Theorems · Theorem · functional analysis
RCLike.map_apply
∀ (𝕜 : Type u_3) (𝕜' : Type u_4) [inst : RCLike 𝕜] [inst_1 : RCLike 𝕜'] (x : 𝕜), (RCLike.map 𝕜 𝕜') x = ↑(RCLike.re x) + ↑(RCLike.im x) * RCLike.I
- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 25,697
- RingHom.idstatement · cited by 18,349
- ContinuousLinearMapstatement · cited by 5,352
- 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.mapstatement and proof · cited by 14
Cited by12
Results whose statement or proof uses this declaration.
- RCLike.sqrt_eq_iteproof · cited by 4
- RCLike.map_same_eq_idproof · cited by 1
- RCLike.sqrt_neg_of_nonnegproof · cited by 1
- RCLike.sqrt_oneproof · cited by 1
- RCLike.re_sqrt_ofRealproof · cited by 1
- RCLike.map_nonneg_iffproof · cited by 1
- RCLike.map_to_realproof · cited by 0
- RCLike.sqrt_eq_real_add_iteproof · cited by 0
- RCLike.sqrt_mapproof · cited by 0
- RCLike.sqrt_zeroproof · cited by 0
- Complex.sqrt_mapproof · cited by 0
- RCLike.map_from_realproof · cited by 0