Theorems · Theorem · linear algebra
Submodule.prod_map_fst
∀ {R : Type u} {M : Type v} {M₂ : Type w} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid M₂]
[inst_3 : Module R M] [inst_4 : Module R M₂] (p : Submodule R M) (q : Submodule R M₂),
Submodule.map (LinearMap.fst R M M₂) (p.prod q) = p- Defined in
- Mathlib.LinearAlgebra.Prod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- Submodule.mapstatement · cited by 614
- Submodule.extproof · cited by 204
- ZeroMemClass.zero_memproof · cited by 162
- LinearMap.fststatement · cited by 64
- Submodule.prodstatement · cited by 55
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.range_fstproof · cited by 1