Theorems · Theorem · group theory
inv_eq_one_div
∀ {G : Type u_1} [inst : DivInvMonoid G] (x : G), x⁻¹ = 1 / x- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- DivInvMonoid
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.
- one_mulproof · cited by 2,841
- div_eq_mul_invproof · cited by 715
- DivInvMonoidstatement and proof · cited by 103
Cited by33
Results whose statement or proof uses this declaration.
- one_divproof · cited by 624
- Complex.inv_Iproof · cited by 22
- neg_invproof · cited by 11
- coeIdeal_differentIdealproof · cited by 8
- div_le_iff_of_negproof · cited by 6
- div_neg_eq_neg_divproof · cited by 6
- Real.rpowIntegrand₀₁_eq_pow_divproof · cited by 6
- ProbabilityTheory.Fernique.logRatio_posproof · cited by 4
- ApproximatesLinearOn.surjOn_closedBall_of_nonlinearRightInverseproof · cited by 3
- Complex.norm_log_one_add_half_le_selfproof · cited by 2
- Real.not_summable_one_div_natCastproof · cited by 2
- NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discrproof · cited by 2