Theorems · Theorem · ring theory
IsStarProjection.one_sub
∀ {R : Type u_1} {p : R} [inst : NonAssocRing R] [inst_1 : StarRing R], IsStarProjection p → IsStarProjection (1 - p)- Defined in
- Mathlib.Algebra.Star.StarProjection
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRingStarRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- NonAssocRingstatement and proof · cited by 483
- IsStarProjectionstatement and proof · cited by 64
- IsIdempotentElem.one_subproof · cited by 20
- IsStarProjection.isSelfAdjointproof · cited by 18
- IsStarProjection.isIdempotentElemproof · cited by 17
- IsSelfAdjoint.subproof · cited by 13
- IsSelfAdjoint.oneproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- isStarProjection_one_sub_iffproof · cited by 1
- IsStarProjection.one_sub_nonnegproof · cited by 1