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<b>let </b><font color="Maroon" title="c1">g</font> be  <a href="comput_1.html#NV2" title="COMPUT_1:NV.2">to-naturals</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">g</font> is  <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> , <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><br/>

<a NAME="E1:36"/><i><font color="Green" title="E20">A1</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 
<b>by </b><i><a class="ref" href="comput_1.html#D2" target="_self" title="COMPUT_1:def.2">Def2</a></i>;<br/>
<a NAME="E2:36"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="valued_0.html#D6" title="VALUED_0:def.6">VALUED_0:def 6</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c2">g'</font> = <font color="Maroon" title="c1">g</font> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> , <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="#E1:36"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>
<a NAME="E4:36"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <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>   st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">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="Olive" title="b2">y</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">g</font> holds <br/><font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">g</font>
 
<b>by </b><i><a class="ref" href="comput_1.html#D3" target="_self" title="COMPUT_1:def.3">Def3</a></i>;<br/>
<a NAME="E5:36"/><b>then </b>
<font color="Maroon" title="c2">g'</font> is <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a>
 
<b>by </b><i><a class="ref" href="unialg_1.html#D2" title="UNIALG_1:def.2">UNIALG_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E6:36"/>
<font color="Maroon" title="c1">g</font> is  <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> , <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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