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<span class="kw">let </span><font color="Maroon" title="c1">i1</font>, <font color="Maroon" title="c2">i2</font>, <font color="Maroon" title="c3">i</font>, <font color="Maroon" title="c4">i3</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">i2</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c3">i</font> implies <font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">i3</font>,<font color="Maroon" title="c2">i2</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">i3</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c3">i</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:19"/>
<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">i2</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c3">i</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">i3</font>,<font color="Maroon" title="c2">i2</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">i3</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c3">i</font></span><br/>

<a NAME="E2:19"/><span class="kw">then </span>
<font color="Maroon" title="c3">i</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_2.html#T15" title="INT_2:th.15">INT_2:15</a></span>;<br/>
<a NAME="E3:19"/><span class="kw">then </span>
<font color="Maroon" title="c3">i</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <span class="p1">(<span class="default"><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></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">i3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_2.html#T2" title="INT_2:th.2">INT_2:2</a></span>;<br/>
<a NAME="E4:19"/><span class="kw">then </span>
<font color="Maroon" title="c3">i</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">i3</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">i2</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">i3</font></span>)</span>
 
;<br/>
<span class="kw">hence </span><a NAME="E5:19"/>
<font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">i3</font>,<font color="Maroon" title="c2">i2</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">i3</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c3">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_2.html#T15" title="INT_2:th.15">INT_2:15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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