Theorems · Theorem · number theory
QuadraticMap.polar_neg_left
∀ {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 y : M),
QuadraticMap.polar (⇑Q) (-x) y = -QuadraticMap.polar (⇑Q) x y- Cited by
- 1 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.
Cites8
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
- QuadraticMapstatement and proof · cited by 262
- QuadraticMap.polarstatement and proof · cited by 50
- neg_one_smulproof · cited by 23
- QuadraticMap.polar_smul_leftproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- QuadraticMap.polar_sub_leftproof · cited by 0