Theorems · Theorem · commutative algebra
Submodule.fg_pi
∀ {R : Type u_1} [inst : Semiring R] {ι : Type u_5} {M : ι → Type u_6} [Finite ι]
[inst_2 : (i : ι) → AddCommMonoid (M i)] [inst_3 : (i : ι) → Module R (M i)] {p : (i : ι) → Submodule R (M i)},
(∀ (i : ι), (p i).FG) → (Submodule.pi Set.univ p).FG- Defined in
- Mathlib.RingTheory.Finiteness.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- RingHom.idproof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapproof · cited by 10,215
- RingHomproof · cited by 10,189
- Submodulestatement and proof · cited by 7,192
- Set.imageproof · cited by 5,609
- Set.univstatement and proof · cited by 3,945
- Finitestatement and proof · cited by 3,029
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