Theorems · Theorem · commutative algebra
SModEq.prod
∀ {A : Type u_3} [inst : CommRing A] {I : Ideal A} {ι : Type u_6} {s : Finset ι} {x y : ι → A},
(∀ i ∈ s, x i ≡ y i [SMOD I]) → ∏ i ∈ s, x i ≡ ∏ i ∈ s, y i [SMOD I]- Defined in
- Mathlib.LinearAlgebra.SModEq.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Finsetstatement and proof · cited by 13,712
- Idealstatement and proof · cited by 4,748
- Finset.prodstatement and proof · cited by 2,356
- Finset.consproof · cited by 221
- Finset.cons_inductionproof · cited by 85
- SModEqstatement and proof · cited by 80
- Finset.prod_consproof · cited by 60
- Finset.mem_cons_of_memproof · cited by 16
- Finset.mem_cons_selfproof · cited by 16
- SModEq.reflproof · cited by 4
- SModEq.mulproof · cited by 2
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