Theorems · Theorem · group theory
spinGroup.mem_iff
∀ {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 ∈ spinGroup Q ↔ x ∈ pinGroup Q ∧ x ∈ CliffordAlgebra.even QAn element is in spinGroup Q if and only if it is in pinGroup Q and even Q.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Submonoidstatement · cited by 3,086
- Subalgebrastatement · cited by 1,353
- QuadraticFormstatement and proof · cited by 507
- CliffordAlgebrastatement and proof · cited by 309
- pinGroupstatement · cited by 25
- spinGroupstatement · cited by 23
- CliffordAlgebra.evenstatement · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- spinGroup.star_memproof · cited by 1