Theorems · Theorem · linear algebra
LinearIndepOn.image_of_comp
∀ {ι : Type u'} {ι' : Type u_1} {R : Type u_2} {s : Set ι} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] (f : ι → ι') (g : ι' → M), LinearIndepOn R (g ∘ f) s → LinearIndepOn R g (f '' s)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 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.
Cites13
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Set.imagestatement · cited by 5,609
- Nontrivialproof · cited by 2,416
- Set.InjOnproof · cited by 543
- LinearIndepOnstatement and proof · cited by 211
- Function.Injective.of_compproof · cited by 82
- LinearIndependent.injectiveproof · cited by 21
- Set.injOn_iff_injectiveproof · cited by 20
- Equiv.Set.imageOfInjOnproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- LinearIndepOn.id_imageproof · cited by 8
- LinearMap.le_rank_iff_exists_linearIndependentproof · cited by 0