Theorems · Theorem · functional analysis
IsUnit.isStrictlyPositive_star_left_conjugate_iff
∀ {A : Type u_1} [inst : Semiring A] [inst_1 : StarRing A] [inst_2 : PartialOrder A] [StarOrderedRing A] {u a : A},
IsUnit u → (IsStrictlyPositive (star u * a * u) ↔ IsStrictlyPositive a)- Defined in
- Mathlib.Algebra.Algebra.StrictPositivity
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- StarRingstatement and proof · cited by 1,686
- IsUnitstatement and proof · cited by 1,602
- Star.starstatement and proof · cited by 1,082
- StarOrderedRingstatement and proof · cited by 587
- star_starproof · cited by 135
- IsStrictlyPositivestatement and proof · cited by 75
- IsUnit.starproof · cited by 11
- IsUnit.isStrictlyPositive_star_right_conjugate_iffproof · cited by 1
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