Theorems · Theorem · linear algebra
Module.Basis.nonempty_unique_index_of_finrank_eq_one
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Module.Free R M]
[StrongRankCondition R] {ι : Type u_2} (b : Module.Basis ι R M), Module.finrank R M = 1 → Nonempty (Unique ι)If a finite module of finrank 1 has a basis, then this basis has a unique element.
- Defined in
- Mathlib.LinearAlgebra.Dimension.Free
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- 0 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
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- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypeproof · cited by 7,736
- Finiteproof · cited by 3,029
- Nontrivialproof · cited by 2,416
- Module.finrankstatement and proof · cited by 1,770
- Module.Basisstatement and proof · cited by 1,477
- Module.Finiteproof · cited by 1,032
- Module.Freestatement and proof · cited by 597
- Uniquestatement · cited by 400
- StrongRankConditionstatement and proof · cited by 286
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