Lemma

Associating left and then right is like doing nothing.

assocLR : (x : (a * b) * c) -> assocR (assocL x) === x
assocLR ((xa && xb) && xc) = Refl

Lemma

Associating left and then right is like doing nothing.

assocRL : (x : a * (b * c)) -> assocL (assocR x) === x
assocRL (xa && (xb && xc)) = Refl

Lemma

Associativity of product forms an isomorphism.

assocIso : (a * (b * c))  ((a * b) * c)
assocIso = MkIso assocR assocL assocLR assocRL