reserve x,y,z for set;
reserve f,f1,f2,f3 for FinSequence,
  p,p1,p2,p3 for set,
  i,k for Nat;
reserve D for non empty set,
  p,p1,p2,p3 for Element of D,
  f,f1,f2 for FinSequence of D;

theorem Th40:
  p in rng f implies f-:p = (f -| p)^<*p*>
proof
  assume p in rng f;
  hence (f -| p)^<*p*> = f|(p..f) by FINSEQ_5:24
    .= f-:p by FINSEQ_5:def 1;
end;
