Theorems · Theorem · functional analysis
RCLike.nonneg_iff
∀ {K : Type u_1} [inst : RCLike K] {z : K}, 0 ≤ z ↔ 0 ≤ RCLike.re z ∧ RCLike.im z = 0- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 8 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.
Cites10
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
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- map_zeroproof · cited by 1,614
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement and proof · cited by 319
- RCLike.imstatement and proof · cited by 161
- RCLike.toPartialOrderstatement · cited by 106
- RCLike.le_iff_re_improof · cited by 11
Cited by8
Results whose statement or proof uses this declaration.
- RCLike.nonneg_iff_exists_ofRealproof · cited by 4
- RCLike.re_nonneg_of_nonnegproof · cited by 2
- Matrix.isPositive_toEuclideanLin_iffproof · cited by 2
- RCLike.sqrt_neg_of_nonnegproof · cited by 1
- RCLike.norm_of_nonneg'proof · cited by 1
- RCLike.map_nonneg_iffproof · cited by 1
- RCLike.toStarOrderedRingproof · cited by 0
- Matrix.PosSemidef.re_dotProduct_nonnegproof · cited by 0