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<b>let </b><font color="Maroon">i1</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">i2</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">i3</font> be   <a href="int_1.html#NM1">Integer</a>;<br/>





<b>assume </b><a NAME="E1:38"/>
<font color="Maroon">i1</font>,<font color="Maroon">i2</font> <a href="int_1.html#R1" target="_self">are_congruent_mod</a> <font color="Maroon">i3</font>
 ;<br/>

<b>then consider </b><font color="Maroon">i0</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:38"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">i1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i3</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">i0</font>
 <b>by </b><i/>;<br/>
<a NAME="E4:38"/>
<font color="Maroon">i2</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i3</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">i0</font></span>)</span>
 
<b>by </b><i><a class="txt" href="int_1.html#E1"><i><font color="Green">Lemma20</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:38"/>
<font color="Maroon">i2</font>,<font color="Maroon">i1</font> <a href="int_1.html#R1" target="_self">are_congruent_mod</a> <font color="Maroon">i3</font>
 <b>by </b><i/>;<br/>


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