Theorems · Theorem · complex analysis
realPart.norm_le
∀ {A : Type u_1} [inst : SeminormedAddCommGroup A] [inst_1 : StarAddMonoid A] [inst_2 : NormedSpace ℂ A]
[inst_3 : StarModule ℂ A] [NormedStarGroup A] (x : A), ‖realPart x‖ ≤ ‖x‖- Defined in
- Mathlib.Analysis.Complex.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- LinearMapstatement · cited by 10,215
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- LE.le.transproof · cited by 3,151
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- le_of_ltproof · cited by 1,175
- Star.starproof · cited by 1,082
Cited by2
Results whose statement or proof uses this declaration.
- imaginaryPart.norm_leproof · cited by 1
- CStarAlgebra.exists_sum_four_nonnegproof · cited by 1