Theorems · Theorem · functional analysis
IsStarProjection.nonneg
∀ {R : Type u_1} [inst : NonUnitalSemiring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R]
{p : R}, IsStarProjection p → 0 ≤ pA star projection is non-negative in a star-ordered ring.
- Defined in
- Mathlib.Algebra.Order.Star.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- StarOrderedRingstatement and proof · cited by 587
- NonUnitalSemiringstatement and proof · cited by 339
- IsStarProjectionstatement and proof · cited by 64
- IsStarProjection.isSelfAdjointproof · cited by 18
- IsStarProjection.isIdempotentElemproof · cited by 17
- IsSelfAdjoint.mul_self_nonnegproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- IsStarProjection.le_tfaeproof · cited by 4
- IsStarProjection.one_sub_nonnegproof · cited by 1
- IsStarProjection.le_of_mul_eq_leftproof · cited by 0
- IsStarProjection.le_of_mul_eq_rightproof · cited by 0
- IsStarProjection.mem_Iccproof · cited by 0