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 Th10:
  H is negative or H is next implies len(H) = 1+len(
  the_argument_of H) & len(the_argument_of H) < len(H)
proof
  assume
A1: H is negative or H is next;
  per cases by A1;
  suppose
    H is negative;
    then H = 'not' the_argument_of H by Def18;
    then len(H) = 1+len(the_argument_of H) by FINSEQ_5:8;
    hence thesis by NAT_1:19;
  end;
  suppose
    H is next;
    then H = 'X' the_argument_of H by Th5;
    then len(H) = 1+len(the_argument_of H) by FINSEQ_5:8;
    hence thesis by NAT_1:19;
  end;
end;
