Theorems · Theorem · commutative algebra
Module.Free.infinite
∀ (R : Type u) (M : Type v) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Module.Free R M] [Infinite R] [Nontrivial M], Infinite M
- Defined in
- Mathlib.LinearAlgebra.FreeModule.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Nontrivialstatement and proof · cited by 2,416
- Module.Freestatement and proof · cited by 597
- Module.Basis.reprproof · cited by 498
- Infinitestatement and proof · cited by 352
- Module.Free.chooseBasisproof · cited by 121
- LinearEquiv.toEquivproof · cited by 105
- Equiv.infinite_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Projectivization.cardproof · cited by 3
- Subspace.biUnion_ne_univ_of_top_notMemproof · cited by 1