theorem Th121:
  ((a,b) followed_by c).0 = a
proof
  dom (0,1) --> (a,b) = {0,1} by FUNCT_4:62;
  then
A1: 0 in dom (0,1) --> (a,b) by TARSKI:def 2;
  thus ((a,b) followed_by c).0 = ((NAT --> c) +* ((0,1) --> (a,b))).0
    .= ((0,1) --> (a,b)).0 by A1,FUNCT_4:13
    .= a by FUNCT_4:63;
end;
