Theorems · Theorem · order theory
Left.add_pos_of_nonneg_of_pos
∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : Preorder α] [AddLeftStrictMono α] {a b : α},
0 ≤ a → 0 < b → 0 < a + bAssumes left covariance.
The lemma assuming right covariance is Right.add_pos_of_nonneg_of_pos.
- Cited by
- 5 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
- AddLeftStrictMonostatement and proof · cited by 203
- lt_add_of_le_of_posproof · cited by 11
Cited by5
Results whose statement or proof uses this declaration.
- add_pos_of_nonneg_of_posproof · cited by 11
- 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
- Orientation.abs_oangle_sub_left_toReal_lt_pi_div_twoproof · cited by 1
- Left.pos_add_of_rightproof · cited by 0