let B, C be Category; :: thesis: for S being Functor of C opp ,B
for c being Object of C holds (/* S) . (id c) = id ((Obj S) . (c opp))
let S be Functor of C opp ,B; :: thesis: for c being Object of C holds (/* S) . (id c) = id ((Obj S) . (c opp))
let c be Object of C; :: thesis: (/* S) . (id c) = id ((Obj S) . (c opp))
reconsider i = id c as Morphism of C ;
A1: Hom (c,c) <> {} ;
thus (/* S) . (id c) = S . (i opp) by Def8
.= S . ((id c) opp) by A1, Def6
.= S . (id (c opp)) by Th18
.= id ((Obj S) . (c opp)) by CAT_1:68 ; :: thesis: verum