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;
reserve BASSIGN for non empty Subset of ModelSP(Inf_seq(S));
reserve t for Element of Inf_seq(S);
reserve f,g for Assign of Inf_seqModel(S,BASSIGN);
reserve r for Element of Inf_seq(AtomicFamily);

theorem Th65:
  r|= H1 '&' H2 iff r|= H1 & r|= H2
proof
  r|= H1 '&' H2 iff r|= Evaluate(H1,AtomicKai) '&' Evaluate(H2,AtomicKai)
  by Th51;
  then
  r|= H1 '&' H2 iff r|= Evaluate(H1,AtomicKai) & r|= Evaluate(H2,AtomicKai
  ) by Th58;
  hence thesis;
end;
