Theorems · Theorem · linear algebra
Submodule.iSup_map_single
∀ {R : Type u} {ι : Type x} [inst : Semiring R] {φ : ι → Type u_1} [inst_1 : (i : ι) → AddCommMonoid (φ i)]
[inst_2 : (i : ι) → Module R (φ i)] {p : (i : ι) → Submodule R (φ i)} [inst_3 : DecidableEq ι] [Finite ι],
⨆ i, Submodule.map (LinearMap.single R φ i) (p i) = Submodule.pi Set.univ p- Defined in
- Mathlib.LinearAlgebra.Pi
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Fintypeproof · cited by 7,736
- Submodulestatement and proof · cited by 7,192
- Set.univstatement and proof · cited by 3,945
- Finitestatement and proof · cited by 3,029
- iSupstatement and proof · cited by 2,415
- Submodule.mapstatement and proof · cited by 614
- LE.le.antisymmproof · cited by 507
- nonempty_fintypeproof · cited by 261
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.fg_piproof · cited by 0