Theorems · Theorem · commutative algebra
DividedPowers.dpow_add
∀ {A : Type u_1} [inst : CommSemiring A] {I : Ideal A} (self : DividedPowers I) {n : ℕ} {x y : A},
x ∈ I → y ∈ I → self.dpow n (x + y) = ∑ k ∈ Finset.HasAntidiagonal.antidiagonal n, self.dpow k.1 x * self.dpow k.2 y- Defined in
- Mathlib.RingTheory.DividedPowers.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 70 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.
Cites6
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
- Finset.sumstatement · cited by 5,195
- Idealstatement and proof · cited by 4,748
- Finset.HasAntidiagonal.antidiagonalstatement · cited by 218
- DividedPowersstatement and proof · cited by 112
- DividedPowers.dpowstatement · cited by 85
Cited by4
Results whose statement or proof uses this declaration.
- DividedPowers.dpow_add'proof · cited by 3
- DividedPowers.dpow_sumproof · cited by 2
- DividedPowers.exp_addproof · cited by 0
- DividedPowers.coincide_on_smulproof · cited by 0