{A} `{HasEquivs A} {a b c : A} (g : b $<~> c) (f : a $<~> b) : g $o f $o (f^-1$ $o g^-1$) $== Id c. Proof. refine (cat_assoc _ _ _ $@ _). refine ((_ $@L cat_assoc_opp _ _ _) $@ _). refine ((_ $@L (cate_isretr _ $@R _)) $@ _). refine ((_ $@L cat_idl _) $@ _). apply cate_isretr. Defined.
Require Import Basics.Utf8 Basics.Overture Basics.Tactics Basics.Equivalences. Require Import WildCat.Core. Require Import WildCat.Opposite.