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<a NAME="E1:32_1_1"/>
( ( <font color="Maroon">D1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">D1</font>,<font color="Maroon">D1</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) &amp; ( <font color="Maroon">D2</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">D2</font>,<font color="Maroon">D2</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T113">ZFMISC_1:113</a></i>;<br/>
<a NAME="E2:32_1_1"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">D1</font>,<font color="Maroon">D1</font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D1</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">D2</font>,<font color="Maroon">D2</font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D2</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<a NAME="E3:32_1_1"/><b>then </b><i><font color="Green">E68</font></i>: 
( <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">f1</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">f2</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">D1</font>,<font color="Maroon">D2</font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_4.html#K3">|:</a><span class="default"><font color="Maroon">f1</font>,<font color="Maroon">f2</font></span><a href="funct_4.html#K3">:|</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">f1</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">f2</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_4.html#K3">|:</a><span class="default"><font color="Maroon">f1</font>,<font color="Maroon">f2</font></span><a href="funct_4.html#K3">:|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">D1</font>,<font color="Maroon">D2</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">D1</font>,<font color="Maroon">D2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_4.html#T59">FUNCT_4:59</a>, <a class="ref" href="funct_4.html#T61">FUNCT_4:61</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E4:32_1_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_4.html#K3">|:</a><span class="default"><font color="Maroon">f1</font>,<font color="Maroon">f2</font></span><a href="funct_4.html#K3">:|</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">D1</font>,<font color="Maroon">D2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E5:32_1_1"/>
<span class="p1"><a href="funct_4.html#K3">|:</a><span class="default"><font color="Maroon">f1</font>,<font color="Maroon">f2</font></span><a href="funct_4.html#K3">:|</a></span> is   <a href="binop_1.html#NM2">BinOp</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">D1</font>,<font color="Maroon">D2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i>, <a class="ref" href="funct_2.html#T4">FUNCT_2:4</a></i>;<br/>


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