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<div><span class="kw">theorem </span><a NAME="T31"><span class="comment"><font color="firebrick">:: BAGORD_2:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R1</font>, <font color="Olive" title="b2">R2</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>   <a href="necklace.html#V2" title="NECKLACE:attr.2">asymmetric</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>   st  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">R1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">R2</font> &amp;  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Olive" title="b1">R1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Olive" title="b2">R2</font> holds <br/> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="bagord_2.html#K1" title="BAGORD_2:func.1">DershowitzMannaOrder</a> <font color="Olive" title="b1">R1</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="bagord_2.html#K1" title="BAGORD_2:func.1">DershowitzMannaOrder</a> <font color="Olive" title="b2">R2</font></span>)</span></div></div>
