Theorems · Theorem · order theory
div_le_div_iff_of_pos_right
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [MulPosReflectLT G₀] {a b c : G₀},
0 < c → (a / c ≤ b / c ↔ a ≤ b)- Cited by
- 20 results in Mathlib
- Foundations
- Depth 26 from the axioms · 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
- LT.lt.ne'proof · cited by 1,417
- GroupWithZerostatement and proof · cited by 691
- div_mul_cancel₀proof · cited by 122
- div_le_iff₀proof · cited by 97
- MulPosReflectLTstatement and proof · cited by 93
Cited by20
Results whose statement or proof uses this declaration.
- Real.two_le_piproof · cited by 5
- image_le_of_liminf_slope_right_lt_deriv_boundary'proof · cited by 4
- Real.pi_le_fourproof · cited by 3
- Real.logb_le_logbproof · cited by 2
- UpperHalfPlane.dist_le_iff_le_sinhproof · cited by 2
- CircleDeg1Lift.tendsto_translationNumber_of_dist_bounded_auxproof · cited by 2
- PadicInt.fwdDiff_iter_le_of_forall_leproof · cited by 1
- seminormFromBounded_isNonarchimedeanproof · cited by 1
- EuclideanGeometry.mul_dist_le_mul_dist_add_mul_distproof · cited by 1
- seminormFromConst_seq_antitoneproof · cited by 1
- MeasureTheory.Measure.haar.prehaar_monoproof · cited by 1
- CircleDeg1Lift.tendsto_translation_number₀'proof · cited by 1