Theorems · Theorem · order theory
exists_nonneg_add_of_le
∀ {α : Type u} [inst : AddZeroClass α] [inst_1 : Preorder α] [ExistsAddOfLE α] {a b : α} [AddLeftReflectLE α],
a ≤ b → ∃ c, 0 ≤ c ∧ a + c = b- Cited by
- 5 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- AddZeroClassstatement and proof · cited by 1,237
- ExistsAddOfLEstatement and proof · cited by 330
- AddLeftReflectLEstatement and proof · cited by 119
- ExistsAddOfLE.exists_add_of_leproof · cited by 42
- nonneg_of_le_add_rightproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- mul_add_mul_le_mul_add_mulproof · cited by 4
- Set.vadd_Iccproof · cited by 1
- smul_add_smul_le_smul_add_smulproof · cited by 1
- Set.Icc_add_Iccproof · cited by 0
- le_iff_exists_nonneg_addproof · cited by 0