Theorems · Theorem · order theory
WithTop.monotone_map_iff
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
Monotone (WithTop.map f) ↔ Monotone f- Defined in
- Mathlib.Order.WithBot
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Preorderstatement and proof · cited by 7,952
- WithTopstatement · cited by 3,754
- Monotonestatement · cited by 1,397
- WithTop.someproof · cited by 1,128
- le_topproof · cited by 411
- WithTop.mapstatement and proof · cited by 68
- WithTop.coe_le_coeproof · cited by 65
- WithTop.monotone_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Monotone.withTop_mapproof · cited by 0
- ENat.monotone_map_iffproof · cited by 0