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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font>, <font color="Maroon" title="c4">D</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c3">C</font></span>)</span> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c4">D</font> &amp; <font color="Maroon" title="c4">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">C</font> implies ( <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> <a href="ordinal3.html#K6" title="ORDINAL3:func.6">div^</a> <font color="Maroon" title="c3">C</font> &amp; <font color="Maroon" title="c4">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> <a href="ordinal3.html#K7" title="ORDINAL3:func.7">mod^</a> <font color="Maroon" title="c3">C</font> ) )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:81"/><span class="lab"><font color="Green" title="E44">A1</font></span>: 
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c3">C</font></span>)</span> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c4">D</font>
 <span class="kw">and </span><br/><a NAME="E2:81"/><span class="lab"><font color="Green" title="E45">A2</font></span>: 
<font color="Maroon" title="c4">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> <a href="ordinal3.html#K6" title="ORDINAL3:func.6">div^</a> <font color="Maroon" title="c3">C</font> &amp; <font color="Maroon" title="c4">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> <a href="ordinal3.html#K7" title="ORDINAL3:func.7">mod^</a> <font color="Maroon" title="c3">C</font> )</span><br/>

<span class="kw">thus </span><a NAME="E3:81"/>
<font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> <a href="ordinal3.html#K6" title="ORDINAL3:func.6">div^</a> <font color="Maroon" title="c3">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:81"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E2:81"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="ordinal3.html#D7" target="_self" title="ORDINAL3:def.7">Def7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> <a href="ordinal3.html#K7" title="ORDINAL3:func.7">mod^</a> <font color="Maroon" title="c3">C</font></span><br/>

<span class="kw">hence </span><a NAME="E4:81"/>
<font color="Maroon" title="c4">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> <a href="ordinal3.html#K7" title="ORDINAL3:func.7">mod^</a> <font color="Maroon" title="c3">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:81"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="ordinal3.html#T65" target="_self" title="ORDINAL3:th.65">Th65</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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