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Theorems · Theorem · group theory

Pi.single_sub

∀ {I : Type u} {f : I → Type v} [inst : DecidableEq I] [inst_1 : (i : I) → AddGroup (f i)] (i : I) (x y : f i),
  Pi.single i (x - y) = Pi.single i x - Pi.single i y
Defined in
Mathlib.Algebra.Group.Pi.Lemmas
Cited by
3 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqAddGroup
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Around this declaration

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

PiLp.single_sub · cited by 1PiLp.single_subRestrictedProduct.single_sub · cited by 0RestrictedProduct.single_…lp.single_sub · cited by 0lp.single_subAddGroup · cited by 4410AddGroupPi.single · cited by 518Pi.singleAddMonoidHom.single · cited by 19AddMonoidHom.singleAddMonoidHom.map_sub · cited by 18AddMonoidHom.map_subPi.single_subCITED BYCITES

Cites4

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Cited by3

Results whose statement or proof uses this declaration.