reserve X for non empty set;
reserve e,e1,e2,e19,e29 for Equivalence_Relation of X,
  x,y,x9,y9 for set;
reserve A for non empty set,
  L for lower-bounded LATTICE;
reserve T,L1 for Sequence,
  O,O1,O2,O3,C for Ordinal;

theorem
  for d being distance_function of A,L for q being QuadrSeq of d st O c=
DistEsti(d) holds ConsecutiveDelta(q,O) is distance_function of ConsecutiveSet(
  A,O),L by Th33,Th34,Th35;
