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Theorem size-three

⊦ 2 < # s → (∃ a, b, c. a ∈ s ∧ b ∈ s ∧ c ∈ s ∧ a ≠ b ∧ a ≠ c ∧ b ≠ c)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 10
Used lemmas: add, Size-insert, in-04, eq, ne, size-exgr, size-one-01, two-01, ne-02, selsize, size-zero,
Used spec theorems:
- Used simplifier rules:
  - nat-basic1/f
  - nat/fle
  - nat/lels
  - nat-basic2/a
  - nat-basic2/c