Theorems · Theorem · commutative algebra
Module.Free.exists_set
∀ (R : Type u) (M : Type v) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Module.Free R M], ∃ S, Nonempty (Module.Basis (↑S) R M)
- Defined in
- Mathlib.LinearAlgebra.FreeModule.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 83 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.coeproof · cited by 62,936
- 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.Elemstatement and proof · cited by 7,166
- Set.rangeproof · cited by 4,705
- Module.Basisstatement and proof · cited by 1,477
- Module.Freestatement and proof · cited by 597
- Module.Free.exists_basisproof · cited by 26
- Module.Basis.reindexRangeproof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- Module.free_iff_setproof · cited by 1
- lift_rank_le_iff_exists_linearMapproof · cited by 0