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 Th41:
  p in rng f implies f:-p = <*p*>^(f |-- p)
proof
  assume p in rng f;
  hence <*p*>^(f |-- p) = <*p*>^(f/^(p..f)) by FINSEQ_5:35
    .= f:-p by FINSEQ_5:def 2;
end;
