Theorems · Theorem · functional analysis
RCLike.norm_le_im_iff_eq_I_mul_norm
∀ {K : Type u_1} [inst : RCLike K] {z : K}, ‖z‖ ≤ RCLike.im z ↔ z = RCLike.I * ↑‖z‖- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 170 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.
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
- Norm.normstatement and proof · cited by 5,413
- AddMonoidHomstatement · cited by 3,230
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
- neg_negproof · cited by 960
- neg_mulproof · cited by 654
- map_negproof · cited by 378
- RCLike.ofRealstatement and proof · cited by 350
Cited by1
Results whose statement or proof uses this declaration.
- RCLike.im_le_neg_norm_iff_eq_neg_I_mul_normproof · cited by 0