Theorems · Theorem · group theory
Pi.single_neg
∀ {I : Type u} {f : I → Type v} [inst : DecidableEq I] [inst_1 : (i : I) → AddGroup (f i)] (i : I) (x : f i),
Pi.single i (-x) = -Pi.single i x- 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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- Pi.singlestatement · cited by 518
- AddMonoidHom.map_negproof · cited by 22
- AddMonoidHom.singleproof · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- lp.single_negproof · cited by 1
- PiLp.single_negproof · cited by 0
- RestrictedProduct.single_negproof · cited by 0