reserve a,a1,a2,b,c,d for Ordinal,
  n,m,k for Nat,
  x,y,z,t,X,Y,Z for set;
reserve f,g for Function;

theorem Th9:
  f is segmental implies
  for a,b,c st a c= b & b c= c & a in dom f & c in dom f holds b in dom f
  proof given x,y being Ordinal such that
A1: dom f = x\y;
    let a,b,c; assume
A2: a c= b & b c= c & a in dom f & c in dom f; then
    y c= a & c in x by A1,ORDINAL6:5; then
    y c= b & b in x by A2,ORDINAL1:12;
    hence thesis by A1,ORDINAL6:5;
  end;
