Theorems · Theorem · ring theory
IsStarProjection.sub_iff_mul_eq_left
∀ {R : Type u_1} [inst : NonUnitalRing R] [inst_1 : StarRing R] [IsAddTorsionFree R] {p q : R},
IsStarProjection p → IsStarProjection q → (IsStarProjection (q - p) ↔ p * q = p)q - p is a star projection iff p * q = p.
- Defined in
- Mathlib.Algebra.Star.StarProjection
- Cited by
- 1 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.
Cites13
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
- IsSelfAdjointproof · cited by 545
- NonUnitalRingstatement and proof · cited by 422
- IsAddTorsionFreestatement and proof · cited by 155
- StarMul.star_mulproof · cited by 72
- IsStarProjectionstatement and proof · cited by 64
- IsStarProjection.isSelfAdjointproof · cited by 18
- IsStarProjection.isIdempotentElemproof · cited by 17
- IsSelfAdjoint.subproof · cited by 13
- isStarProjection_iffproof · cited by 6
- star_eq_iff_star_eqproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- IsStarProjection.sub_iff_mul_eq_rightproof · cited by 0