Theorems · Theorem · order theory
add_eq_zero_iff_of_nonneg
∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : PartialOrder α] [AddLeftMono α] [AddRightMono α] {a b : α},
0 ≤ a → 0 ≤ b → (a + b = 0 ↔ a = 0 ∧ b = 0)- Cited by
- 8 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- add_zeroproof · cited by 2,707
- le_antisymmproof · cited by 2,068
- le_rflproof · cited by 1,558
- AddZeroClassstatement and proof · cited by 1,237
- AddLeftMonostatement and proof · cited by 687
- AddRightMonostatement and proof · cited by 367
- le_add_of_le_of_nonnegproof · cited by 8
- le_add_of_nonneg_of_leproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- Finset.sum_eq_zero_iff_of_nonnegproof · cited by 19
- InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zeroproof · cited by 3
- Quaternion.normSq_eq_zeroproof · cited by 2
- Convex.exists_mem_add_smul_eqproof · cited by 2
- IsCoprime.sq_add_sq_ne_zeroproof · cited by 2
- QuadraticMap.posDef_prod_iffproof · cited by 1
- mul_self_add_mul_self_eq_zeroproof · cited by 1
- Zsqrtd.norm_eq_zero_iffproof · cited by 0