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<b>let </b><font color="Maroon" title="c1">i1</font>, <font color="Maroon" title="c2">i2</font>, <font color="Maroon" title="c3">i3</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/>





<b>assume </b><a NAME="E1:38"/>
<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">i2</font> <a href="int_1.html#R1" title="INT_1:pred.1">are_congruent_mod</a> <font color="Maroon" title="c3">i3</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">i0</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:38"/><i><font color="Green" title="E20">A1</font></i>: 
<font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i3</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">i0</font>
 <b>by </b><i><a class="ref" href="int_1.html#D3" target="_self" title="INT_1:def.3">Def3</a></i>;<br/>
<a NAME="E4:38"/>
<font color="Maroon" title="c2">i2</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i3</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c4">i0</font></span>)</span>
 
<b>by </b><i><a class="txt" href="int_1.html#E3:38"><i><font color="Green" title="E20">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:38"/>
<font color="Maroon" title="c2">i2</font>,<font color="Maroon" title="c1">i1</font> <a href="int_1.html#R1" title="INT_1:pred.1">are_congruent_mod</a> <font color="Maroon" title="c3">i3</font>
 <b>by </b><i><a class="ref" href="int_1.html#D3" target="_self" title="INT_1:def.3">Def3</a></i>;<br/>


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