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Theorems · Theorem · group theory

Pi.single_add

∀ {I : Type u} {f : I → Type v} [inst : DecidableEq I] [inst_1 : (i : I) → AddZeroClass (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
4 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqAddZeroClass
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Around this declaration

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

HahnSeries.single_add · cited by 0HahnSeries.single_addPiLp.single_add · cited by 0PiLp.single_addlp.single_add · cited by 0lp.single_addRestrictedProduct.single_add · cited by 0RestrictedProduct.single_…AddZeroClass · cited by 1237AddZeroClassPi.single · cited by 518Pi.singleAddMonoidHom.map_add · cited by 48AddMonoidHom.map_addAddMonoidHom.single · cited by 19AddMonoidHom.singlePi.single_addCITED BYCITES

Cites4

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

Cited by4

Results whose statement or proof uses this declaration.