Theorems · Theorem · order theory
Left.add_pos_of_pos_of_nonneg
∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : Preorder α] [AddLeftMono α] {a b : α}, 0 < a → 0 ≤ b → 0 < a + bAssumes left covariance.
The lemma assuming right covariance is Right.add_pos_of_pos_of_nonneg.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
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.
- Preorderstatement and proof · cited by 7,952
- AddZeroClassstatement and proof · cited by 1,237
- AddLeftMonostatement and proof · cited by 687
- lt_add_of_lt_of_nonnegproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- add_pos_of_pos_of_nonnegproof · cited by 63
- InnerProductGeometry.angle_add_eq_arcsin_of_inner_eq_zeroproof · cited by 5
- InnerProductGeometry.sin_angle_add_mul_norm_of_inner_eq_zeroproof · cited by 3
- InnerProductGeometry.angle_add_lt_pi_div_two_of_inner_eq_zeroproof · cited by 2
- InnerProductGeometry.angle_add_pos_of_inner_eq_zeroproof · cited by 2
- Left.pos_add_of_leftproof · cited by 1