
theorem Th56:
  for C1, C2 being Coherence_Space for X being Subset of [:union
C1, union C2:] st (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)
ex f being U-linear
  Function of C1,C2 st X = LinTrace f
proof
  let C1, C2 be Coherence_Space;
  let X be Subset of [:union C1, union C2:];
  assume
A1: not thesis;
  then ex f being U-linear Function of C1,C2 st X = LinTrace f & for a being
  Element of C1 holds f.a = X.:a by Lm6;
  hence thesis by A1;
end;
