Theorems · Theorem · group theory
div_eq_inv_mul
∀ {α : Type u_1} [inst : DivisionCommMonoid α] (a b : α), a / b = b⁻¹ * a- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 146 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 63 definitions · uses propext
- Assumes
- DivisionCommMonoid
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.
- mul_commproof · cited by 2,262
- div_eq_mul_invproof · cited by 715
- DivisionCommMonoidstatement and proof · cited by 80
Cited by146
Results whose statement or proof uses this declaration.
- dist_eq_norm_divproof · cited by 12
- mul_div_cancel_leftproof · cited by 9
- slope_def_fieldproof · cited by 7
- Balanced.smul_monoproof · cited by 6
- Seminorm.smul_ball_zeroproof · cited by 5
- Complex.div_ofRealproof · cited by 5
- slope_fun_def_fieldproof · cited by 5
- cfc_re_idproof · cited by 4
- inv_le_inv_of_negproof · cited by 4
- cfcₙ_re_idproof · cited by 4
- AbsoluteValue.isEquiv_iff_exists_rpow_eqproof · cited by 4
- Real.mul_le_sinproof · cited by 4