Theorems · Theorem · order theory
le_of_add_le_add_right
∀ {α : Type u_1} [inst : Add α] [inst_1 : LE α] [AddRightReflectLE α] {a b c : α}, b + a ≤ c + a → b ≤ c- Cited by
- 15 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- AddLEAddRightReflectLE
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.
- AddRightReflectLEstatement and proof · cited by 53
- AddRightReflectLE.le_of_add_le_add_rightproof · cited by 2
Cited by15
Results whose statement or proof uses this declaration.
- mul_le_mul_of_nonpos_rightproof · cited by 13
- mul_le_mul_of_nonpos_leftproof · cited by 11
- add_tsub_add_eq_tsub_rightproof · cited by 5
- WithTop.le_of_add_le_add_rightproof · cited by 4
- Group.nilpotencyClass_quotient_centerproof · cited by 3
- Filter.Tendsto.atTop_of_add_constproof · cited by 3
- ProbabilityTheory.IsMeasurableRatCDF.tendsto_stieltjesFunction_atTopproof · cited by 3
- MonomialOrder.coeff_mul_of_add_of_degree_leproof · cited by 3
- AddGroup.nilpotencyClass_quotient_centerproof · cited by 2
- Set.Ioc_add_bijproof · cited by 1
- WithBot.le_of_add_le_add_rightproof · cited by 1
- Set.Icc_add_bijproof · cited by 1