Theorems · Theorem · order theory
abs_sub_map_le_sub
∀ {F : Type u_2} {α : Type u_3} {β : Type u_4} [inst : FunLike F α β] [inst_1 : AddGroup α] [inst_2 : AddCommGroup β]
[inst_3 : LinearOrder β] [IsOrderedAddMonoid β] [AddGroupSeminormClass F α β] (f : F) (x y : α),
|f x - f y| ≤ f (x - y)- Defined in
- Mathlib.Algebra.Order.Hom.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- AddGroupstatement and proof · cited by 4,410
- FunLikestatement and proof · cited by 2,560
- absstatement · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- sub_le_iff_le_add'proof · cited by 41
- abs_sub_le_iffproof · cited by 34
- AddGroupSeminormClassstatement and proof · cited by 18
- le_map_add_map_subproof · cited by 1
- le_map_add_map_sub'proof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Seminorm.norm_sub_map_le_subproof · cited by 1