Theorems · Theorem · order theory
le_add_of_nonneg_right
∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : LE α] [AddLeftMono α] {a b : α}, 0 ≤ b → a ≤ a + b- Cited by
- 69 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- AddZeroClassLEAddLeftMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_zeroproof · cited by 2,707
- AddZeroClassstatement and proof · cited by 1,237
- AddLeftMonostatement and proof · cited by 687
- add_le_add_rightproof · cited by 37
Cited by71
Results whose statement or proof uses this declaration.
- Nat.mono_castproof · cited by 76
- ProbabilityTheory.integrable_exp_mul_of_le_of_leproof · cited by 7
- max_le_add_of_nonnegproof · cited by 6
- InnerProductGeometry.cos_angle_add_of_inner_eq_zeroproof · cited by 5
- Nat.floor_add_natCastproof · cited by 4
- ProbabilityTheory.add_half_inf_sub_mem_Iooproof · cited by 4
- ProbabilityTheory.sub_half_inf_sub_mem_Iooproof · cited by 4
- Associates.factors_monoproof · cited by 3
- List.single_le_sumproof · cited by 3
- nsmul_left_monotoneproof · cited by 3
- Filter.Tendsto.atTop_add_zero_eventuallyLEproof · cited by 3
- ascPochhammer_posproof · cited by 3