theorem Th14:
  1 in dom <*c,d*> & 2 in dom <*c,d*> &
  (f^<*c,d*>).(len f + 1) = c & (f^<*c,d*>).(len f + 2) = d
proof
A1: 2 <= len <*c,d*> by FINSEQ_1:44;
  then 2 in dom <*c,d*> by FINSEQ_3:25;
  then
A2: (f^<*c,d*>).(len f+2) = <*c,d*>.2 by FINSEQ_1:def 7;
  1 <= 2;
  then
A3: 1 <= len <*c,d*> by FINSEQ_1:44;
  then 1 in dom <*c,d*> by FINSEQ_3:25;
  then (f^<*c,d*>).(len f+1) = <*c,d*>.1 by FINSEQ_1:def 7;
  hence thesis by A3,A1,A2,FINSEQ_3:25;
end;
