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;

theorem
  <* d1,d2,d3 *>/.1 = d1 & <* d1,d2,d3 *>/.2 = d2 & <* d1,d2,d3 *>/.3 = d3
proof
  set s = <* d1,d2,d3 *>;
A1: s.2 = d2 & s.3 = d3;
A2: 1 in {1,2,3} & 2 in {1,2,3} by FINSEQ_3:1;
A3: 3 in {1,2,3} by FINSEQ_3:1;
  dom s = {1,2,3} & s.1 = d1 by FINSEQ_1:89,FINSEQ_3:1;
  hence thesis by A1,A2,A3,PARTFUN1:def 6;
end;
