Mathlib Map

Theorems · Theorem · group theory

mul_one_div

∀ {G : Type u_3} [inst : DivInvMonoid G] (x y : G), x * (1 / y) = x / y
Defined in
Mathlib.Algebra.Group.Basic
Cited by
45 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
DivInvMonoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

div_neg_eq_neg_div · cited by 6div_neg_eq_neg_divHurwitzZeta.completedHurwitzZetaEven_eq · cited by 4HurwitzZeta.completedHurw…Pell.exists_of_not_isSquare · cited by 3Pell.exists_of_not_isSqua…volume_iUnion_setOfPred_liouvilleWith · cited by 2volume_iUnion_setOfPred_l…ProbabilityTheory.lintegral_gammaPDF_eq_one · cited by 2ProbabilityTheory.lintegr…MeasureTheory.hahn_decomposition · cited by 2MeasureTheory.hahn_decomp…PowerSeries.exp_mul_exp_eq_exp_add · cited by 2PowerSeries.exp_mul_exp_e…logDeriv_zpow · cited by 2logDeriv_zpowComplex.hasSum_sin · cited by 2Complex.hasSum_sinStirling.stirlingSeq_one · cited by 2Stirling.stirlingSeq_onesum_range_pow · cited by 2sum_range_powNNReal.rpow_add_rpow_le · cited by 2NNReal.rpow_add_rpow_lePolynomial.Splits.eval_derivative_eq_eval_mul_sum · cited by 1Splits.eval_derivative_eq…Real.hasDerivAt_Gamma_one_half · cited by 1Real.hasDerivAt_Gamma_one…MeasureTheory.tendsto_Lp_finite_of_tendsto_ae_of_meas · cited by 1MeasureTheory.tendsto_Lp_…one_mul · cited by 2841one_muldiv_eq_mul_inv · cited by 715div_eq_mul_invDivInvMonoid · cited by 103DivInvMonoidmul_one_divCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by45

Results whose statement or proof uses this declaration.