Theorems · Definition · order theory
StrictMono
{α : Type u} → {β : Type v} → [Preorder α] → [Preorder β] → (α → β) → PropA function f is strictly monotone if a < b implies f a < f b.
- Defined in
- Mathlib.Order.Monotone.Defs
- Cited by
- 706 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 5 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
Cited by758
Results whose statement or proof uses this declaration.
- StrictMono.monotonestatement and proof · cited by 118
- StrictMono.le_iff_lestatement and proof · cited by 104
- StrictMono.injectivestatement and proof · cited by 94
- StrictMono.lt_iff_ltstatement and proof · cited by 86
- List.SortedLTproof · cited by 66
- Order.IsNormal.strictMonostatement · cited by 44
- StrictMono.compstatement and proof · cited by 36
- StrictMono.le_applystatement and proof · cited by 32
- IsSeqCompactproof · cited by 26
- OrderEmbedding.strictMonostatement · cited by 26
- OrderIso.strictMonostatement · cited by 26
- StrictMono.strictMonoOnstatement and proof · cited by 24
Showing the 200 most cited of 758.