reserve f for Function;
reserve p,q for FinSequence;
reserve A,B,C for set,x,x1,x2,y,z for object;
reserve k,l,m,n for Nat;
reserve a for Nat;
reserve D for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve L,M for Element of NAT;

theorem
  x in rng p & p is one-to-one implies p -| x is one-to-one
proof
  assume x in rng p;
  then p = (p -| x) ^ <* x *> ^ (p |-- x) by Th51
    .= (p -| x) ^ (<* x *> ^ (p |-- x)) by FINSEQ_1:32;
  hence thesis by FINSEQ_3:91;
end;
