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 Th8:
  (SAT M).[n,A 'or' B]=1 iff ((SAT M).[n,A]=1 or(SAT M).[n,B]=1)
 proof
  hereby assume(SAT M).[n,A 'or' B]=1;
   then A1: (SAT M).[n,('not' A)'&&'('not' B)]=0 by Th5;
   per cases by A1,Th7;
   suppose not(SAT M).[n,('not' A)]=1;
    hence (SAT M).[n,A]=1 or(SAT M).[n,B]=1 by XBOOLEAN:def 3,Th5;
   end;
   suppose not(SAT M).[n,('not' B)]=1;
    hence (SAT M).[n,A]=1 or(SAT M).[n,B]=1 by XBOOLEAN:def 3,Th5;
   end;
  end;
  assume A2: (SAT M).[n,A]=1 or(SAT M).[n,B]=1;
  per cases by A2;
  suppose(SAT M).[n,A]=1;
   then not(SAT M).[n,'not' A]=1 by Th5;
   then not(SAT M).[n,('not' A)'&&'('not' B)]=1 by Th7;
   hence thesis by Th5,XBOOLEAN:def 3;
  end;
  suppose(SAT M).[n,B]=1;
   then not(SAT M).[n,'not' B]=1 by Th5;
   then not(SAT M).[n,('not' A)'&&'('not' B)]=1 by Th7;
   hence thesis by Th5,XBOOLEAN:def 3;
  end;
 end;
