Theorems · Theorem · order theory
AntivaryOn.dual_right
∀ {ι : Type u_1} {α : Type u_3} {β : Type u_4} [inst : Preorder α] [inst_1 : Preorder β] {f : ι → α} {g : ι → β}
{s : Set ι}, AntivaryOn f g s → MonovaryOn f (⇑OrderDual.toDual ∘ g) s- Defined in
- Mathlib.Order.Monotone.Monovary
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses 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.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Preorderstatement and proof · cited by 7,952
- OrderDualstatement · cited by 927
- OrderDual.toDualstatement · cited by 481
- MonovaryOnstatement · cited by 139
- AntivaryOnstatement · cited by 138
- Function.swap₂proof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- AntivaryOn.sum_comp_perm_smul_eq_sum_smul_iffproof · cited by 3
- AntivaryOn.sum_smul_comp_perm_eq_sum_smul_iffproof · cited by 3
- AntivaryOn.sum_smul_le_sum_comp_perm_smulproof · cited by 3
- AntivaryOn.sum_smul_le_sum_smul_comp_permproof · cited by 3
- AntivaryOn.card_smul_sum_le_sum_smul_sumproof · cited by 1