Theorems · Theorem · order theory
abs_lt
∀ {α : Type u_1} [inst : AddGroup α] [inst_1 : LinearOrder α] [AddLeftMono α] {a b : α} [AddRightMono α],
|a| < b ↔ -b < a ∧ a < b- Cited by
- 43 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- max_lt_iffproof · cited by 22
- neg_ltproof · cited by 21
Cited by43
Results whose statement or proof uses this declaration.
- abs_sub_lt_iffproof · cited by 8
- Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_posproof · cited by 6
- ArchimedeanClass.lt_of_mk_lt_mk_of_nonposproof · cited by 6
- nhds_eq_iInf_abs_subproof · cited by 5
- ArchimedeanClass.lt_of_mk_lt_mk_of_nonnegproof · cited by 5
- TFAE_exists_lt_isLittleO_powproof · cited by 4
- nhds_basis_Ioo_posproof · cited by 4
- CircleDeg1Lift.dist_map_map_zero_ltproof · cited by 3
- Real.le_mk_of_forall_leproof · cited by 3
- Real.exists_isLUBproof · cited by 3
- PhragmenLindelof.horizontal_stripproof · cited by 3
- CauSeq.pos_add_limZeroproof · cited by 2