Theorems · Theorem · order theory
le_add_of_le_of_nonneg
∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : Preorder α] [AddLeftMono α] {a b c : α}, b ≤ c → 0 ≤ a → b ≤ c + a- Cited by
- 8 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- 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 by8
Results whose statement or proof uses this declaration.
- add_eq_zero_iff_of_nonnegproof · cited by 8
- Left.add_nonnegproof · cited by 3
- MeasureTheory.hahn_decompositionproof · cited by 2
- Real.exists_int_int_abs_mul_sub_leproof · cited by 2
- mellin_hasDerivAt_of_isBigO_rpowproof · cited by 2
- Padic.exi_rat_seq_convproof · cited by 2
- abs_sub_le_of_nonneg_of_leproof · cited by 1
- NumberField.mixedEmbedding.norm_le_convexBodySumFunproof · cited by 1