Theorems · Theorem · order theory
StrictMono.apply_eq
∀ {α : Type u_4} [inst : LinearOrder α] [Finite α] {f : α → α} {x : α}, StrictMono f → f x = xA strictly monotone self-map of a finite linear order fixes every point.
- Defined in
- Mathlib.Order.Preorder.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderFinite
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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
- StrictMonostatement and proof · cited by 706
- StrictMono.eq_idproof · cited by 1
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