Theorems · Theorem · linear algebra
rank_quotient_eq_of_le_torsion
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{M' : Submodule R M}, M' ≤ Submodule.torsion R M → Module.rank R (M ⧸ M') = Module.rank R M- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement and proof · cited by 7,192
- Set.Elemproof · cited by 7,166
- Finset.sumproof · cited by 5,195
- Cardinalstatement and proof · cited by 2,598
- Nontrivialproof · cited by 2,416
- Finset.sum_congrproof · cited by 2,323
- HasQuotient.Quotientstatement and proof · cited by 2,301
Cited by1
Results whose statement or proof uses this declaration.
- finrank_quotient_eq_of_le_torsionproof · cited by 1