Theorems · Theorem · commutative algebra
DividedPowers.isSubDPIdeal_sup
∀ {A : Type u_1} [inst : CommSemiring A] {I : Ideal A} {hI : DividedPowers I} {J K : Ideal A},
hI.IsSubDPIdeal J → hI.IsSubDPIdeal K → hI.IsSubDPIdeal (J ⊔ K)- Cited by
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- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coeproof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Ideal.spanproof · cited by 948
- Set.subset_union_leftproof · cited by 142
- Set.subset_union_rightproof · cited by 123
- DividedPowersstatement and proof · cited by 112
- Ideal.subset_spanproof · cited by 86
- DividedPowers.dpowproof · cited by 85
- DividedPowers.IsSubDPIdealstatement and proof · cited by 26
- Set.union_subset_iffproof · cited by 21
- Ideal.span_monoproof · cited by 16
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