Theorems · Theorem · group theory
UnitalShelf.act_act_self_eq
∀ {S : Type u_1} [inst : UnitalShelf S] (x y : S), Shelf.act (Shelf.act x y) x = Shelf.act x yA monoid is graphic if, for all x and y, the graphic identity
(x * y) * x = x * y holds. For a unital shelf, this graphic
identity holds.
- Defined in
- Mathlib.Algebra.Quandle
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- UnitalShelf
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.
- Shelf.actstatement and proof · cited by 37
- Shelf.self_distribproof · cited by 8
- UnitalShelfstatement and proof · cited by 6
- UnitalShelf.act_oneproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- UnitalShelf.assocproof · cited by 0