English
If I is an AddMonoid with a TensorSigns structure, then the triple product on c gives an associative operation on a ComplexShape, with the standard unit and associativity identities encoded by ε₁, ε₂ and ε-add.
Русский
Пусть I — моноид аддитивной структуры с знак-тензорами; тогда тройное произведение на ComplexShape образует ассоциативную операцию, удовлетворяющую стандартным единичным и ассоциативным тождествам через ε₁, ε₂ и ε-add.
LaTeX
$$$\\text{Associative } c\\,c\\,c\\,c\\,c\\,c\\text{ with } assoc=add\\_assoc,\\; ε_1\\_eq\\_mul = 1,\\; ε_2\\_ε\\_1 = 1,\\; ε_2\\_eq\\_mul = ε\\_add.$$$
Lean4
instance {I : Type*} [AddMonoid I] (c : ComplexShape I) [c.TensorSigns] : Associative c c c c c c
where
assoc := add_assoc
ε₁_eq_mul _ _ _ := by dsimp; rw [one_mul]
ε₂_ε₁ _ _ _ := by dsimp; rw [one_mul, mul_one]
ε₂_eq_mul _ _ _ := by dsimp; rw [ε_add]
