Theorems · Theorem · ring theory
CliffordAlgebra.changeForm.add_proof
∀ {R : Type u1} [inst : CommRing R] {M : Type u2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{Q Q' Q'' : QuadraticForm R M} {B B' : LinearMap.BilinForm R M},
LinearMap.BilinMap.toQuadraticMap B = Q' - Q →
LinearMap.BilinMap.toQuadraticMap B' = Q'' - Q' → LinearMap.BilinMap.toQuadraticMap (B + B') = Q'' - QAuxiliary lemma used as an argument to CliffordAlgebra.changeForm
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
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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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- QuadraticFormstatement and proof · cited by 507
- LinearMap.BilinFormstatement and proof · cited by 501
- QuadraticMapstatement and proof · cited by 262
- LinearMap.BilinMap.toQuadraticMapstatement and proof · cited by 53
- sub_add_sub_cancel'proof · cited by 18
Cited by2
Results whose statement or proof uses this declaration.
- CliffordAlgebra.changeForm_changeFormstatement and proof · cited by 1
- CliffordAlgebra.changeForm_comp_changeFormstatement · cited by 0