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- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- IsLocalizedModule.smul_mem_finsetIntegerMultiple_spanproof · cited by 1