Theorems · Theorem · order theory
abs_pos_of_neg
∀ {α : Type u_1} [inst : AddGroup α] [inst_1 : LinearOrder α] [AddLeftMono α] {a : α}, a < 0 → 0 < |a|- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
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.
- LinearOrderstatement and proof · cited by 8,572
- AddGroupstatement and proof · cited by 4,410
- absstatement · cited by 1,814
- LT.lt.neproof · cited by 872
- AddLeftMonostatement and proof · cited by 687
- abs_posproof · cited by 45
Cited by2
Results whose statement or proof uses this declaration.
- not_summable_of_antitone_of_negproof · cited by 1
- EReal.sign_mul_inv_abs'proof · cited by 0