theorem Th122:
  ((a,b) followed_by c).1 = b
proof
  dom (0,1) --> (a,b) = {0,1} by FUNCT_4:62;
  then
A1: 1 in dom (0,1) --> (a,b) by TARSKI:def 2;
  thus ((a,b) followed_by c).1 = ((NAT --> c) +* ((0,1) --> (a,b))).1
    .= ((0,1) --> (a,b)).1 by A1,FUNCT_4:13
    .= b by FUNCT_4:63;
end;
