Theorems · Theorem · functional analysis
IsUnit.star_right_conjugate_nonneg_iff
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R] {u x : R},
IsUnit u → (0 ≤ u * x * star u ↔ 0 ≤ x)- Defined in
- Mathlib.Algebra.Order.Star.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- StarRingstatement and proof · cited by 1,686
- mul_assocproof · cited by 1,667
- IsUnitstatement and proof · cited by 1,602
- Star.starstatement and proof · cited by 1,082
- StarOrderedRingstatement and proof · cited by 587
- StarMul.star_mulproof · cited by 72
- star_oneproof · cited by 33
- IsUnit.exists_left_invproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- IsUnit.isStrictlyPositive_star_right_conjugate_iffproof · cited by 1
- IsUnit.star_left_conjugate_nonneg_iffproof · cited by 0