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<b>let </b><font color="Maroon">T</font> be    <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">H</font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">S</font>;<br/>







<a NAME="E1:44"/><i><font color="Green">E33</font></i>: 
<span class="p1">(<span class="default"><a href="funct_3.html#K3">"</a> <font color="Maroon">f</font></span>)</span> <a href="relat_1.html#K9">.:</a> <font color="Maroon">H</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_3.html#K3">"</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T144">RELAT_1:144</a></i>;<br/>
<a NAME="E2:44"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_3.html#K3">"</a> <font color="Maroon">f</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_3.html#T25">FUNCT_3:25</a></i>;<br/>
<a NAME="E3:44"/><b>then </b>
<span class="p1">(<span class="default"><a href="funct_3.html#K3">"</a> <font color="Maroon">f</font></span>)</span> <a href="relat_1.html#K9">.:</a> <font color="Maroon">H</font> <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:44"/><b>then </b>
( <span class="p1">(<span class="default"><a href="funct_3.html#K3">"</a> <font color="Maroon">f</font></span>)</span> <a href="relat_1.html#K9">.:</a> <font color="Maroon">H</font> is   <a href="setfam_1.html#NM1">Subset-Family</a> of <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font></span>)</span> &amp;  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:44"/>
<span class="p1">(<span class="default"><a href="funct_3.html#K3">"</a> <font color="Maroon">f</font></span>)</span> <a href="relat_1.html#K9">.:</a> <font color="Maroon">H</font> is   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">T</font>
 ;<br/>


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