theorem Th73:
  for P,Q st [:P,Q:] c= Indices M & card P = card Q holds card P
  <= len M & card Q <= width M
proof
  let P,Q such that
A1: [:P,Q:] c= Indices M and
A2: card P = card Q;
  Q c= Seg width M by A1,A2,Th67;
  then
A3: card Q <=card Seg width M by NAT_1:43;
  P c= Seg len M by A1,A2,Th67;
  then card P<=card Seg len M by NAT_1:43;
  hence thesis by A3,FINSEQ_1:57;
end;
