Theorems · Theorem · order theory
tsub_le_tsub_iff_left
∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [CanonicallyOrderedAdd α] [inst_3 : Sub α]
[OrderedSub α] {a b c : α} [AddLeftReflectLE α], c ≤ a → (a - b ≤ a - c ↔ c ≤ b)- Defined in
- Mathlib.Algebra.Order.Sub.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- OrderedSubstatement and proof · cited by 236
- CanonicallyOrderedAddstatement and proof · cited by 229
- AddLeftReflectLEstatement and proof · cited by 119
- Contravariant.AddLECancellableproof · cited by 45
- AddLECancellable.tsub_le_tsub_iff_leftproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Finset.prod_Ico_reflectproof · cited by 2
- Finset.erdos_ko_radoproof · cited by 0