Theorems · Theorem · order theory
Antitone.dual_right
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
Antitone f → Monotone (⇑OrderDual.toDual ∘ f)Alias of the reverse direction of monotone_toDual_comp_iff.
- Defined in
- Mathlib.Order.Monotone.Basic
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Equivstatement · cited by 8,337
- Preorderstatement and proof · cited by 7,952
- Monotonestatement · cited by 1,397
- OrderDualstatement · cited by 927
- Antitonestatement · cited by 563
- OrderDual.toDualstatement · cited by 481
- monotone_toDual_comp_iffproof · cited by 3
Cited by42
Results whose statement or proof uses this declaration.
- Antitone.le_of_tendstoproof · cited by 7
- Antitone.map_csInf_of_continuousAtproof · cited by 2
- Antitone.countable_setOfPred_two_preimagesproof · cited by 1
- Antitone.iInf_nat_addproof · cited by 1
- Antitone.image_lowerBounds_subset_upperBounds_imageproof · cited by 1
- Antitone.image_upperBounds_subset_lowerBounds_imageproof · cited by 1
- Antitone.map_bddAboveproof · cited by 1
- Antitone.map_bddBelowproof · cited by 1
- Antitone.map_csSup_of_continuousAtproof · cited by 1
- Antitone.map_isLeastproof · cited by 1
- Monotone.antivaryproof · cited by 1
- Antitone.monovaryproof · cited by 1