Theorems · Theorem · order theory
AddHom.le_map_tsub
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Add α] [inst_2 : Sub α] [OrderedSub α]
[inst_4 : Preorder β] [inst_5 : Add β] [inst_6 : Sub β] [OrderedSub β] (f : α →ₙ+ β),
Monotone ⇑f → ∀ (a b : α), f a - f b ≤ f (a - b)- Defined in
- Mathlib.Algebra.Order.Sub.Unbundled.Hom
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
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 and proof · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- Monotonestatement and proof · cited by 1,397
- AddHomstatement and proof · cited by 294
- OrderedSubstatement and proof · cited by 236
- tsub_le_iff_rightproof · cited by 49
- le_tsub_addproof · cited by 10
- AddHom.map_addproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- le_mul_tsubproof · cited by 1
- AddMonoidHom.le_map_tsubproof · cited by 0
- OrderIso.map_tsubproof · cited by 0