Theorems · Theorem · group theory
mul_div_mul_left
∀ {G₀ : Type u_3} [inst : CommGroupWithZero G₀] {c : G₀} (a b : G₀), c ≠ 0 → c * a / (c * b) = a / b- Cited by
- 25 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommGroupWithZero
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.
- Ne.isUnitproof · cited by 99
- CommGroupWithZerostatement and proof · cited by 94
- IsUnit.mul_div_mul_leftproof · cited by 1
Cited by25
Results whose statement or proof uses this declaration.
- RatFunc.num_div_denomproof · cited by 18
- InnerProductGeometry.angle_smul_right_of_posproof · cited by 6
- EuclideanGeometry.dist_smul_vadd_eq_distproof · cited by 4
- WeierstrassCurve.Projective.Point.toAffine_smulproof · cited by 3
- Real.tendsto_exp_div_pow_atTopproof · cited by 3
- WeierstrassCurve.Jacobian.Point.toAffine_smulproof · cited by 3
- LiouvilleWith.add_ratproof · cited by 2
- CircleDeg1Lift.transnumAuxSeq_dist_ltproof · cited by 2
- AddCircle.ae_empty_or_univ_of_forall_vadd_ae_eq_selfproof · cited by 2
- LiouvilleWith.mul_ratproof · cited by 2
- ArithmeticFunction.vonMangoldt.eqOn_LFunctionResidueClassAuxproof · cited by 2
- InnerProductGeometry.angle_smul_smulproof · cited by 1