Theorems · Theorem · commutative algebra
Ideal.sup_pow_add_le_pow_sup_pow
∀ {R : Type u} [inst : CommSemiring R] {I J : Ideal R} {n m : ℕ}, (I ⊔ J) ^ (n + m) ≤ I ^ n ⊔ J ^ m- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- LE.le.transproof · cited by 3,151
- Finset.rangeproof · cited by 1,341
- Nat.chooseproof · cited by 494
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- Finset.sup_leproof · cited by 44
- Ideal.pow_le_pow_rightproof · cited by 39
- add_powproof · cited by 24
- Ideal.mul_le_rightproof · cited by 20
- Ideal.mul_le_leftproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.exists_pow_le_of_le_radical_of_fgproof · cited by 2