Theorems · Theorem · commutative algebra
IsRegular.prod
∀ {ι : Type u_2} {R : Type u_3} [inst : CommMonoid R] {s : Finset ι} {f : ι → R},
(∀ i ∈ s, IsRegular (f i)) → IsRegular (∏ i ∈ s, f i)- Defined in
- Mathlib.Algebra.Regular.Pow
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- IsRegularstatement and proof · cited by 116
- IsRegular.leftproof · cited by 39
- IsRegular.rightproof · cited by 19
- IsLeftRegular.prodproof · cited by 1
- IsRightRegular.prodproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_prod_of_regularproof · cited by 1
- MvPolynomial.isRegular_prod_Xproof · cited by 0