Theorems · Theorem · order theory
Left.add_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.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 9 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_lt_of_posproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- add_posproof · cited by 28
- AffineSubspace.wOppSide_iff_exists_wbtwproof · cited by 1
- AddSubmonoid.mem_closure_image_pos_iffproof · cited by 0
- sbtw_of_sbtw_of_sbtw_of_mem_affineSpan_pairproof · cited by 0