Theorems · Theorem · group theory
mul_comm_div
∀ {α : Type u_1} [inst : DivisionCommMonoid α] (a b c : α), a / b * c = a * (c / b)- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- DivisionCommMonoid
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_commproof · cited by 2,262
- div_eq_mul_invproof · cited by 715
- mul_left_commproof · cited by 184
- DivisionCommMonoidstatement and proof · cited by 80
Cited by14
Results whose statement or proof uses this declaration.
- NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discrproof · cited by 2
- summable_powerSeries_of_norm_ltproof · cited by 1
- ContinuousOn.isBigOWith_rev_principalproof · cited by 1
- AddCircle.natCast_div_mul_eq_nsmulproof · cited by 1
- LSeries.term_convolutionproof · cited by 1
- smul_sdiv_smul_commproof · cited by 1
- BoxIntegral.unitPartition.integralSum_eq_tsum_divproof · cited by 1
- trapezoidal_integral_oneproof · cited by 1
- mul_eq_mul_of_div_eq_divproof · cited by 1
- IsUnit.mul_eq_mul_of_div_eq_divproof · cited by 0
- AddCircle.intCast_div_mul_eq_zsmulproof · cited by 0
- DirichletCharacter.IsPrimitive.completedLFunction_one_subproof · cited by 0