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<b>let </b><font color="Maroon" title="c1">u</font> be  <a href="real_3.html#NV1" title="REAL_3:NV.1">integer-yielding</a> <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</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>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">m</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="c1">u</font> holds <br/>(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <font color="Maroon" title="c1">u</font>,<font color="Olive" title="b1">m</font> &amp;  <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <font color="Maroon" title="c1">u</font>,<font color="Olive" title="b1">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Olive" title="b1">m</font> )</span><br/><b>let </b><font color="Maroon" title="c2">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"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">m</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="c1">u</font> implies (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c2">m</font> &amp;  <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Maroon" title="c2">m</font> ) )</span><br/>



<b>assume </b><a NAME="E1:58"/><i><font color="Green" title="E41">AS</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">u</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="c2">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c2">m</font> &amp;  <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Maroon" title="c2">m</font> )</span><br/>

<b>set </b><font color="Maroon" title="c3">z</font> =  <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c2">m</font>;<br/>
<b>consider </b><font color="Maroon" title="c4">c</font> being    <a href="int_6.html#M1" title="INT_6:mode.1">CR_coefficients</a> of <font color="Maroon" title="c2">m</font>;<br/>
<a NAME="E3:58"/>
 <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c2">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"><font color="Maroon" title="c1">u</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c4">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="c2">m</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:58"><i><font color="Green" title="E41">AS</font></i></a>, <a class="ref" href="int_6.html#D5" target="_self" title="INT_6:def.5">Df5</a></i>;<br/>
<b>hence </b><a NAME="E4:58"/>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c2">m</font> &amp;  <a href="int_6.html#K2" title="INT_6:func.2">to_int</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Maroon" title="c2">m</font> )
 <b>by </b><i><a class="ref" href="int_3.html#T9" title="INT_3:th.9">INT_3:9</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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