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Theorems · Theorem · group theory

DirectSum.map_eq_iff

∀ {ι : Type u_3} {α : ι → Type u_4} {β : ι → Type u_5} [inst : (i : ι) → AddCommMonoid (α i)]
  [inst_1 : (i : ι) → AddCommMonoid (β i)] (f : (i : ι) → α i →+ β i) (x y : DirectSum ι fun i => α i),
  (DirectSum.map f) x = (DirectSum.map f) y ↔ ∀ (i : ι), (f i) (x i) = (f i) (y i)
Defined in
Mathlib.Algebra.DirectSum.Basic
Cited by
1 results in Mathlib
Foundations
Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidAddCommMonoid
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Around this declaration

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

DirectSum.lmap_eq_iff · cited by 0DirectSum.lmap_eq_iffDFunLike.coe · cited by 62936DFunLike.coeAddCommMonoid · cited by 12281AddCommMonoidAddMonoidHom · cited by 3230AddMonoidHomDFinsupp · cited by 694DFinsuppDirectSum · cited by 446DirectSumDirectSum.map · cited by 15DirectSum.mapDirectSum.map_apply · cited by 2DirectSum.map_applyDirectSum.map_eq_iffCITED BYCITES

Cites7

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Cited by1

Results whose statement or proof uses this declaration.