Theorems · Theorem · ring theory
Module.Finite.exists_nat_not_surjective
∀ (R : Type u) [inst : Semiring R] [RankCondition R] (M : Type u_1) [inst_2 : AddCommMonoid M] [inst_3 : Module R M] [Module.Finite R M], ∃ n, ∀ (f : M →ₗ[R] Fin n → R), ¬Function.Surjective ⇑f
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- LinearMap.compproof · cited by 1,642
- Module.Finitestatement and proof · cited by 1,032
- RankConditionstatement and proof · cited by 15
- Module.Finite.exists_fin'proof · cited by 10
- le_of_fin_surjectiveproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Module.finite_dual_iffproof · cited by 2