Theorems · Theorem · group theory
mul_eq_mul_of_div_eq_div
∀ {G₀ : Type u_3} [inst : CommGroupWithZero G₀] {b d : G₀} (a c : G₀), b ≠ 0 → d ≠ 0 → a / b = c / d → a * d = c * b- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- div_selfproof · cited by 237
- div_mul_cancel₀proof · cited by 122
- CommGroupWithZerostatement and proof · cited by 94
- div_mul_eq_mul_divproof · cited by 51
- mul_comm_divproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- RatFunc.liftMonoidWithZeroHom_injectiveproof · cited by 2