Theorems · Theorem · group theory
div_eq_iff
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] {a b c : G₀}, b ≠ 0 → (a / b = c ↔ a = c * b)- Cited by
- 37 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupWithZero
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.
- GroupWithZerostatement and proof · cited by 691
- Ne.isUnitproof · cited by 99
- IsUnit.div_eq_iffproof · cited by 4
Cited by37
Results whose statement or proof uses this declaration.
- AnalyticAt.hasFPowerSeriesAtproof · cited by 7
- Complex.cos_eq_zero_iffproof · cited by 5
- Real.logb_rpowproof · cited by 5
- Complex.Gammaℝ_eq_zero_iffproof · cited by 5
- smul_sphere'proof · cited by 3
- Orientation.oangle_eq_of_angle_eq_of_sign_eqproof · cited by 3
- RatFunc.num_mul_eq_mul_denom_iffproof · cited by 3
- Icc_subset_segmentproof · cited by 3
- BoxIntegral.unitPartition.tag_index_eq_self_of_mem_smul_spanproof · cited by 2
- PowerSeries.exp_mul_exp_eq_exp_addproof · cited by 2
- EulerSine.integral_cos_pow_eqproof · cited by 2
- Valuation.exists_div_eq_of_unitproof · cited by 2