Theorems · Theorem · commutative algebra
Submodule.CoFG.cofg_of_le
Deprecated since 2026-05-13Use Submodule.CoFG.of_le instead.
∀ {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.CoFGAlias of Submodule.CoFG.of_le.
A submodule that contains a CoFG submodule is CoFG.
- Defined in
- Mathlib.RingTheory.Finiteness.Cofinite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement · cited by 20,661
- AddCommGroupstatement · cited by 12,871
- Ringstatement · cited by 7,463
- Submodulestatement · cited by 7,192
- Submodule.CoFGstatement · cited by 28
- Submodule.CoFG.of_leproof · cited by 4
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