Theorems · Theorem · functional analysis
norm_of_subsingleton
∀ {E : Type u_5} [inst : SeminormedAddGroup E] [Subsingleton E] (a : E), ‖a‖ = 0- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- norm_zeroproof · cited by 366
- SeminormedAddGroupstatement and proof · cited by 331
Cited by8
Results whose statement or proof uses this declaration.
- norm_apply_le_norm_cfcproof · cited by 5
- selfAdjoint.norm_sq_expUnitary_sub_oneproof · cited by 3
- ContinuousLinearMap.opNorm_subsingletonproof · cited by 3
- Unitization.lipschitzWith_addEquivproof · cited by 2
- Unitization.antilipschitzWith_addEquivproof · cited by 2
- Unitary.norm_sub_one_lt_two_iffproof · cited by 1
- tsum_geometric_le_of_norm_lt_oneproof · cited by 1
- Filter.IsIncreasingApproximateUnit.pure_oneproof · cited by 0