theorem Th37:
for x,y be Point of product G
 holds proj(i).(x-y) = proj(i).x - proj(i).y
proof
   let x,y be Point of product G;
   reconsider v=x-y as Element of product carr G by Th10;
   reconsider s=x as Element of product carr G by Th10;
   reconsider t=y as Element of product carr G by Th10;
   proj(i).(x-y)= v.i & proj(i).x = s.i & proj(i).y = t.i by Def3;
   hence thesis by Th15;
end;
