Theorems · Theorem · functional analysis
dist_eq_norm_inv_mul
∀ {E : Type u_5} [inst : SeminormedGroup E] (a b : E), dist a b = ‖a⁻¹ * b‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- SeminormedGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- Dist.diststatement · cited by 1,539
- SeminormedGroupstatement and proof · cited by 250
- SeminormedGroup.dist_eqproof · cited by 2
Cited by41
Results whose statement or proof uses this declaration.
- norm_mul_le'proof · cited by 15
- norm_inv_mulproof · cited by 5
- nndist_eq_nnnorm_inv_mulproof · cited by 3
- IsUltrametricDist.norm_mul_eq_max_of_norm_ne_normproof · cited by 3
- IsUltrametricDist.norm_mul_le_maxproof · cited by 3
- norm_div_revproof · cited by 3
- MonoidHomClass.lipschitz_of_boundproof · cited by 3
- tendsto_norm_inv_mul_selfproof · cited by 3
- abs_norm_sub_norm_le_norm_inv_mulproof · cited by 3
- dist_eq_norm_inv_mul'proof · cited by 3
- pow_mem_ballproof · cited by 2
- preimage_mul_ballproof · cited by 2