Theorems · Theorem · number theory
QuadraticMap.polarBilin_apply_apply
∀ {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) (m y : M),
(Q.polarBilin m) y = QuadraticMap.polar (⇑Q) m y- Cited by
- 11 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- QuadraticMap.polarstatement · cited by 50
- QuadraticMap.polarBilinstatement and proof · cited by 25
Cited by11
Results whose statement or proof uses this declaration.
- QuadraticMap.radical_eq_ker_polarBilinproof · cited by 3
- QuadraticMap.map_sumproof · cited by 2
- QuadraticMap.Ring.polarBilin_piproof · cited by 1
- QuadraticMap.radical_eq_ker_associatedproof · cited by 1
- QuadraticMap.map_sum'proof · cited by 1
- QuadraticMap.isOrtho_polarBilinproof · cited by 1
- QuadraticMap.polarBilin_compproof · cited by 0
- QuadraticMap.choose_exists_companionproof · cited by 0
- QuadraticMap.radical_le_ker_polarBilinproof · cited by 0
- LinearMap.compQuadraticMap_polarBilinproof · cited by 0
- QuadraticMap.le_radical_iffproof · cited by 0