Theorems · Theorem · ring theory
IsStarProjection.add
∀ {R : Type u_1} {p q : R} [inst : NonUnitalNonAssocSemiring R] [inst_1 : StarRing R],
IsStarProjection p → IsStarProjection q → p * q = 0 → IsStarProjection (p + q)The sum of star projections is a star projection if their product is 0.
- Defined in
- Mathlib.Algebra.Star.StarProjection
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- zero_addproof · cited by 2,366
- StarRingstatement and proof · cited by 1,686
- Star.starproof · cited by 1,082
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- StarMul.star_mulproof · cited by 72
- IsStarProjectionstatement and proof · cited by 64
- IsSelfAdjoint.star_eqproof · cited by 58
- star_zeroproof · cited by 58
- IsStarProjection.isSelfAdjointproof · cited by 18
- IsStarProjection.isIdempotentElemproof · cited by 17
- IsSelfAdjoint.addproof · cited by 8
- IsIdempotentElem.addproof · cited by 2
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