let C, B be Category; :: thesis: for S being Contravariant_Functor of C opp ,B
for c being Object of C holds (/* S) . (id c) = id ((Obj (/* S)) . c)
let S be Contravariant_Functor of C opp ,B; :: thesis: for c being Object of C holds (/* S) . (id c) = id ((Obj (/* S)) . c)
let c be Object of C; :: thesis: (/* S) . (id c) = id ((Obj (/* S)) . c)
thus (/* S) . (id c) = S . ((id c) opp) by Def6
.= S . (id (c opp))
.= id ((Obj S) . (c opp)) by Th32
.= id ((Obj (/* S)) . c) by Th37 ; :: thesis: verum