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<b>let </b><font color="Maroon" title="c1">f1</font>, <font color="Maroon" title="c2">f2</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <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="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:146"/><i><font color="Green" title="E96">A1</font></i>: 
<font color="Maroon" title="c1">f1</font> is <a href="comput_1.html#V3" title="COMPUT_1:attr.3">len-total</a>
 <b>and </b><br/><a NAME="E2:146"/><i><font color="Green" title="E97">A2</font></i>: 
 <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c3">p</font> = <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="comput_1.html#E2:146"><i><font color="Green" title="E97">A2</font></i></a></i>;<br/>
<a NAME="E4:146"/><i><font color="Green" title="E98">A3</font></i>: 
<font color="Maroon" title="c3">p</font> <a href="comput_1.html#K1" title="COMPUT_1:func.1">+*</a> 1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font>
 
<b>by </b><i><a class="ref" href="funct_7.html#T97" title="FUNCT_7:th.97">FUNCT_7:97</a></i>;<br/>
<a NAME="E5:146"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E6:146"/><b>then </b>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">p</font>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="comput_1.html#K8" title="COMPUT_1:func.8">primrec</a> <font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font>,1</span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span> = 
<font color="Maroon" title="c1">f1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c3">p</font>,1</span>)</span>
<b>by </b><i><a class="txt" href="comput_1.html#E1:146"><i><font color="Green" title="E96">A1</font></i></a>, <a class="txt" href="comput_1.html#E4:146"><i><font color="Green" title="E98">A3</font></i></a>, <a class="ref" href="comput_1.html#T64" target="_self" title="COMPUT_1:th.64">Th64</a></i>
<br/>.= 
<font color="Maroon" title="c1">f1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="ref" href="wsierp_1.html#T26" title="WSIERP_1:th.26">WSIERP_1:26</a></i>
;<br/><br/>


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