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;
reserve f for Function of A,B;
reserve f for Function;
reserve x1,x2,x3,x4,x5 for object;
reserve p for FinSequence;
reserve ND for non empty set;
reserve y1,y2,y3,y4,y5 for Element of ND;

theorem
  <*y1,y2,y3,y4,y5*>/.1 = y1 & <*y1,y2,y3,y4,y5*>/.2 = y2 & <*y1,y2,y3,
  y4,y5*>/.3 = y3 & <*y1,y2,y3,y4,y5*>/.4=y4 & <*y1,y2,y3,y4,y5*>/.5=y5
proof
  set s = <* y1,y2,y3,y4,y5 *>, i5={1,2,3,4,5};
A1: 1 in i5 & 2 in i5 by FINSEQ_3:3;
A2: 3 in i5 & 4 in i5 by FINSEQ_3:3;
A3: s.4 = y4 & s.5=y5;
A4: s.2 = y2 & s.3 = y3;
A5: 5 in i5 by FINSEQ_3:3;
  dom s =i5 & s.1 = y1 by FINSEQ_1:89,FINSEQ_3:3;
  hence thesis by A4,A3,A1,A2,A5,PARTFUN1:def 6;
end;
