Theorems · Theorem · order theory
inv_pos_of_pos
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [PosMulReflectLT G₀] {a : G₀}, 0 < a → 0 < a⁻¹Alias of the reverse direction of inv_pos.
- Cited by
- 123 results in Mathlib
- Foundations
- Depth 19 from the axioms, rests on 176 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- PosMulReflectLTstatement and proof · cited by 278
- inv_posproof · cited by 124
Cited by123
Results whose statement or proof uses this declaration.
- Function.hasTemperateGrowth_one_add_norm_sq_rpowproof · cited by 9
- Real.summable_ofDigitsTermproof · cited by 5
- EReal.inv_pos_of_pos_ne_topproof · cited by 4
- Affine.Simplex.excenterWeights_empty_posproof · cited by 4
- harmonic_posproof · cited by 3
- Real.ofDigitsTerm_leproof · cited by 3
- MeasureTheory.eLpNorm'_le_eLpNormEssSup_mul_rpow_measure_univproof · cited by 3
- PeriodPair.summable_weierstrassPExceptSummandproof · cited by 3
- Real.ofDigits_le_oneproof · cited by 3
- Manifold.exists_lt_locally_constant_of_riemannianEDist_ltproof · cited by 3
- InnerProductGeometry.angle_normalize_leftproof · cited by 3
- Real.sigmoid_posproof · cited by 3