Mathlib Map

Theorems · Theorem · commutative algebra

IsLocalizedModule.finsetIntegerMultiple_image

∀ {R : Type u_1} [inst : CommSemiring R] (S : Submonoid R) {M : Type u_2} [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] {M' : Type u_3} [inst_3 : AddCommMonoid M'] [inst_4 : Module R M'] (f : M →ₗ[R] M')
  [inst_5 : IsLocalizedModule S f] [inst_6 : DecidableEq M] (s : Finset M'),
  ⇑f '' ↑(IsLocalizedModule.finsetIntegerMultiple S f s) = IsLocalizedModule.commonDenomOfFinset S f s • ↑s
Defined in
Mathlib.Algebra.Module.LocalizedModule.Int
Cited by
1 results in Mathlib
Foundations
Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringAddCommMonoidModuleAddCommMonoidModuleIsLocalizedModuleDecidableEq

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites23

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
  • Setstatement and proof · cited by 53,352
  • Modulestatement and proof · cited by 20,661
  • RingHom.idstatement and proof · cited by 18,349
  • Finsetstatement and proof · cited by 13,712
  • AddCommMonoidstatement and proof · cited by 12,281
  • CommSemiringstatement and proof · cited by 10,911
  • LinearMapstatement and proof · cited by 10,215
  • SetLike.coestatement and proof · cited by 8,199
  • Set.imagestatement and proof · cited by 5,609
  • Submonoidstatement and proof · cited by 3,086
  • Set.extproof · cited by 2,266

Cited by1

Results whose statement or proof uses this declaration.