Theorems · Theorem · functional analysis
AddSubgroup.norm_normedMk_le
∀ {M : Type u_1} [inst : SeminormedAddCommGroup M] (S : AddSubgroup M), ‖S.normedMk‖ ≤ 1The operator norm of the projection is at most 1.
- Defined in
- Mathlib.Analysis.Normed.Group.Quotient
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 and proof · cited by 5,413
- AddSubgroupstatement and proof · cited by 3,232
- one_mulproof · cited by 2,841
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- HasQuotient.Quotientstatement · cited by 2,301
- QuotientAddGroup.mkproof · cited by 348
- zero_le_oneproof · cited by 316
- NormedAddGroupHomstatement · cited by 216
- NormedAddGroupHom.opNorm_le_boundproof · cited by 12
- AddSubgroup.normedMkstatement and proof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.norm_normedMkproof · cited by 0