Theorems · Theorem · functional analysis
QuotientAddGroup.norm_mk_le_norm
∀ {M : Type u_1} [inst : SeminormedAddCommGroup M] {S : AddSubgroup M} {m : M}, ‖↑m‖ ≤ ‖m‖The norm of the projection is smaller or equal to the norm of the original element.
- Defined in
- Mathlib.Analysis.Normed.Group.Quotient
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 155 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.
Cites9
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
- AddSubgroupstatement and proof · cited by 3,232
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- HasQuotient.Quotientstatement · cited by 2,301
- QuotientAddGroup.mkstatement and proof · cited by 348
- LE.le.trans_eqproof · cited by 328
- dist_zero_leftproof · cited by 15
- Metric.infDist_le_dist_of_memproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.Quotient.norm_mk_leproof · cited by 0
- Submodule.Quotient.norm_mk_leproof · cited by 0