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 Th49:
  f1 is-Evaluation-for Kai & f2 is-Evaluation-for Kai implies f1 = f2
proof
  assume
A1: f1 is-Evaluation-for Kai & f2 is-Evaluation-for Kai;
  for H being object st H in LTL_WFF holds f1.H=f2.H
  proof
    let H be object;
    assume H in LTL_WFF;
    then reconsider H as LTL-formula by Th1;
    set n=len(H);
    f1 is-PreEvaluation-for n, Kai & f2 is-PreEvaluation-for n, Kai by A1;
    hence thesis by Lm24;
  end;
  hence thesis by FUNCT_2:12;
end;
