Theorems · Theorem · order theory
one_div_pos
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [PosMulReflectLT G₀] {a : G₀}, 0 < 1 / a ↔ 0 < a- Cited by
- 27 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- GroupWithZerostatement and proof · cited by 691
- one_divproof · cited by 624
- PosMulReflectLTstatement and proof · cited by 278
- inv_posproof · cited by 124
Cited by27
Results whose statement or proof uses this declaration.
- integral_rpow_mul_exp_neg_rpowproof · cited by 4
- MeasureTheory.eLpNorm_le_eLpNorm_mul_eLpNorm_of_nnnormproof · cited by 4
- WeakFEPair.h_feq'proof · cited by 3
- Real.HolderTriple.one_div_posproof · cited by 3
- NNReal.strictConcaveOn_rpowproof · cited by 3
- eventually_residual_liouvilleproof · cited by 2
- Real.HolderTriple.one_div_pos'proof · cited by 2
- NNReal.HolderTriple.one_div_posproof · cited by 2
- NNReal.HolderTriple.one_div_pos'proof · cited by 2
- MeasureTheory.volume_sum_rpow_lt_oneproof · cited by 2
- seminormFromBounded_auxproof · cited by 2
- MeasureTheory.MemLp.eLpNorm_indicator_norm_ge_leproof · cited by 1