
theorem
  and3b.<*0,0,0*>=0 & and3b.<*0,0,1*>=1 & and3b.<*0,1,0*>=0 & and3b.<*0,
1,1*>=0 & and3b.<*1,0,0*>=0 & and3b.<*1,0,1*>=0 & and3b.<*1,1,0*>=0 & and3b.<*1
  ,1,1*>=0
proof
  thus and3b.<*0,0,0*> = 'not' FALSE '&' 'not' FALSE '&' FALSE by Def11
    .= 0;
  thus and3b.<*0,0,1*> = TRUE '&' 'not' FALSE '&' TRUE by Def11
    .= 1;
  thus and3b.<*0,1,0*> = 'not' FALSE '&' 'not' TRUE '&' FALSE by Def11
    .= 0;
  thus and3b.<*0,1,1*> = 'not' FALSE '&' 'not' TRUE '&' TRUE by Def11
    .= 0;
  thus and3b.<*1,0,0*> = 'not' TRUE '&' 'not' FALSE '&' FALSE by Def11
    .= 0;
  thus and3b.<*1,0,1*> = 'not' TRUE '&' 'not' FALSE '&' TRUE by Def11
    .= 0;
  thus and3b.<*1,1,0*> = 'not' TRUE '&' 'not' TRUE '&' FALSE by Def11
    .= 0;
  thus and3b.<*1,1,1*> = FALSE '&' 'not' TRUE '&' TRUE by Def11
    .= 0;
end;
