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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E49">Th36</font></span>: <a NAME="T52"><span class="comment"><font color="firebrick">:: BAGORD_2:52</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</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> <br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b5">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b6">p</font> being    <a href="bagord_2.html#M2" title="BAGORD_2:mode.2">partition</a> of <font color="Olive" title="b3">b</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">-'</a> <font color="Olive" title="b2">a</font><br/>  for <font color="Olive" title="b7">q</font> being    <a href="bagord_2.html#M2" title="BAGORD_2:mode.2">partition</a> of <font color="Olive" title="b3">b</font>  st <font color="Olive" title="b7">q</font> is  <a href="bagord_2.html#V4" title="BAGORD_2:attr.4">ordered</a>  &amp; <font color="Olive" title="b7">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="bagord_2.html#K4" title="BAGORD_2:func.4">&lt;*</a><span class="default"><font color="Olive" title="b2">a</font></span><a href="bagord_2.html#K4" title="BAGORD_2:func.4">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b6">p</font> &amp; <font color="Olive" title="b4">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b6">p</font> &amp; <font color="Olive" title="b4">c</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">x</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> ex <font color="Olive" title="b8">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font> st <br/>( <font color="Olive" title="b2">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b8">y</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b5">x</font> <a href="bagord_2.html#R1" title="BAGORD_2:pred.1">&lt;=</a> <font color="Olive" title="b8">y</font> )</div></div>
