Theorems · Theorem · linear algebra
Submodule.range_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], (LinearMap.fst R M M₂).range = ⊤- Defined in
- Mathlib.LinearAlgebra.Prod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- LinearMap.rangestatement · cited by 893
- Submodule.mapproof · cited by 614
- LinearMap.fststatement and proof · cited by 64
- LinearMap.range_eq_mapproof · cited by 27
- Submodule.prod_topproof · cited by 2
- Submodule.prod_map_fstproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.prod_eq_top_iffproof · cited by 0