
theorem
  for C1, C2 being Coherence_Space ex f being U-linear Function of C1,
  C2 st LinTrace f = {}
proof
  let C1, C2 be Coherence_Space;
  reconsider X = {} as Subset of [:union C1, union C2:] by XBOOLE_1:2;
  ( for a,b being set st {a,b} in C1
for y1,y2 being object st [a,y1] in X &
[ b,y2] in X holds {y1,y2} in C2)& for a,b being set st {a,b} in C1 for y being
  object st [a,y] in X & [b,y] in X holds a = b;
  hence thesis by Th56;
end;
