reserve k,n,m for Nat,
  a,x,X,Y for set,
  D,D1,D2,S for non empty set,
  p,q for FinSequence of NAT;
reserve F,F1,G,G1,H,H1,H2 for LTL-formula;
reserve sq,sq9 for FinSequence;

theorem Th12:
  for F,G holds ('not' F).1 = 0 & (F '&' G).1 = 1 & (F 'or' G).1 =
  2 & ('X' F).1 = 3 & (F 'U' G).1 = 4 & (F 'R' G).1 = 5
proof
  let F,G;
  thus ('not' F).1 = 0 by FINSEQ_1:41;
  thus (F '&' G).1 = (<*1*>^(F^G)).1 by FINSEQ_1:32
    .= 1 by FINSEQ_1:41;
  thus (F 'or' G).1 = (<*2*>^(F^G)).1 by FINSEQ_1:32
    .= 2 by FINSEQ_1:41;
  thus ('X' F).1 = 3 by FINSEQ_1:41;
  thus (F 'U' G).1 = (<*4*>^(F^G)).1 by FINSEQ_1:32
    .= 4 by FINSEQ_1:41;
  thus (F 'R' G).1 = (<*5*>^(F^G)).1 by FINSEQ_1:32
    .= 5 by FINSEQ_1:41;
end;
