Theorems · Theorem · functional analysis
IsStarProjection.le_of_mul_eq_right
∀ {R : Type u_1} [inst : NonUnitalRing R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R] {p q : R},
IsStarProjection p → IsStarProjection q → q * p = p → p ≤ qA star projection p is less than or equal to a star projection q when q * p = p.
- Defined in
- Mathlib.Algebra.Order.Star.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- NonUnitalRingstatement and proof · cited by 422
- sub_nonnegproof · cited by 167
- IsStarProjectionstatement and proof · cited by 64
- IsStarProjection.nonnegproof · cited by 6
- IsStarProjection.sub_of_mul_eq_rightproof · cited by 1
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