reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;

theorem
  p is one-to-one & x in rng p implies len(p - {x}) = len p - 1
proof
  assume that
A1: p is one-to-one and
A2: x in rng p;
  {x} c= rng p by A2,ZFMISC_1:31;
  then len(p - {x}) = len p - card{x} by A1,Th87;
  hence thesis by CARD_1:30;
end;
