Theorems · Theorem · commutative algebra

Function.support_smul

∀ {α : Type u_1} {R : Type u_2} {M : Type u_3} [inst : Semiring R] [IsDomain R] [inst_2 : AddCommMonoid M]
  [inst_3 : Module R M] [Module.IsTorsionFree R M] (f : α → R) (g : α → M),
  Function.support (f • g) = Function.support f ∩ Function.support g

Defined in: Mathlib.Algebra.Module.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring IsDomain AddCommMonoid Module Module.IsTorsionFree

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

Setstatement · cited by 53,352
Modulestatement and proof · cited by 20,661
Semiringstatement and proof · cited by 13,802
AddCommMonoidstatement and proof · cited by 12,281
Set.extproof · cited by 2,266
IsDomainstatement and proof · cited by 2,196
Function.supportstatement · cited by 610
Module.IsTorsionFreestatement and proof · cited by 600
smul_ne_zero_iffproof · cited by 8

Cited by1

Results whose statement or proof uses this declaration.

PartitionOfUnity.sum_finsupport_smul_eq_finsumproof · cited by 1