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