Theorems · Theorem · group theory
pinGroup.star_mem
∀ {R : Type u_1} [inst : CommRing R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{Q : QuadraticForm R M} {x : CliffordAlgebra Q}, x ∈ pinGroup Q → star x ∈ pinGroup QSee star_mem_iff for both directions.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coeproof · cited by 8,199
- mul_oneproof · cited by 3,885
- Submonoidstatement · cited by 3,086
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- Star.starstatement and proof · cited by 1,082
- QuadraticFormstatement and proof · cited by 507
- CliffordAlgebrastatement and proof · cited by 309
Cited by2
Results whose statement or proof uses this declaration.
- spinGroup.star_memproof · cited by 1
- pinGroup.star_mem_iffproof · cited by 0