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;
reserve L,L9 for FinSequence;
reserve j for Nat;
reserve j1 for Element of NAT;
reserve V for LTLModel;
reserve Kai for Function of atomic_LTL,the BasicAssign of V;
reserve f,f1,f2 for Function of LTL_WFF,the carrier of V;

theorem Th53:
  Evaluate('X' H,Kai) = 'X' Evaluate(H,Kai)
proof
  consider f1 be Function of LTL_WFF,the carrier of V such that
A1: f1 is-Evaluation-for Kai and
A2: Evaluate('X' H,Kai) = f1.('X' H) by Def35;
A3: ex f2 be Function of LTL_WFF,the carrier of V st f2
  is-Evaluation-for Kai & Evaluate(H,Kai) = f2.H by Def35;
A4: 'X' H is next;
  then
A5: not 'X' H is negative by Lm19;
  Evaluate('X' H,Kai) = (the NEXT of V).(f1.(the_argument_of('X' H)) ) by A1,A2
,A4
    .= (the NEXT of V).(f1.H ) by A4,A5,Def18
    .= 'X' Evaluate(H,Kai) by A1,A3,Th49;
  hence thesis;
end;
