Theorems · Theorem · group theory
div_inv_eq_mul
∀ {α : Type u_1} [inst : DivisionMonoid α] (a b : α), a / b⁻¹ = a * b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- DivisionMonoid
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.
- div_eq_mul_invproof · cited by 715
- inv_invproof · cited by 494
- DivisionMonoidstatement and proof · cited by 201
Cited by53
Results whose statement or proof uses this declaration.
- UniformContinuous.mulproof · cited by 7
- isLittleO_exp_neg_mul_rpow_atTopproof · cited by 4
- singleton_mul_ballproof · cited by 3
- ProbabilityTheory.complexMGF_id_gaussianRealproof · cited by 3
- Real.hasStrictDerivAt_arctanproof · cited by 3
- NNReal.strictConcaveOn_rpowproof · cited by 3
- tendsto_log_mul_rpow_nhdsGT_zeroproof · cited by 3
- Finset.ruzsa_covering_mulproof · cited by 2
- Finset.ruzsa_triangle_inequality_div_mul_mulproof · cited by 2
- Finset.ruzsa_triangle_inequality_mul_div_divproof · cited by 2
- NNReal.inner_le_weight_mul_Lpproof · cited by 2
- Real.mulExpNegMulSq_one_le_oneproof · cited by 2