Theorems · Theorem · functional analysis
RCLike.abs_re_le_norm
∀ {K : Type u_1} [inst : RCLike K] (z : K), |RCLike.re z| ≤ ‖z‖- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Norm.normstatement and proof · cited by 5,413
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- absstatement · cited by 1,814
- norm_nonnegproof · cited by 725
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement and proof · cited by 319
- abs_nonnegproof · cited by 168
- abs_mul_abs_selfproof · cited by 21
- mul_self_le_mul_self_iffproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- RCLike.re_le_normproof · cited by 5
- StrongDual.norm_extendRCLikeproof · cited by 2
- RCLike.norm_re_le_normproof · cited by 2
- ContinuousLinearMap.rayleighQuotient_le_normproof · cited by 2
- RCLike.isCauSeq_reproof · cited by 0
- RCLike.abs_re_div_norm_le_oneproof · cited by 0