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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be  <a href="comput_1.html#V4" target="_self">homogeneous</a> <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">X</font> <a href="finseq_2.html#K3">*</a> ,<font color="Maroon">X</font>;<br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_1"/>
( <font color="Maroon">X</font> is <a href="xboole_0.html#V1">empty</a> or  not <font color="Maroon">X</font> is <a href="xboole_0.html#V1">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_1"><b>suppose </b></a><a NAME="E1:46_1_1"/>
<font color="Maroon">X</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><a NAME="E2:46_1_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/><a NAME="E3:46_1_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/><a NAME="E4:46_1_1"/><b>then </b>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#T64">RELAT_1:64</a></i>;<br/><b>hence </b><a NAME="E5:46_1_1"/>
( ( <font color="Maroon">f</font> is <a href="unialg_1.html#V2">quasi_total</a> &amp; not <font color="Maroon">f</font> is <a href="xboole_0.html#V1">empty</a> ) iff  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="comput_1.html#K3" target="_self">arity</a> <font color="Maroon">f</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">X</font> )
 <b>by </b><i>, , <a class="ref" href="relat_1.html#T60">RELAT_1:60</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_2"><b>suppose </b></a><a NAME="E1:46_1_2"/>
not <font color="Maroon">X</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:46_1_2"/>
( ( <font color="Maroon">f</font> is <a href="unialg_1.html#V2">quasi_total</a> &amp; not <font color="Maroon">f</font> is <a href="xboole_0.html#V1">empty</a> ) iff  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="comput_1.html#K3" target="_self">arity</a> <font color="Maroon">f</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">X</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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