Theorems · Theorem · number theory
IsCyclotomicExtension.singleton_one_of_bot_eq_top
∀ {A : Type u} {B : Type v} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B],
⊥ = ⊤ → IsCyclotomicExtension {1} A BIf (⊥ : SubAlgebra A B) = ⊤, then IsCyclotomicExtension {1} A B.
- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Top.topstatement and proof · cited by 9,680
- Bot.botstatement and proof · cited by 4,720
- Subalgebrastatement · cited by 1,353
- IsCyclotomicExtensionstatement and proof · cited by 220
- Set.union_singletonproof · cited by 107
- IsCyclotomicExtension.eq_self_sdiff_zeroproof · cited by 5
- Set.insert_sdiff_eq_singletonproof · cited by 3
- IsCyclotomicExtension.iff_union_singleton_oneproof · cited by 2
- IsCyclotomicExtension.singleton_zero_of_bot_eq_topproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.singleton_one_of_algebraMap_bijectiveproof · cited by 1