Theorems · Theorem · number theory
QuadraticMap.choose_exists_companion
∀ {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), ⋯.choose = Q.polarBilinIn a ring the companion bilinear form is unique and equal to QuadraticMap.polar.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- 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
- QuadraticMapstatement and proof · cited by 262
- add_sub_cancel_leftproof · cited by 198
- LinearMap.BilinMapstatement · cited by 85
- sub_subproof · cited by 54
- QuadraticMap.polarBilinstatement · cited by 25
- LinearMap.ext₂proof · cited by 17
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.