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<div><span class="kw">theorem </span><a NAME="T18"><span class="comment"><font color="firebrick">:: PUA2MSS1:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">partial</a>   <a href="unialg_1.html#V4" title="UNIALG_1:attr.4">non-empty</a>   <a href="unialg_1.html#L1" title="UNIALG_1:struct.1">UAStr</a> <br/>  for <font color="Olive" title="b2">i</font>, <font color="Olive" title="b3">j</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b4">R</font> being   <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">A</font> holds  <font color="Olive" title="b4">R</font> <a href="pua2mss1.html#K8" title="PUA2MSS1:func.8">|^</a> (<font color="Olive" title="b1">A</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b3">j</font></span>)</span>) <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">R</font> <a href="pua2mss1.html#K8" title="PUA2MSS1:func.8">|^</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">i</font>)</span>)</span> <a href="pua2mss1.html#K8" title="PUA2MSS1:func.8">|^</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b3">j</font>)</div></div>
