Theorems · Theorem · linear algebra
Module.finrank_of_infinite_dimensional
∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V],
¬FiniteDimensional K V → Module.finrank K V = 0- Cited by
- 7 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- AddCommGroupstatement and proof · cited by 12,871
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement · cited by 1,770
- DivisionRingstatement and proof · cited by 1,062
- Module.finrank_of_not_finiteproof · cited by 8
Cited by7
Results whose statement or proof uses this declaration.
- Field.finSepDegree_eq_finrank_of_isSeparableproof · cited by 7
- IntermediateField.finrank_eq_fixingSubgroup_indexproof · cited by 1
- finrank_vectorSpan_insert_leproof · cited by 1
- Ideal.finrank_prime_pow_ramificationIdxproof · cited by 1
- Field.finSepDegree_dvd_finrankproof · cited by 1
- Submodule.det_reflectionproof · cited by 1
- Field.finSepDegree_mul_finInsepDegreeproof · cited by 0