Theorems · Theorem · linear algebra
Module.finrank_eq_zero_of_subsingleton
∀ (R : Type u) (M : Type v) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [StrongRankCondition R] [Module.Free R M] [Subsingleton M], Module.finrank R M = 0
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Module.finrankstatement · cited by 1,770
- Module.Freestatement and proof · cited by 597
- StrongRankConditionstatement and proof · cited by 286
- Module.finrank_eq_zero_iff_of_freeproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProdproof · cited by 2
- MeasureTheory.Measure.toSphere_apply_univproof · cited by 2
- LinearMap.index_of_surjectiveproof · cited by 1
- LinearMap.normDet_smulproof · cited by 1
- LinearMap.normDet_zeroproof · cited by 1
- Algebra.finrank_eq_one_iff_bijective_algebraMapproof · cited by 1
- Representation.char_orthonormalproof · cited by 0
- LinearMap.index_idproof · cited by 0