Theorems · Theorem · functional analysis
mul_star_self_pos
∀ {R : Type u_1} [inst : NonUnitalSemiring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R]
[Nontrivial R] {x : R}, IsRegular x → 0 < x * star x- Defined in
- Mathlib.Algebra.Order.Star.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, 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.
- PartialOrderstatement and proof · cited by 6,410
- Nontrivialstatement and proof · cited by 2,416
- 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
- IsRegularstatement and proof · cited by 116
- IsRegular.starproof · cited by 5
- star_mul_self_posproof · cited by 2
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