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<b>let </b><font color="Maroon">f</font> be    <a href="comput_1.html#M1" target="_self">Element</a> of  <a href="comput_1.html#K11" target="_self">PrimRec</a> ;<br/>

<b>set </b><font color="Maroon">prd</font> =  <a href="comput_1.html#K15" target="_self">PrimRec-Approximation</a> ;<br/>
<a NAME="E1:138_1_1"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="prob_1.html#K2">Union</a> <a href="comput_1.html#K15" target="_self">PrimRec-Approximation</a> 
 
<b>by </b><i><a class="ref" href="comput_1.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E2:138_1_1"/><b>then </b>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <a href="comput_1.html#K15" target="_self">PrimRec-Approximation</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="card_3.html#D4">CARD_3:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon">X</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:138_1_1"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <a href="comput_1.html#K15" target="_self">PrimRec-Approximation</a>  )
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<a NAME="E5:138_1_1"/>
 ex <font color="Olive">m</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <a href="comput_1.html#K15" target="_self">PrimRec-Approximation</a>  &amp; <a href="comput_1.html#K15" target="_self">PrimRec-Approximation</a>  <a href="funct_1.html#K1">.</a> <font color="Olive">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> )
 
<b>by </b><i><a class="ref" href="comput_1.html#D4" target="_self">Def4</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E6:138_1_1"/>
( <font color="Maroon">f</font> is <a href="unialg_1.html#V2">quasi_total</a> &amp; <font color="Maroon">f</font> is <a href="comput_1.html#V4" target="_self">homogeneous</a> )
 <b>by </b><i><a class="ref" href="comput_1.html#D4" target="_self">Def4</a>, <a class="ref" href="comput_1.html#D3" target="_self">Def3</a></i>;<br/>


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