Theorems · Theorem · linear algebra
Finsupp.supported_comap_lmapDomain
∀ {α : Type u_1} (M : Type u_2) (R : Type u_5) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{α' : Type u_7} (f : α → α') (s : Set α'),
Finsupp.supported M R (f ⁻¹' s) ≤ Submodule.comap (Finsupp.lmapDomain M R f) (Finsupp.supported M R s)- Defined in
- Mathlib.LinearAlgebra.Finsupp.Supported
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- 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 · cited by 7,192
- Finsuppstatement and proof · cited by 5,255
- Set.preimagestatement and proof · cited by 4,946
- Submodule.comapstatement · cited by 347
- Finset.coe_imageproof · cited by 222
- Set.Subset.transproof · cited by 218
- Set.image_subset_iffproof · cited by 203
Cited by1
Results whose statement or proof uses this declaration.
- Finsupp.lmapDomain_supportedproof · cited by 2