{a a'} (f : a $-> a') b c : twist a' b c $o fmap10 cat_tensor f (cat_tensor b c) $== fmap01 cat_tensor b (fmap10 cat_tensor f c) $o twist a b c. Proof. refine ((_ $@L _^$) $@ twist_nat a a' b b c c f (Id _) (Id _) $@ (_ $@R _)). - refine (fmap12 _ _ _ $@ fmap10_is_fmap11 _ _ _). rapply fmap11_id. - refine (fmap12 _ _ _ $@ fmap01_is_fmap11 _ _ _). rapply fmap10_is_fmap11. Defined.
Require Import Basics.Overture Basics.Tactics Types.Forall WildCat.Monoidal. Require Import WildCat.Core WildCat.Bifunctor WildCat.Prod WildCat.Equiv. Require Import WildCat.NatTrans WildCat.Square WildCat.Opposite.