Theorems · Theorem · linear algebra
Module.finrank_of_not_finite
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Module.Free R M]
[StrongRankCondition R], ¬Module.Finite R M → Module.finrank R M = 0- Defined in
- Mathlib.LinearAlgebra.Dimension.Free
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 113 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.
- 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.Finitestatement and proof · cited by 1,032
- Module.Freestatement and proof · cited by 597
- Module.rankproof · cited by 496
- not_ltproof · cited by 306
- StrongRankConditionstatement and proof · cited by 286
- Module.rank_lt_aleph0_iffproof · cited by 8
- Cardinal.toNat_eq_zeroproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- Module.finite_of_finrank_posproof · cited by 8
- Module.finrank_of_infinite_dimensionalproof · cited by 7
- Algebra.norm_eq_norm_adjoinproof · cited by 3
- NumberField.InfinitePlace.even_finrank_of_not_isUnramifiedproof · cited by 2
- finrank_quotient_span_eq_natDegreeproof · cited by 2
- Projectivization.card_of_finrankproof · cited by 1
- RatFunc.finrank_eq_max_natDegreeproof · cited by 1
- RatFunc.finrank_ratFunc_ratFuncproof · cited by 1