reserve A,B,C,D,p,q,r for Element of LTLB_WFF,
        F,G,X for Subset of LTLB_WFF,
        M for LTLModel,
        i,j,n for Element of NAT,
        f,f1,f2,g for FinSequence of LTLB_WFF;

theorem th218:
  F |= A & (for B st B in F holds {}LTLB_WFF |= B)
    implies {}LTLB_WFF |= A
proof
  assume
Z1: F |= A & (for B st B in F holds {}LTLB_WFF |= B);
  let M;
  assume
Z2: M |= {}LTLB_WFF;
  now
    let B;
    assume B in F;then
    {}LTLB_WFF |= B by Z1;
    hence M |= B by Z2;
  end;then
  M |= F;
  hence M |= A by Z1;
end;
