Theorems · Theorem · commutative algebra
Submodule.CoFG.of_le
∀ {R : Type u_1} [inst : Ring R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {S T : Submodule R M},
S ≤ T → S.CoFG → T.CoFGA submodule that contains a CoFG submodule is CoFG.
- Defined in
- Mathlib.RingTheory.Finiteness.Cofinite
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- sup_eq_rightproof · cited by 53
- Submodule.CoFGstatement and proof · cited by 28
- Module.Finite.equivproof · cited by 20
- Submodule.quotientQuotientEquivQuotientSupproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.IsFredholm.of_isInvertible_restrictproof · cited by 1
- Submodule.ClosedComplemented.of_disjoint_of_finiteDimensional_quotientproof · cited by 1
- LinearMap.FiniteRangeSetoid.equiv_of_eqOn_coFGproof · cited by 0
- Submodule.CoFG.cofg_of_leproof · cited by 0