Theorems · Theorem · functional analysis
norm_inv_mul
∀ {E : Type u_5} [inst : SeminormedCommGroup E] (a b : E), ‖a⁻¹ * b‖ = ‖a / b‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- SeminormedCommGroup
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 and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- SeminormedCommGroupstatement and proof · cited by 191
- dist_eq_norm_inv_mulproof · cited by 41
- dist_eq_norm_divproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- abs_norm_sub_norm_le'proof · cited by 2
- NormedCommGroup.tendsto_nhds_nhdsproof · cited by 0
- NormedCommGroup.nhds_basis_norm_ltproof · cited by 0
- NormedCommGroup.uniformity_basis_distproof · cited by 0
- ball_eq'proof · cited by 0