
theorem Th61:
  for C1, C2 being Coherence_Space for f being U-linear Function
  of C1,C2 for X being Subset of LinTrace f ex g being U-linear Function of C1,
  C2 st LinTrace g = X
proof
  let C1, C2 be Coherence_Space;
  let f be U-linear Function of C1,C2;
  let X be Subset of LinTrace f;
A1: for a,b be set st {a,b} in C1
for y be object st [a,y] in X & [b,y] in X
  holds a = b by Th54;
  X is Subset of [:union C1, union C2:] & for a,b be set st {a,b} in C1
  for y1,y2 be object st [a,y1] in X & [b,y2] in X holds {y1,y2} in C2
   by Th53,XBOOLE_1:1;
  hence thesis by A1,Th56;
end;
