Theorems · Theorem · number theory
QuadraticMap.polar_self
∀ {R : Type u_3} {M : Type u_4} {N : Type u_5} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup N]
[inst_3 : Module R M] [inst_4 : Module R N] (Q : QuadraticMap R M N) (x : M), QuadraticMap.polar (⇑Q) x x = 2 • Q x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- SemigroupAction.mul_smulproof · cited by 291
- QuadraticMapstatement and proof · cited by 262
- sub_eq_iff_eq_addproof · cited by 74
- two_smulproof · cited by 57
- sub_subproof · cited by 54
- QuadraticMap.polarstatement · cited by 50
- QuadraticMap.map_add_selfproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- QuadraticMap.map_sum'proof · cited by 1
- QuadraticMap.toQuadraticMap_polarBilinproof · cited by 0
- CliffordAlgebra.forall_mul_self_eq_iffproof · cited by 0