Theorems · Theorem · order theory
inv_nonneg
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [PosMulReflectLT G₀] {a : G₀}, 0 ≤ a⁻¹ ↔ 0 ≤ a- Cited by
- 56 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
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 and proof · cited by 6,410
- GroupWithZerostatement and proof · cited by 691
- PosMulReflectLTstatement and proof · cited by 278
Cited by56
Results whose statement or proof uses this declaration.
- div_nonnegproof · cited by 103
- div_le_div₀proof · cited by 53
- inv_nonneg_of_nonnegproof · cited by 24
- ENNReal.ofReal_div_of_posproof · cited by 14
- one_div_nonnegproof · cited by 11
- Real.div_rpowproof · cited by 10
- zpow_nonnegproof · cited by 7
- EReal.inv_nonneg_of_nonnegproof · cited by 6
- wbtw_iff_left_eq_or_right_mem_image_Iciproof · cited by 4
- MeasureTheory.MemLp.eLpNorm_eq_integral_rpow_normproof · cited by 4
- Real.mul_le_sinproof · cited by 4