Theorems · Theorem · group theory
div_mul_cancel_of_imp
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] {a b : G₀}, (b = 0 → a = 0) → a / b * b = a- Cited by
- 5 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulZeroClass.mul_zeroproof · cited by 2,091
- eq_or_neproof · cited by 1,117
- GroupWithZerostatement and proof · cited by 691
- div_zeroproof · cited by 251
- IsUnit.div_mul_cancelproof · cited by 37
Cited by5
Results whose statement or proof uses this declaration.
- Asymptotics.isLittleO_iff_tendsto'proof · cited by 7
- Asymptotics.isEquivalent_of_tendsto_oneproof · cited by 5
- Asymptotics.IsBigOWith.eventually_mul_div_cancelproof · cited by 3
- InnerProductGeometry.cos_angle_mul_norm_mul_normproof · cited by 2
- mul_div_cancel_of_imp'proof · cited by 0