Theorems · Definition · functional analysis
RCLike.im
{K : semiOutParam (Type u_1)} → [self : RCLike K] → K →+ ℝThe imaginary part as an additive monoid homomorphism
- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 161 results in Mathlib
- Foundations
- Depth 95 from the axioms, rests on 1,756 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- AddMonoid.toZerostatement · cited by 325
Cited by168
Results whose statement or proof uses this declaration.
- RCLike.ofReal_imstatement · cited by 41
- RCLike.mul_restatement · cited by 26
- RCLike.normSqproof · cited by 26
- RCLike.re_add_imstatement · cited by 21
- RCLike.mapproof · cited by 14
- RCLike.ext_iffstatement and proof · cited by 13
- RCLike.mul_imstatement · cited by 13
- RCLike.map_applystatement · cited by 12
- RCLike.le_iff_re_imstatement · cited by 11
- RCLike.complexRingEquivstatement and proof · cited by 10
- RCLike.mul_conjproof · cited by 10
- RCLike.re_ofReal_mulproof · cited by 10