Theorems · Theorem · order theory
abs_eq_zero
∀ {α : Type u_1} [inst : AddGroup α] [inst_1 : LinearOrder α] [AddLeftMono α] {a : α} [AddRightMono α], |a| = 0 ↔ a = 0- Cited by
- 17 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
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
- not_iff_notproof · cited by 159
- abs_ne_zeroproof · cited by 9
Cited by17
Results whose statement or proof uses this declaration.
- AddCircle.norm_eqproof · cited by 6
- ProbabilityTheory.gaussianReal_map_const_mulproof · cited by 4
- abs_nonpos_iffproof · cited by 3
- eq_of_abs_sub_eq_zeroproof · cited by 2
- dist_integral_mulExpNegMulSq_comp_leproof · cited by 1
- InnerProductGeometry.sin_eq_one_iff_angle_eq_pi_div_twoproof · cited by 1
- NumberField.mixedEmbedding.norm_eq_zero_iff'proof · cited by 1
- norm_cauchyPowerSeries_leproof · cited by 1
- mellin_comp_rpowproof · cited by 1
- FractionalIdeal.absNorm_span_singletonproof · cited by 1
- FractionalIdeal.abs_det_basis_changeproof · cited by 1