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 Th21:
  (SAT M).[n,(B 'U' C)=>('X'('F' C))]=1
 proof
  set sm=SAT M;
  A1: now assume that
    A2: sm.[n,B 'U' C]=1 and
    A3: sm.[n,'X'('F' C)]=0;
   consider i such that
    A4: 0<i and
    A5: sm.[n+i,C]=1 and
    for j st 1<=j & j<i holds sm.[n+j,B]=1 by A2,Def11;
   i+(-1)>=1+(-1) by A4,NAT_1:25,XREAL_1:6;
   then A6: n+1+(i-' 1)=n+1+(i-1) by XREAL_0:def 2
    .=n+i;
   sm.[n+1,'F' C]=0 by A3,Th9;
   hence contradiction by A5,A6,Th11;
  end;
  sm.[n,B 'U' C]=0 or sm.[n,B 'U' C]=1 by XBOOLEAN:def 3;
  then sm.[n,B 'U' C]=>sm.[n,'X'('F' C)]=1 by A1,XBOOLEAN:def 3;
  hence thesis by Def11;
 end;
