theorem Th24:
  (fire e)*id Funcs(P, NAT) = fire e
proof
A1: compose(<*fire e*>, Funcs(P, NAT)) = (fire e)*id Funcs(P, NAT)
  by FUNCT_7:45;
  dom fire e c= Funcs(P, NAT) by Def8;
  hence thesis by A1,FUNCT_7:46;
end;
