Theorems · Theorem · order theory
StrictMono.eq_id
∀ {α : Type u_4} [inst : LinearOrder α] [Finite α] {f : α → α}, StrictMono f → f = idA strictly monotone self-map of a finite linear order is the identity.
- Defined in
- Mathlib.Order.Preorder.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Finitestatement and proof · cited by 3,029
- le_antisymmproof · cited by 2,068
- StrictMonostatement and proof · cited by 706
- StrictMono.id_leproof · cited by 14
- StrictMono.le_idproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- StrictMono.apply_eqproof · cited by 0