reserve k,n,n1,m,m1,m0,h,i,j for Nat,
  a,x,y,X,X1,X2,X3,X4,Y for set;
reserve L,L1,L2 for FinSequence;
reserve F,F1,G,G1,H for LTL-formula;
reserve W,W1,W2 for Subset of Subformulae H;
reserve v for LTL-formula;
reserve N,N1,N2,N10,N20,M for strict LTLnode over v;
reserve w for Element of Inf_seq(AtomicFamily);
reserve R1,R2 for Real_Sequence;
reserve s,s0,s1,s2 for elementary strict LTLnode over v;
reserve q for sequence of LTLStates(v);
reserve U for Choice_Function of BOOL Subformulae v;

theorem
  (H is conjunctive or H is disjunctive or H is Until or H is Release) &
  H is neg-inner-most implies the_left_argument_of H is neg-inner-most &
  the_right_argument_of H is neg-inner-most
proof
  assume that
A1: H is conjunctive or H is disjunctive or H is Until or H is Release and
A2: H is neg-inner-most;
  set F2 = the_right_argument_of H;
A3: F2 is_subformula_of H by A1,MODELC_2:31;
A4: for G being LTL-formula st G is_subformula_of F2 holds G is negative
  implies the_argument_of G is atomic
  by A3,A2,MODELC_2:35;
  set F1 = the_left_argument_of H;
A5: F1 is_subformula_of H by A1,MODELC_2:31;
  for G being LTL-formula st G is_subformula_of F1 holds G is negative
  implies the_argument_of G is atomic
  by A5,A2,MODELC_2:35;
  hence thesis by A4;
end;
