Theorems · Theorem · group theory
div_mul_eq_div_div_swap
∀ {α : Type u_1} [inst : DivisionMonoid α] (a b c : α), a / (b * c) = a / c / b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- DivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_assocproof · cited by 1,667
- div_eq_mul_invproof · cited by 715
- mul_inv_revproof · cited by 270
- DivisionMonoidstatement and proof · cited by 201
Cited by8
Results whose statement or proof uses this declaration.
- mul_div_mul_right_eq_divproof · cited by 4
- SzemerediRegularity.energy_incrementproof · cited by 1
- Nat.abundancyIndex_le_of_dvdproof · cited by 1
- UpperHalfPlane.dist_le_dist_coe_div_sqrtproof · cited by 0
- Filter.tendsto_div_const_iffproof · cited by 0
- Filter.tendsto_div_const_iff'proof · cited by 0
- MeasureTheory.measurePreserving_mul_prod_inv_rightproof · cited by 0