
theorem Th87:
  for C1,C2 being Coherence_Space for x being set st x in C1 "\/"
C2 ex a being Element of C1, b being Element of C2 st x = a U+ b & (a = {} or b
  = {})
proof
  let C1,C2 be Coherence_Space, x be set;
  assume x in C1 "\/" C2;
  then x in the set of all a U+ {} where a is Element of C1 or x in the set of
all {}
  U+ b where b is Element of C2 by XBOOLE_0:def 3;
  then
  {} in C2 & (ex a being Element of C1 st x = a U+ {}) or {} in C1 & ex b
  being Element of C2 st x = {} U+ b by COH_SP:1;
  hence thesis;
end;
