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 Th50:
  Evaluate('not' H,Kai) = 'not' 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('not' H,Kai) = f1.('not' 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: 'not' H is negative;
  then
  Evaluate('not' H,Kai) = (the Compl of V).(f1.(the_argument_of('not' H)) )
  by A1,A2
    .= (the Compl of V).(f1.H ) by A4,Def18
    .= 'not' Evaluate(H,Kai) by A1,A3,Th49;
  hence thesis;
end;
