Theorems · Theorem · number theory

ClassGroup.mem_finsetApprox

∀ {R : Type u_1} {S : Type u_2} [inst : EuclideanDomain R] [inst_1 : CommRing S] [inst_2 : IsDomain S]
  [inst_3 : Algebra R S] {abv : AbsoluteValue R ℤ} {ι : Type u_5} [inst_4 : DecidableEq ι] [inst_5 : Fintype ι]
  (bS : Module.Basis ι R S) (adm : abv.IsAdmissible) [inst_6 : Infinite R] [inst_7 : DecidableEq R] {x : R},
  x ∈ ClassGroup.finsetApprox bS adm ↔
    ∃ i j, i ≠ j ∧ (ClassGroup.distinctElems bS adm) i - (ClassGroup.distinctElems bS adm) j = x

Defined in: Mathlib.NumberTheory.ClassNumber.Finite
Cited by: 1 results in Mathlib
Foundations: Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: EuclideanDomain CommRing IsDomain Algebra DecidableEq Fintype Infinite DecidableEq

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Cites20

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
CommRingstatement and proof · cited by 17,173
Finsetstatement · cited by 13,712
Algebrastatement and proof · cited by 11,388
Fintypestatement and proof · cited by 7,736
Finset.univproof · cited by 3,473
IsDomainstatement and proof · cited by 2,196
Module.Basisstatement and proof · cited by 1,477
sub_selfproof · cited by 996
Function.Embeddingstatement · cited by 988
sub_eq_zeroproof · cited by 407
AbsoluteValuestatement and proof · cited by 363

Cited by1

Results whose statement or proof uses this declaration.

ClassGroup.exists_mem_finsetApproxproof · cited by 1