Theorems · Theorem · group theory
div_eq_mul_inv
∀ {G : Type u_1} [inst : DivInvMonoid G] (a b : G), a / b = a * b⁻¹Dividing by an element is the same as multiplying by its inverse.
This is a duplicate of DivInvMonoid.div_eq_mul_inv ensuring that the types unfold better.
- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 715 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 35 definitions · uses no axioms
- Assumes
- DivInvMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DivInvMonoidstatement and proof · cited by 103
- DivInvMonoid.div_eq_mul_invproof · cited by 1
Cited by715
Results whose statement or proof uses this declaration.
- div_oneproof · cited by 629
- div_posproof · cited by 337
- div_zeroproof · cited by 251
- zero_divproof · cited by 222
- mul_div_assocproof · cited by 149
- div_eq_inv_mulproof · cited by 146
- div_nonnegproof · cited by 103
- div_le_iff₀proof · cited by 97
- inv_divproof · cited by 92
- add_divproof · cited by 89
- div_le_div_of_nonneg_rightproof · cited by 77
- le_div_iff₀proof · cited by 75
Showing the 200 most cited of 715.