Theorems · Theorem · linear algebra
LinearMap.BilinForm.dualSubmoduleParing_spec
∀ {R : Type u_1} {S : Type u_3} {M : Type u_2} [inst : CommRing R] [inst_1 : Field S] [inst_2 : AddCommGroup M]
[inst_3 : Algebra R S] [inst_4 : Module R M] [inst_5 : Module S M] [inst_6 : IsScalarTower R S M]
(B : LinearMap.BilinForm S M) {N : Submodule R M} (x : ↥(B.dualSubmodule N)) (y : ↥N),
(algebraMap R S) (B.dualSubmoduleParing x y) = (B ↑x) ↑y- Cited by
- 1 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Submodulestatement and proof · cited by 7,192
- Algebra.algebraMapstatement · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.dualSubmoduleToDual_injectiveproof · cited by 0