Theorems · Theorem · order theory
OrderIso.monotone
∀ {α : Type u_2} {β : Type u_3} [inst : Preorder α] [inst_1 : Preorder β] (e : α ≃o β), Monotone ⇑e- Defined in
- Mathlib.Order.Hom.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses Quot.sound
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.
- DFunLike.coestatement · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- Monotonestatement · cited by 1,397
- OrderIsostatement and proof · cited by 874
- OrderEmbedding.monotoneproof · cited by 26
- OrderIso.toOrderEmbeddingproof · cited by 22
Cited by24
Results whose statement or proof uses this declaration.
- OrderIso.equivalenceproof · cited by 16
- OrderIso.limsup_applyproof · cited by 5
- Tuple.monotone_sortproof · cited by 3
- Disjoint.map_orderIsoproof · cited by 3
- OrderIso.upperBounds_imageproof · cited by 3
- Real.monotone_arcsinproof · cited by 2
- Codisjoint.map_orderIsoproof · cited by 2
- IsUpperSet.imageproof · cited by 2
- IsLowerSet.imageproof · cited by 2
- iSupIndep.map_orderIsoproof · cited by 1
- Real.arctan_add_arctan_lt_pi_div_twoproof · cited by 1
- BddBelow.range_invproof · cited by 1