Theorems · Theorem · functional analysis
RCLike.nonneg_iff_exists_ofReal
∀ {K : Type u_1} [inst : RCLike K] {z : K}, 0 ≤ z ↔ ∃ x ≥ 0, ↑x = z- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 161 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RCLikestatement and proof · cited by 2,829
- RCLike.ofRealstatement and proof · cited by 350
- RCLike.reproof · cited by 319
- RCLike.improof · cited by 161
- RCLike.toPartialOrderstatement · cited by 106
- RCLike.ofReal_reproof · cited by 60
- RCLike.ofReal_improof · cited by 41
- RCLike.ext_iffproof · cited by 13
- RCLike.nonneg_iffproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- Complex.sqrt_neg_of_nonnegproof · cited by 2
- Complex.sqrt_of_nonnegproof · cited by 2
- convex_RCLike_iff_convex_realproof · cited by 1
- with_gaugeSeminormFamilyproof · cited by 0