Theorems · Theorem · functional analysis
RCLike.ofReal_im
∀ {K : Type u_1} [inst : RCLike K] (r : ℝ), RCLike.im ↑r = 0- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 41 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.
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
- RCLike.ofRealstatement · cited by 350
- AddMonoid.toZerostatement · cited by 325
- RCLike.imstatement · cited by 161
- RCLike.ofReal_im_axproof · cited by 2
Cited by41
Results whose statement or proof uses this declaration.
- RCLike.conj_ofRealproof · cited by 18
- RCLike.re_ofReal_mulproof · cited by 10
- RCLike.mul_conjproof · cited by 10
- StrongDual.re_extendRCLike_applyproof · cited by 9
- RCLike.im_eq_zeroproof · cited by 5
- RCLike.im_ofReal_mulproof · cited by 5
- RCLike.one_improof · cited by 5
- RCLike.nonneg_iff_exists_ofRealproof · cited by 4
- ConvexOn.exists_affine_le_of_ltproof · cited by 4
- Module.Dual.re_extendRCLike_applyproof · cited by 2
- RCLike.ofReal_le_ofRealproof · cited by 2
- RCLike.ofReal_lt_ofRealproof · cited by 2