Mathlib Map

Theorems · Theorem · functional analysis

RCLike.re_add_im_ax

∀ {K : semiOutParam (Type u_1)} [self : RCLike K] (z : K),
  (algebraMap ℝ K) (RCLike.re z) + (algebraMap ℝ K) (RCLike.im z) * RCLike.I = z
Defined in
Mathlib.Analysis.RCLike.Basic
Cited by
1 results in Mathlib
Foundations
Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RCLike
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

RCLike.re_add_im · cited by 21RCLike.re_add_imDFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealRingHom · cited by 10189RingHomAlgebra.algebraMap · cited by 4706Algebra.algebraMapAddMonoidHom · cited by 3230AddMonoidHomRCLike · cited by 2829RCLikeAddMonoid.toZero · cited by 325AddMonoid.toZeroRCLike.re · cited by 319RCLike.reRCLike.im · cited by 161RCLike.imRCLike.I · cited by 100RCLike.IRCLike.re_add_im_axCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.