Theorems · Theorem · functional analysis
RCLike.re_add_im
∀ {K : Type u_1} [inst : RCLike K] (z : K), ↑(RCLike.re z) + ↑(RCLike.im z) * RCLike.I = z- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 159 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.
Cites10
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
- RCLike.ofRealstatement · cited by 350
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement · cited by 319
- RCLike.imstatement · cited by 161
- RCLike.Istatement · cited by 100
- RCLike.re_add_im_axproof · cited by 1
Cited by21
Results whose statement or proof uses this declaration.
- RCLike.ext_iffproof · cited by 13
- RCLike.is_real_TFAEproof · cited by 5
- RCLike.im_eq_zeroproof · cited by 5
- RCLike.add_conjproof · cited by 3
- RCLike.conj_eq_re_sub_improof · cited by 3
- MeasureTheory.memLp_re_im_iffproof · cited by 2
- integral_coe_re_add_coe_improof · cited by 1
- Module.Dual.exists_extension_of_le_seminormproof · cited by 1
- RCLike.span_one_Iproof · cited by 1
- RCLike.hasSum_iffproof · cited by 1
- WeakBilin.continuous_of_continuous_eval_reproof · cited by 1