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<b>let </b><font color="Maroon" title="c1">u</font>, <font color="Maroon" title="c2">v</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">m</font> being  <a href="int_6.html#NM1" title="INT_6:NM.1">CR_Sequence</a><br/> for <font color="Olive" title="b2">i</font> being <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b2">i</font> <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="Olive" title="b1">m</font> holds <br/> <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Olive" title="b1">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">m</font></span>)</span></span>)</span>,<font color="Olive" title="b1">m</font>,<font color="Maroon" title="c1">u</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">v</font> <a href="int_1.html#R1" title="INT_1:pred.1">are_congruent_mod</a> <font color="Olive" title="b1">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">i</font></span><br/><b>let </b><font color="Maroon" title="c3">m</font> be   <a href="int_6.html#NM1" title="INT_6:NM.1">CR_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">i</font> being <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b1">i</font> <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">m</font> holds <br/> <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c1">u</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">v</font> <a href="int_1.html#R1" title="INT_1:pred.1">are_congruent_mod</a> <font color="Maroon" title="c3">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font></span><br/><b>let </b><font color="Maroon" title="c4">i</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">i</font> <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">m</font> implies  <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c1">u</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">v</font> <a href="int_1.html#R1" title="INT_1:pred.1">are_congruent_mod</a> <font color="Maroon" title="c3">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> )</span><br/>





<b>assume </b><a NAME="E1:66"/><i><font color="Green" title="E48">AS</font></i>: 
<font color="Maroon" title="c4">i</font> <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">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c1">u</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">v</font> <a href="int_1.html#R1" title="INT_1:pred.1">are_congruent_mod</a> <font color="Maroon" title="c3">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span><br/>

<b>set </b><font color="Maroon" title="c5">z</font> =  <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">m</font>;<br/>
<b>consider </b><font color="Maroon" title="c6">c</font> being    <a href="int_6.html#M1" title="INT_6:mode.1">CR_coefficients</a> of <font color="Maroon" title="c3">m</font>;<br/>
<a NAME="E3:66"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span> <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="c3">m</font>
 
<b>by </b><i><a class="ref" href="int_6.html#D3" target="_self" title="INT_6:def.3">Df1</a></i>;<br/>
<a NAME="E4:66"/><b>then </b>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <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="c3">m</font> )
 
<b>by </b><i><a class="ref" href="int_6.html#D3" target="_self" title="INT_6:def.3">Df1</a></i>;<br/>
<a NAME="E5:66"/><b>then </b><i><font color="Green" title="E49">E</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <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="c3">m</font>
 
<b>by </b><i><a class="txt" href="int_6.html#E7"><i><font color="Green" title="E7">length3</font></i></a></i>;<br/>
<a NAME="E6:66"/><b>then </b>
 <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K16" title="RVSUM_1:func.16">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p4">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c6">c</font></span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Maroon" title="c3">m</font></span>)</span>
 
<b>by </b><i><a class="ref" href="int_6.html#D5" target="_self" title="INT_6:def.5">Df5</a></i>;<br/>
<a NAME="E7:66"/><b>then </b>
<span class="p1">(<span class="default"><a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p3">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K16" title="RVSUM_1:func.16">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p4">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c6">c</font></span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Maroon" title="c3">m</font></span>)</span>
 
<b>by </b><i><a class="ref" href="int_3.html#T13" title="INT_3:th.13">INT_3:13</a></i>;<br/>
<a NAME="E8:66"/><b>then </b><i><font color="Green" title="E50">G</font></i>: 
 <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">m</font>, <a href="rvsum_1.html#K16" title="RVSUM_1:func.16">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p3">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="int_1.html#R1" title="INT_1:pred.1">are_congruent_mod</a>  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Maroon" title="c3">m</font>
 
<b>by </b><i><a class="ref" href="int_3.html#T12" title="INT_3:th.12">INT_3:12</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">y</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E10:66"/><i><font color="Green" title="E51">H</font></i>: 
<font color="Maroon" title="c7">y</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Maroon" title="c3">m</font>
 <b>by </b><i><a class="txt" href="int_6.html#E1:66"><i><font color="Green" title="E48">AS</font></i></a>, <a class="ref" href="int_6.html#T10" target="_self" title="INT_6:th.10">x000</a></i>;<br/>
<a NAME="E11:66"/><i><font color="Green" title="E52">F</font></i>: 
 <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">m</font>, <a href="rvsum_1.html#K16" title="RVSUM_1:func.16">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p3">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="int_1.html#R1" title="INT_1:pred.1">are_congruent_mod</a> <font color="Maroon" title="c3">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
 
<b>by </b><i><a class="txt" href="int_6.html#E8:66"><i><font color="Green" title="E50">G</font></i></a>, <a class="txt" href="int_6.html#E10:66"><i><font color="Green" title="E51">H</font></i></a>, <a class="ref" href="int_1.html#T41" title="INT_1:th.41">INT_1:41</a></i>;<br/>
<a NAME="E12:66"/>
 <a href="rvsum_1.html#K16" title="RVSUM_1:func.16">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p3">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c6">c</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="int_1.html#R1" title="INT_1:pred.1">are_congruent_mod</a> <font color="Maroon" title="c3">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
 
<b>by </b><i><a class="txt" href="int_6.html#E1:66"><i><font color="Green" title="E48">AS</font></i></a>, <a class="txt" href="int_6.html#E5:66"><i><font color="Green" title="E49">E</font></i></a>, <a class="ref" href="int_6.html#T29" target="_self" title="INT_6:th.29">congsum</a></i>;<br/>
<a NAME="E13:66"/><b>then </b><i><font color="Green" title="E53">D</font></i>: 
 <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">m</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="int_1.html#R1" title="INT_1:pred.1">are_congruent_mod</a> <font color="Maroon" title="c3">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
 
<b>by </b><i><a class="txt" href="int_6.html#E11:66"><i><font color="Green" title="E52">F</font></i></a>, <a class="ref" href="int_1.html#T36" title="INT_1:th.36">INT_1:36</a></i>;<br/>
<a NAME="E14:66"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">u</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">v</font> <a href="int_1.html#R1" title="INT_1:pred.1">are_congruent_mod</a> <font color="Maroon" title="c3">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
 
<b>by </b><i><a class="ref" href="int_6.html#T34" target="_self" title="INT_6:th.34">lemat3a</a>, <a class="txt" href="int_6.html#E1:66"><i><font color="Green" title="E48">AS</font></i></a></i>;<br/>
<b>hence </b><a NAME="E15:66"/>
 <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c3">m</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><a href="int_6.html#K1" title="INT_6:func.1">mod</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">m</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c1">u</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">v</font> <a href="int_1.html#R1" title="INT_1:pred.1">are_congruent_mod</a> <font color="Maroon" title="c3">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="int_6.html#E13:66"><i><font color="Green" title="E53">D</font></i></a>, <a class="ref" href="int_1.html#T36" title="INT_1:th.36">INT_1:36</a></i>; <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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