a b c f (g : c $-> _) : braid a b $o f $== g -> f $== braid b a $o g. Proof. intros p. apply (cate_monic_equiv (braide a b)). refine ((cate_buildequiv_fun _ $@R _) $@ p $@ _ $@ cat_assoc _ _ _). refine ((cat_idl _)^$ $@ (_^$ $@R _)). refine ((cate_buildequiv_fun _ $@R _) $@ _). apply braid_braid. Defined.
Require Import Basics.Overture Basics.Tactics Types.Forall. Require Import WildCat.Core WildCat.Bifunctor WildCat.Prod WildCat.Equiv. Require Import WildCat.NatTrans WildCat.Opposite.