Theorems · Theorem · functional analysis
one_le_star_iff
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R] {x : R},
1 ≤ star x ↔ 1 ≤ x- Defined in
- Mathlib.Algebra.Order.Star.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
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
- Star.starstatement and proof · cited by 1,082
- StarOrderedRingstatement and proof · cited by 587
- star_oneproof · cited by 33
- star_le_star_iffproof · cited by 6
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