Theorems · Theorem · field theory
norm_inv
∀ {α : Type u_2} [inst : NormedDivisionRing α] (a : α), ‖a⁻¹‖ = ‖a‖⁻¹- Defined in
- Mathlib.Analysis.Normed.Field.Basic
- Cited by
- 126 results in Mathlib
- Foundations
- Depth 117 from the axioms, rests on 2,478 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedDivisionRing
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
- NormedDivisionRingstatement and proof · cited by 360
- map_inv₀proof · cited by 106
- normHomproof · cited by 8
Cited by126
Results whose statement or proof uses this declaration.
- nnnorm_invproof · cited by 14
- NormedField.exists_norm_ltproof · cited by 11
- dist_left_midpointproof · cited by 7
- Balanced.smul_monoproof · cited by 6
- norm_smul_inv_normproof · cited by 5
- Seminorm.smul_ball_zeroproof · cited by 5
- egauge_ball_le_of_one_lt_normproof · cited by 4
- exists_norm_eqproof · cited by 4
- Complex.angle_eq_abs_argproof · cited by 4
- NormedSpace.norm_normalize_eq_one_iffproof · cited by 3
- smul_sphere'proof · cited by 3
- isConformalMap_complex_linearproof · cited by 3