theorem
 Hom(b,c) <> {} & Hom(c,b) <> {} &
  g*f is coretraction implies f is coretraction
proof assume
A1: Hom(b,c) <> {} & Hom(c,b) <> {};
  assume
A2: Hom(a,c) <> {} & Hom(c,a) <> {};
  given i being Morphism of c,a such that
A3: i*(g*f) = id a;
  thus
A4: Hom(a,b) <> {} & Hom(b,a) <> {} by A1,A2,CAT_1:24;
  take i*g;
  thus (i*g)*f = id a by A4,A1,A2,A3,CAT_1:25;
end;
