let C, B be Category; :: thesis: for S being Contravariant_Functor of C,B
for c being Object of (C opp ) holds (*' S) . (id c) = id ((Obj S) . (opp c))
let S be Contravariant_Functor of C,B; :: thesis: for c being Object of (C opp ) holds (*' S) . (id c) = id ((Obj S) . (opp c))
let c be Object of (C opp ); :: thesis: (*' S) . (id c) = id ((Obj S) . (opp c))
thus (*' S) . (id c) = S . (opp (id c)) by Def8
.= S . (id (opp c))
.= id ((Obj S) . (opp c)) by Th32 ; :: thesis: verum