅ → ¬ s.max < s.min

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: bm-shift, bmax-min, bmax-one, bmax-one-01, bmin-bin, bmin-bls, bmin-bneq, bmin-del-04, bmin-in-04, bmin-min, bmin-one, bmin-one-03, bmin-sub-01, bmin-sub-02, bmin-sub-05, butmin-ins, butmin-ins-01, ls-add, ls-rm, max-bmin, max-del-01, max-ifins, max-q, max-subset, maxunion, min-del, min-delmin, min-delmin-01, min-ins-01, min-ins-02, min-ins-03, min-ins-04, min-insert, min-q, min-sub-01, min-two-02, minmax-02, minmax-03,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 1
Used lemmas: max-gr, Min-in, Max-in,
Used spec theorems:
- Used simplifier rules:
  - set-basic/size-zero-01