Theorems · Theorem · linear algebra
Module.rank_pos_of_free
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Module.Free R M]
[Nontrivial M], 0 < Module.rank R M- 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.
Cites15
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
- Cardinalstatement · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- LT.lt.trans_leproof · cited by 678
- Module.Freestatement and proof · cited by 597
- Module.rankstatement · cited by 496
- Module.Free.ChooseBasisIndexproof · cited by 133
- Module.Free.chooseBasisproof · cited by 121
- Module.Basis.linearIndependentproof · cited by 54
- pos_of_ne_zeroproof · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- Module.length_of_freeproof · cited by 3
- Module.rank_pos_iff_of_freeproof · cited by 1