Theorems · Theorem · functional analysis
star_right_conjugate_nonneg
∀ {R : Type u_1} [inst : NonUnitalSemiring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R]
{a : R}, 0 ≤ a → ∀ (c : R), 0 ≤ c * a * star c- Defined in
- Mathlib.Algebra.Order.Star.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, 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_left_conjugate_nonnegproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.conjugate_nonnegproof · cited by 2
- IsUnit.star_right_conjugate_nonneg_iffproof · cited by 2