Theorems · Theorem · commutative algebra
Algebra.FormallyUnramified.pi_iff
∀ {R : Type u_1} {I : Type u_2} [Finite I] (f : I → Type u_3) [inst : CommRing R] [inst_1 : (i : I) → CommRing (f i)]
[inst_2 : (i : I) → Algebra R (f i)],
Algebra.FormallyUnramified R ((i : I) → f i) ↔ ∀ (i : I), Algebra.FormallyUnramified R (f i)- Defined in
- Mathlib.RingTheory.Unramified.Pi
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites64
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fintypeproof · cited by 7,736
- Finset.sumproof · cited by 5,195
- Idealproof · cited by 4,748
- Bot.botproof · cited by 4,720
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- Finset.univproof · cited by 3,473
- AlgHomproof · cited by 3,236
- Finitestatement and proof · cited by 3,029
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.FormallyEtale.pi_iffproof · cited by 1