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 Th74:
  p in rng f implies f-:p-:p = f-:p
proof
  assume p in rng f;
  then
A1: p..(f-:p) = p..f by Th72;
  thus f-:p-:p = (f-:p)|(p..(f-:p)) by FINSEQ_5:def 1
    .= (f|(p..f))|(p..f) by A1,FINSEQ_5:def 1
    .= f-:p by FINSEQ_5:def 1;
end;
