Theorems · Theorem · order theory
div_pos
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [PosMulReflectLT G₀] {a b : G₀},
0 < a → 0 < b → 0 < a / b- Cited by
- 337 results in Mathlib
- Foundations
- Depth 21 from the axioms, rests on 177 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- div_eq_mul_invproof · cited by 715
- GroupWithZerostatement and proof · cited by 691
- mul_posproof · cited by 374
- PosMulReflectLTstatement and proof · cited by 278
- inv_posproof · cited by 124
Cited by337
Results whose statement or proof uses this declaration.
- half_posproof · cited by 83
- Asymptotics.IsBigO.mul_isLittleOproof · cited by 15
- exists_pos_mul_ltproof · cited by 13
- Asymptotics.IsLittleO.mul_isBigOproof · cited by 11
- MeasureTheory.eLpNorm_lt_top_iff_lintegral_rpow_enorm_lt_topproof · cited by 9
- Function.hasTemperateGrowth_one_add_norm_sq_rpowproof · cited by 9
- Asymptotics.isLittleOTVS_iff_isLittleOproof · cited by 7
- UpperHalfPlane.im_inv_neg_coe_posproof · cited by 7
- Real.sin_pi_over_two_pow_succproof · cited by 6
- ContinuousLinearMap.isOpenMapproof · cited by 6
- strictConcaveOn_log_Ioiproof · cited by 5
Showing the 200 most cited of 337.