Theorems · Theorem · order theory
zero_lt_iff
∀ {α : Type u_1} {a : α} [inst : PartialOrder α] [inst_1 : Zero α] [IsBotZeroClass α], 0 < a ↔ a ≠ 0Alias of pos_iff_ne_zero.
- Defined in
- Mathlib.Algebra.Order.IsBotOne
- Cited by
- 29 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement · cited by 6,410
- pos_iff_ne_zeroproof · cited by 180
- IsBotZeroClassstatement · cited by 71
Cited by29
Results whose statement or proof uses this declaration.
- Valuation.pos_iffproof · cited by 5
- Valuation.map_sum_ltproof · cited by 4
- IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvdproof · cited by 3
- norm_root_le_spectralValueproof · cited by 3
- Valuation.isEquiv_of_val_le_oneproof · cited by 3
- MeasureTheory.upcrossingsBefore_leproof · cited by 3
- Valuation.IsEquiv.pos_iffproof · cited by 2
- LinearMap.continuous_of_isClosed_kerproof · cited by 2
- LieModule.chainTopCoeff_add_oneproof · cited by 2
- IsDiscreteValuationRing.exists_lift_of_le_oneproof · cited by 2
- Polynomial.eq_one_of_roots_leproof · cited by 2
- Valuation.exists_div_eq_of_unitproof · cited by 2