reserve a,b,c for boolean object;
reserve p,q,r,s,A,B,C for Element of LTLB_WFF,
        F,G,X,Y for Subset of LTLB_WFF,
        i,j,k,n for Element of NAT,
        f,f1,f2,g for FinSequence of LTLB_WFF;
reserve M for LTLModel;

theorem Th22:
  M|=F & M|=G iff M|=F\/G
 proof
  hereby assume A1: M|=F & M|=G;
   thus M|=F\/G
   proof
    let p;
    assume p in F\/G;
    then p in F or p in G by XBOOLE_0:def 3;
    hence M|=p by A1;
   end;
  end;
  assume A2: M|=F\/G;
  thus M|=F
  proof
   let p;
   assume p in F;
   then p in F\/G by XBOOLE_0:def 3;
   hence M|=p by A2;
  end;
  thus M|=G
  proof
   let p;
   assume p in G;
   then p in F\/G by XBOOLE_0:def 3;
   hence M|=p by A2;
  end;
 end;
