Theorems · Theorem · number theory
IsCyclotomicExtension.singleton_one
∀ (A : Type u) (B : Type v) [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B]
[h : IsCyclotomicExtension {1} A B], ⊥ = ⊤If IsCyclotomicExtension {1} A B, then the image of A in B equals B.
- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Top.topstatement · cited by 9,680
- Set.ofPredproof · cited by 6,101
- Bot.botstatement · cited by 4,720
- Subalgebrastatement · cited by 1,353
- pow_oneproof · cited by 894
- Algebra.adjoinproof · cited by 535
- IsCyclotomicExtensionstatement and proof · cited by 220
- Algebra.eq_top_iffproof · cited by 13
- isCyclotomicExtension_iffproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.iff_union_singleton_oneproof · cited by 2