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<span class="kw">let </span><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font>, <font color="Maroon" title="c3">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">n</font> &amp; <font color="Maroon" title="c2">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">n</font> &amp; <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c3">n</font> implies <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">j</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:25"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
( <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">n</font> &amp; <font color="Maroon" title="c2">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">n</font> &amp; <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c3">n</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">j</font></span><br/>

<a NAME="E2:25"/>
( <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</font> or <font color="Maroon" title="c2">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">i</font> )
 
;<br/>
<span class="kw">hence </span><a NAME="E3:25"/>
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="ref" href="int_1.html#T14" onmouseover="rs('int_1/T14')" onmouseout="rh()">INT_1:14</a>, <a class="txt" href="hilb10_6.html#E24"><span class="lab"><font color="Green" title="E23">Lm6</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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