Theorems · Theorem · functional analysis
RCLike.norm_le_re_iff_eq_norm
∀ {K : Type u_1} [inst : RCLike K] {z : K}, ‖z‖ ≤ RCLike.re z ↔ z = ↑‖z‖- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 169 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
- le_antisymmproof · cited by 2,068
- RCLike.ofRealstatement and proof · cited by 350
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement and proof · cited by 319
- norm_normproof · cited by 113
- RCLike.ofReal_reproof · cited by 60
- norm_algebraMap'proof · cited by 39
Cited by3
Results whose statement or proof uses this declaration.
- RCLike.norm_le_im_iff_eq_I_mul_normproof · cited by 1
- RCLike.norm_of_nonneg'proof · cited by 1
- RCLike.re_le_neg_norm_iff_eq_neg_normproof · cited by 1