Theorems · Theorem · order theory
le_of_add_le_add_left
∀ {α : Type u_1} [inst : Add α] [inst_1 : LE α] [AddLeftReflectLE α] {a b c : α}, a + b ≤ a + c → b ≤ c- Cited by
- 15 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- AddLEAddLeftReflectLE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddLeftReflectLEstatement and proof · cited by 119
- AddLeftReflectLE.le_of_add_le_add_leftproof · cited by 2
Cited by15
Results whose statement or proof uses this declaration.
- Contravariant.AddLECancellableproof · cited by 45
- ArchimedeanClass.mk_add_eq_mk_leftproof · cited by 4
- WithTop.le_of_add_le_add_leftproof · cited by 3
- Finset.sum_sq_le_sum_mul_sum_of_sq_le_mulproof · cited by 3
- WithBot.le_of_add_le_add_leftproof · cited by 3
- MeasureTheory.hahn_decompositionproof · cited by 2
- nonneg_of_le_add_rightproof · cited by 2
- Filter.Tendsto.atTop_of_const_addproof · cited by 2
- IsMinOn.of_isLocalMinOn_of_convexOn_Iccproof · cited by 1
- IsOrderedAddMonoid.toIsOrderedCancelAddMonoid'proof · cited by 0
- OrderedCommGroup.le_of_add_le_add_leftproof · cited by 0
- Zsqrtd.add_lt_add_leftproof · cited by 0