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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E10">Th6</font></span>: <a NAME="T6"><span class="comment"><font color="firebrick">:: MSAFREE:6</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/>  for <font color="Olive" title="b2">X</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">S</font> holds <br/> (  <a href="lang1.html#K2" title="LANG1:func.2">NonTerminals</a> <span class="p1">(<span class="default"><a href="msafree.html#K5" title="MSAFREE:func.5">DTConMSA</a> <font color="Olive" title="b2">X</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b1">S</font>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">S</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp;  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><a href="msafree.html#K3" title="MSAFREE:func.3">coprod</a> <font color="Olive" title="b2">X</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lang1.html#K1" title="LANG1:func.1">Terminals</a> <span class="p1">(<span class="default"><a href="msafree.html#K5" title="MSAFREE:func.5">DTConMSA</a> <font color="Olive" title="b2">X</font></span>)</span> &amp; ( <font color="Olive" title="b2">X</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>() implies (  <a href="lang1.html#K2" title="LANG1:func.2">NonTerminals</a> <span class="p1">(<span class="default"><a href="msafree.html#K5" title="MSAFREE:func.5">DTConMSA</a> <font color="Olive" title="b2">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b1">S</font>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">S</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp;  <a href="lang1.html#K1" title="LANG1:func.1">Terminals</a> <span class="p1">(<span class="default"><a href="msafree.html#K5" title="MSAFREE:func.5">DTConMSA</a> <font color="Olive" title="b2">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><a href="msafree.html#K3" title="MSAFREE:func.3">coprod</a> <font color="Olive" title="b2">X</font></span>)</span> ) ) )</div></div>
