Theorems · Theorem · functional analysis
RCLike.mul_im
∀ {K : Type u_1} [inst : RCLike K] (z w : K), RCLike.im (z * w) = RCLike.re z * RCLike.im w + RCLike.im z * RCLike.re w- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 13 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.imstatement · cited by 161
- RCLike.mul_im_axproof · cited by 1
Cited by13
Results whose statement or proof uses this declaration.
- RCLike.mul_conjproof · cited by 10
- RCLike.im_ofReal_mulproof · cited by 5
- InnerProductSpaceable.inner_.norm_sqproof · cited by 1
- RCLike.sqrt_neg_of_nonnegproof · cited by 1
- StrongDual.im_extendRCLike_applyproof · cited by 1
- InnerProductSpace.Core.re_inner_smul_ofReal_smul_selfproof · cited by 1
- RCLike.map_nonneg_iffproof · cited by 1
- RCLike.toStarOrderedRingproof · cited by 0
- RCLike.sqrt_mapproof · cited by 0
- RCLike.div_improof · cited by 0
- Module.Dual.im_extendRCLike_applyproof · cited by 0
- Complex.sqrt_mapproof · cited by 0