Theorems · Theorem · group theory
pinGroup.star_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}, star x ∈ pinGroup Q ↔ x ∈ pinGroup QAn element is in pinGroup Q if and only if star x is in pinGroup Q.
See star_mem for only one direction.
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- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
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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 and proof · cited by 3,086
- Star.starstatement and proof · cited by 1,082
- QuadraticFormstatement and proof · cited by 507
- CliffordAlgebrastatement and proof · cited by 309
- star_starproof · cited by 135
- pinGroupstatement and proof · cited by 25
- pinGroup.star_memproof · cited by 2
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