Theorems · Theorem · functional analysis
norm_zero
∀ {E : Type u_5} [inst : SeminormedAddGroup E], ‖0‖ = 0- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 366 results in Mathlib
- Foundations
- Depth 88 from the axioms, rests on 1,597 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
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 · cited by 5,413
- SeminormedAddGroupstatement and proof · cited by 331
- dist_zero_rightproof · cited by 172
- dist_selfproof · cited by 116
Cited by367
Results whose statement or proof uses this declaration.
- Complex.exp_zeroproof · cited by 43
- nnnorm_zeroproof · cited by 40
- NormedSpace.expSeries_radius_eq_topproof · cited by 27
- norm_sum_leproof · cited by 25
- MeasureTheory.norm_integral_le_integral_normproof · cited by 25
- Complex.arg_zeroproof · cited by 22
- norm_indicator_eq_indicator_normproof · cited by 11
- norm_of_subsingletonproof · cited by 8
- Unitization.norm_inrproof · cited by 8
- PadicInt.norm_le_pow_iff_mem_span_powproof · cited by 7
- DirichletCharacter.norm_le_oneproof · cited by 7
- Asymptotics.isLittleO_zeroproof · cited by 7
Showing the 200 most cited of 367.