Theorems · Theorem · functional analysis
RCLike.I_re
∀ {K : Type u_1} [inst : RCLike K], RCLike.re RCLike.I = 0The imaginary unit.
- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 97 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement · cited by 319
- RCLike.Istatement · cited by 100
- RCLike.I_re_axproof · cited by 1
Cited by19
Results whose statement or proof uses this declaration.
- StrongDual.re_extendRCLike_applyproof · cited by 9
- RCLike.I_mul_reproof · cited by 3
- Submodule.norm_eq_iInf_iff_inner_eq_zeroproof · cited by 2
- Module.Dual.re_extendRCLike_applyproof · cited by 2
- InnerProductSpaceable.inner_.norm_sqproof · cited by 1
- RCLike.re_sqrt_ofRealproof · cited by 1
- Module.Dual.exists_extension_of_le_seminormproof · cited by 1
- RCLike.norm_le_im_iff_eq_I_mul_normproof · cited by 1
- WeakBilin.continuous_of_continuous_eval_reproof · cited by 1
- RCLike.sqrt_neg_of_nonnegproof · cited by 1
- RCLike.map_nonneg_iffproof · cited by 1
- StrongDual.im_extendRCLike_applyproof · cited by 1