Theorems · Theorem · commutative algebra
Submodule.decomposition_erase_inf
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{N : Submodule R M} {s : Finset (Submodule R M)},
s.inf id = N → ∃ t ⊆ s, t.inf id = N ∧ ∀ ⦃J : Submodule R M⦄, J ∈ t → ¬(t.erase J).inf id ≤ J- Defined in
- Mathlib.RingTheory.Lasker
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- LE.le.transproof · cited by 3,151
- Finset.erasestatement and proof · cited by 455
- Finset.infstatement and proof · cited by 219
- inf_of_le_rightproof · cited by 128
- Finset.insert_eraseproof · cited by 65
- Finset.Subset.rflproof · cited by 41
- Finset.erase_subsetproof · cited by 31
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.decomposition_erase_infproof · cited by 0