<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">f</font> be  <a href="comput_1.html#NV2" title="COMPUT_1:NV.2">to-naturals</a> <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <a href="comput_1.html#V2" title="COMPUT_1:attr.2">from-natural-fseqs</a> <a href="comput_1.html#V3" title="COMPUT_1:attr.3">len-total</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>

<b>reconsider </b><font color="Maroon" title="c2">f'</font> = <font color="Maroon" title="c1">f</font> as    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="comput_1.html#K4" title="COMPUT_1:func.4">HFuncs</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="comput_1.html#T31" target="_self" title="COMPUT_1:th.31">Th31</a></i>;<br/>
<a NAME="E2:59"/>
<font color="Maroon" title="c2">f'</font> is <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_1.html#D2" title="UNIALG_1:def.2">UNIALG_1:def 2</a><br/>

<b>assume </b><a NAME="E1:59_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">y</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f'</font> )
 ;<br/>

<b>hence </b><a NAME="E2:59_1"/>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f'</font>
 <b>by </b><i><a class="ref" href="comput_1.html#D3" target="_self" title="COMPUT_1:def.3">Def3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:59"/>
<font color="Maroon" title="c1">f</font> is  <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a>  <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="comput_1.html#K4" title="COMPUT_1:func.4">HFuncs</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ;<br/>


</div>
