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<span class="kw">let </span><font color="Maroon" title="c1">f</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="freealg.html#V1" title="FREEALG:attr.1">disjoint_with_NAT</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   holds  not  <a href="freealg.html#K8" title="FREEALG:func.8">FreeGenSetNSG</a> (<font color="Maroon" title="c1">f</font>,<font color="Olive" title="b1">D</font>) is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">D</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="freealg.html#V1" title="FREEALG:attr.1">disjoint_with_NAT</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not  <a href="freealg.html#K8" title="FREEALG:func.8">FreeGenSetNSG</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">D</font>) is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">X</font> =  <a href="freealg.html#K3" title="FREEALG:func.3">DTConUA</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">D</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c4">d</font> =  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">d1</font> =  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D</font> as   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <span class="p1">(<span class="default"><a href="freealg.html#K3" title="FREEALG:func.3">DTConUA</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">D</font>)</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E2:30"/>
 <a href="dtconstr.html#K6" title="DTCONSTR:func.6">Terminals</a> <span class="p1">(<span class="default"><a href="freealg.html#K3" title="FREEALG:func.3">DTConUA</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">D</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="freealg.html#T3" target="_self" onmouseover="rs('freealg/T3')" onmouseout="rh()">Th3</a></span>;<br/>
<a NAME="E3:30"/><span class="kw">then </span>
 <a href="trees_4.html#K2" title="TREES_4:func.2">root-tree</a> <font color="Maroon" title="c5">d1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="trees_4.html#K2" title="TREES_4:func.2">root-tree</a> <font color="Olive" title="b1">k</font></span>)</span> where <font color="Olive" title="b1">k</font> is   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <span class="p1">(<span class="default"><a href="freealg.html#K3" title="FREEALG:func.3">DTConUA</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">D</font>)</span>)</span> : <font color="Olive" title="b1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="dtconstr.html#K6" title="DTCONSTR:func.6">Terminals</a> <span class="p1">(<span class="default"><a href="freealg.html#K3" title="FREEALG:func.3">DTConUA</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">D</font>)</span>)</span> </span> } </span> 
 
;<br/>
<span class="kw">hence </span><a NAME="E4:30"/>
 not  <a href="freealg.html#K8" title="FREEALG:func.8">FreeGenSetNSG</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">D</font>) is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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