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<span class="kw">let </span><font color="Maroon" title="c4">e</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c2">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">v</font>; <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"> ( <font color="Maroon" title="c4">e</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp;  not <font color="Maroon" title="c4">e</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c4">e</font> is  <a href="funct_1.html#V1" title="FUNCT_1:attr.1">Function-like</a>  &amp; <font color="Maroon" title="c4">e</font> is  <a href="relat_1.html#V1" title="RELAT_1:attr.1">Relation-like</a>  )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">e9</font> = <font color="Maroon" title="c4">e</font> as   <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="msafree2.html#T7" target="_self" onmouseover="rs('msafree2/T7')" onmouseout="rh()">Th7</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:32_1_1"/>
<font color="Maroon" title="c4">e</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msafree2.html#T7" target="_self" onmouseover="rs('msafree2/T7')" onmouseout="rh()">Th7</a></span>; <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 <font color="Maroon" title="c4">e</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c4">e</font> is  <a href="funct_1.html#V1" title="FUNCT_1:attr.1">Function-like</a>  &amp; <font color="Maroon" title="c4">e</font> is  <a href="relat_1.html#V1" title="RELAT_1:attr.1">Relation-like</a>  )</span><br/>

<a NAME="E3:32_1_1"/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c5">e9</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>
 
;<br/>
<span class="kw">hence </span><a NAME="E4:32_1_1"/>
 not <font color="Maroon" title="c4">e</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"> ( <font color="Maroon" title="c4">e</font> is  <a href="funct_1.html#V1" title="FUNCT_1:attr.1">Function-like</a>  &amp; <font color="Maroon" title="c4">e</font> is  <a href="relat_1.html#V1" title="RELAT_1:attr.1">Relation-like</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E5:32_1_1"/>
( <font color="Maroon" title="c4">e</font> is  <a href="funct_1.html#V1" title="FUNCT_1:attr.1">Function-like</a>  &amp; <font color="Maroon" title="c4">e</font> is  <a href="relat_1.html#V1" title="RELAT_1:attr.1">Relation-like</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msafree2.html#T7" target="_self" onmouseover="rs('msafree2/T7')" onmouseout="rh()">Th7</a></span>; <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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