
theorem
  for C1, C2 being Coherence_Space for f being c=-monotone Function of
C1,C2 for a,b being Element of C1 st a \/ b in C1 for y1,y2 being set st [a,y1]
  in graph f & [b,y2] in graph f holds {y1,y2} in C2
proof
  let C1, C2 be Coherence_Space;
  let f be c=-monotone Function of C1,C2;
  let a,b be Element of C1 such that
A1: a \/ b in C1;
  let y1,y2 be set;
  assume
A2: [a,y1] in graph f & [b,y2] in graph f;
  then a is finite & b is finite by Th24;
  then reconsider c = a \/ b as finite Element of C1 by A1;
  dom f = C1 by FUNCT_2:def 1;
  then [c,y1] in graph f & [c,y2] in graph f by A2,Th25,XBOOLE_1:7;
  hence thesis by Th26;
end;
