let B, C be Category; :: thesis: for S being Function of the carrier' of (C opp), the carrier' of B
for f being Morphism of (C opp) holds (/* S) . (opp f) = S . f
let S be Function of the carrier' of (C opp), the carrier' of B; :: thesis: for f being Morphism of (C opp) holds (/* S) . (opp f) = S . f
let f be Morphism of (C opp); :: thesis: (/* S) . (opp f) = S . f
thus (/* S) . (opp f) = S . ((opp f) opp) by Def8
.= S . f ; :: thesis: verum