Theorems · Theorem · ring theory
IsStarProjection.sub_of_mul_eq_left
∀ {R : Type u_1} {p q : R} [inst : NonUnitalNonAssocRing R] [inst_1 : StarRing R],
IsStarProjection p → IsStarProjection q → p * q = p → IsStarProjection (q - p)q - p is a star projection when p * q = p.
- Defined in
- Mathlib.Algebra.Star.StarProjection
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- StarRingstatement and proof · cited by 1,686
- Star.starproof · cited by 1,082
- NonUnitalNonAssocRingstatement and proof · cited by 354
- StarMul.star_mulproof · cited by 72
- IsStarProjectionstatement and proof · cited by 64
- IsSelfAdjoint.star_eqproof · cited by 58
- IsStarProjection.isSelfAdjointproof · cited by 18
- IsStarProjection.isIdempotentElemproof · cited by 17
- IsSelfAdjoint.subproof · cited by 13
- IsIdempotentElem.subproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- IsStarProjection.le_tfaeproof · cited by 4
- IsStarProjection.sub_of_mul_eq_rightproof · cited by 1
- IsStarProjection.le_of_mul_eq_leftproof · cited by 0