
theorem
  and3a.<*0,0,0*>=0 & and3a.<*0,0,1*>=0 & and3a.<*0,1,0*>=0 & and3a.<*0,
1,1*>=1 & and3a.<*1,0,0*>=0 & and3a.<*1,0,1*>=0 & and3a.<*1,1,0*>=0 & and3a.<*1
  ,1,1*>=0
proof
  thus and3a.<*0,0,0*> = 'not' FALSE '&' FALSE '&' FALSE by Def10
    .= 0;
  thus and3a.<*0,0,1*> = 'not' FALSE '&' FALSE '&' TRUE by Def10
    .= 0;
  thus and3a.<*0,1,0*> = 'not' FALSE '&' TRUE '&' FALSE by Def10
    .= 0;
  thus and3a.<*0,1,1*> = ('not' FALSE '&' TRUE) '&' TRUE by Def10
    .= 1;
  thus and3a.<*1,0,0*> = 'not' TRUE '&' FALSE '&' FALSE by Def10
    .= 0;
  thus and3a.<*1,0,1*> = 'not' TRUE '&' FALSE '&' TRUE by Def10
    .= 0;
  thus and3a.<*1,1,0*> = 'not' TRUE '&' TRUE '&' FALSE by Def10
    .= 0;
  thus and3a.<*1,1,1*> = 'not' TRUE '&' TRUE by Def10
    .= 0;
end;
