Theorems · Theorem · order theory
abs_nonpos_iff
∀ {α : Type u_1} [inst : AddGroup α] [inst_1 : LinearOrder α] [AddLeftMono α] {a : α} [AddRightMono α], |a| ≤ 0 ↔ a = 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddLeftMonostatement and proof · cited by 687
- AddRightMonostatement and proof · cited by 367
- abs_nonnegproof · cited by 168
- LE.le.ge_iff_eq'proof · cited by 50
- abs_eq_zeroproof · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- ArchimedeanClass.mk_eq_top_iffproof · cited by 7
- NumberField.hermiteTheorem.rank_le_rankOfDiscrBddproof · cited by 4
- PseudoMetricSpace.dist_eq_of_dist_zeroproof · cited by 0