reserve o,m for set;
reserve C for Cartesian_category;
reserve a,b,c,d,e,s for Object of C;
reserve C for Cocartesian_category;
reserve a,b,c,d,e,s for Object of C;

theorem
  for f being Morphism of a,c, g being Morphism of b,c st Hom(a,c) <> {}
  & Hom(b,c) <> {} holds nabla(c)*(f+g) = [$f,g$]
proof
  let f be Morphism of a,c, g be Morphism of b,c such that
A1: Hom(a,c) <> {} and
A2: Hom(b,c) <> {};
  Hom(c,c) <> {};
  hence nabla(c)*(f+g) = [$(id c)*f,(id c)*g$] by A1,A2,Th75
    .= [$f,(id c)*g$] by A1,CAT_1:28
    .= [$f,g$] by A2,CAT_1:28;
end;
