
theorem Th1:
  for nt being NonTerminal of SCM-AE
   holds nt = [0,0] or ... or nt = [0,4]
proof
  let nt be NonTerminal of SCM-AE;
  consider x, y being object such that
A1: x in 1 and
A2: y in 5 and
A3: nt = [x,y] by Lm3,ZFMISC_1:84;
A4: x = 0 by A1,CARD_1:49,TARSKI:def 1;
  consider n being Nat such that
A5: y = n and
A6: n < 5 by A2,Lm2;
  5 = 4+1;
  then n <= 4 by A6,NAT_1:13;
  then n = 0 or ... or n = 4;
  hence thesis by A3,A4,A5;
end;
