Theorems · Theorem · functional analysis
IsStarProjection.mem_Icc
∀ {R : Type u_1} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R] {p : R},
IsStarProjection p → p ∈ Set.Icc 0 1For a star projection p, we have 0 ≤ p ≤ 1.
- Defined in
- Mathlib.Algebra.Order.Star.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Set.Iccstatement · cited by 1,702
- StarRingstatement and proof · cited by 1,686
- StarOrderedRingstatement and proof · cited by 587
- IsStarProjectionstatement and proof · cited by 64
- IsStarProjection.nonnegproof · cited by 6
- IsStarProjection.le_oneproof · cited by 1
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