Theorems · Theorem · group theory
inv_div
∀ {α : Type u_1} [inst : DivisionMonoid α] (a b : α), (a / b)⁻¹ = b / a- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 92 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.
- div_eq_mul_invproof · cited by 715
- inv_invproof · cited by 494
- mul_inv_revproof · cited by 270
- DivisionMonoidstatement and proof · cited by 201
Cited by92
Results whose statement or proof uses this declaration.
- mabs_div_commproof · cited by 8
- nhds_eq_iInf_mabs_divproof · cited by 5
- tendsto_rpow_mul_exp_neg_mul_atTop_nhds_zeroproof · cited by 4
- Real.mul_le_sinproof · cited by 4
- NumberField.hermiteTheorem.rank_le_rankOfDiscrBddproof · cited by 4
- Real.tan_pi_div_two_subproof · cited by 4
- tendsto_natCast_div_add_atTopproof · cited by 3
- Real.tendsto_div_pow_mul_exp_add_atTopproof · cited by 3
- MeasureTheory.eLpNorm'_le_eLpNorm'_mul_rpow_measure_univproof · cited by 3
- PeriodPair.summable_weierstrassPExceptSummandproof · cited by 3
- Complex.Gamma_mul_Gamma_one_subproof · cited by 3
- NNReal.Lr_rpow_le_Lp_mul_Lqproof · cited by 3