Theorems · Theorem · functional analysis
RCLike.toStarOrderedRing
∀ {K : Type u_1} [inst : RCLike K], StarOrderedRing KWith z ≤ w iff w - z is real and nonnegative, ℝ and ℂ are star ordered rings.
(That is, a star ring in which the nonnegative elements are those of the form star z * z.)
Note this is only an instance with open scoped ComplexOrder.
- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 162 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.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RCLikestatement and proof · cited by 2,829
- add_zeroproof · cited by 2,707
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- Star.starproof · cited by 1,082
- map_addproof · cited by 964
- sub_zeroproof · cited by 938
- starRingEndproof · cited by 671
- mul_negproof · cited by 590
- StarOrderedRingstatement · cited by 587
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