Theorems · Theorem · group theory

Set.vadd_graphOn

∀ {F : Type u_1} {α : Type u_2} {β : Type u_3} [inst : AddGroup α] [inst_1 : AddCommGroup β] [inst_2 : FunLike F α β]
  [AddMonoidHomClass F α β] (x : α × β) (s : Set α) (f : F),
  x +ᵥ Set.graphOn (⇑f) s = Set.graphOn (fun a => x.2 - f x.1 + f a) (x.1 +ᵥ s)

Defined in

Mathlib.Algebra.Group.Action.Pointwise.Set.Basic

Cited by

1 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Quot.sound

Assumes

AddGroupAddCommGroupFunLikeAddMonoidHomClass