Theorems · Theorem · functional analysis
mul_star_self_nonneg
∀ {R : Type u_1} [inst : NonUnitalSemiring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R]
(r : R), 0 ≤ r * star r- Defined in
- Mathlib.Algebra.Order.Star.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- StarRingstatement and proof · cited by 1,686
- Star.starstatement and proof · cited by 1,082
- StarOrderedRingstatement and proof · cited by 587
- NonUnitalSemiringstatement and proof · cited by 339
- star_starproof · cited by 135
- star_mul_self_nonnegproof · cited by 17
Cited by5
Results whose statement or proof uses this declaration.
- CStarAlgebra.isStrictlyPositive_TFAEproof · cited by 7
- CStarAlgebra.nonneg_TFAEproof · cited by 6
- CStarModule.norm_inner_leproof · cited by 2
- dotProduct_self_star_eq_zeroproof · cited by 1
- dotProduct_self_star_nonnegproof · cited by 0