Theorems · Theorem · group theory
one_div
∀ {G : Type u_1} [inst : DivInvMonoid G] (a : G), 1 / a = a⁻¹- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 624 results in Mathlib
- Foundations
- Depth 8 from the axioms, rests on 38 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
- inv_eq_one_divproof · cited by 33
Cited by624
Results whose statement or proof uses this declaration.
- one_div_posproof · cited by 27
- Real.sqrt_eq_rpowproof · cited by 25
- norm_inv'proof · cited by 23
- Complex.isPrimitiveRoot_expproof · cited by 14
- MeasureTheory.eLpNorm_measure_zeroproof · cited by 13
- tendsto_rpow_atTopproof · cited by 12
- one_div_nonnegproof · cited by 11
- Cardinal.mk_realproof · cited by 11
- MeasureTheory.MemLp.mono_exponentproof · cited by 11
- bernoulli'_oneproof · cited by 10
- div_eq_mul_one_divproof · cited by 10
- PeriodPair.ω₁_div_two_notMem_latticeproof · cited by 10
Showing the 200 most cited of 624.