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<span class="kw">let </span><font color="Maroon" title="c1">U1</font>, <font color="Maroon" title="c2">U2</font>, <font color="Maroon" title="c3">U3</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</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">U1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">U2</font> &amp; <font color="Maroon" title="c2">U2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">U3</font> implies <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">U3</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:56"/><span class="lab"><font color="Green" title="E40">A1</font></span>: 
<font color="Maroon" title="c1">U1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">U2</font>
 <span class="kw">and </span><br/><a NAME="E2:56"/><span class="lab"><font color="Green" title="E41">A2</font></span>: 
<font color="Maroon" title="c2">U2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">U3</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="c1">U1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">U3</font></span><br/>

<a NAME="E3:56"/><span class="lab"><font color="Green" title="E42">A3</font></span>: 
<font color="Maroon" title="c3">U3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c3">U3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes2.html#T54" target="_self" title="CLASSES2:th.54">Th54</a></span>;<br/>
<a NAME="E4:56"/><span class="lab"><font color="Green" title="E43">A4</font></span>: 
<font color="Maroon" title="c2">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c2">U2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes2.html#T54" target="_self" title="CLASSES2:th.54">Th54</a></span>;<br/>
<a NAME="E5:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A5</font></span>: 
 <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c2">U2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c3">U3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56"><span class="lab"><font color="Green" title="E41">A2</font></span></a>, <a class="txt" href="#E3:56"><span class="lab"><font color="Green" title="E42">A3</font></span></a>, <a class="ref" href="classes1.html#T42" title="CLASSES1:th.42">CLASSES1:42</a></span>;<br/>
<a NAME="E6:56"/><span class="lab"><font color="Green" title="E45">A6</font></span>: 
<font color="Maroon" title="c1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c1">U1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes2.html#T54" target="_self" title="CLASSES2:th.54">Th54</a></span>;<br/>
<a NAME="E7:56"/><span class="kw">then </span>
 <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c2">U2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E40">A1</font></span></a>, <a class="txt" href="#E4:56"><span class="lab"><font color="Green" title="E43">A4</font></span></a>, <a class="ref" href="classes1.html#T42" title="CLASSES1:th.42">CLASSES1:42</a></span>;<br/>
<a NAME="E8:56"/><span class="kw">then </span>
 <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c3">U3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:56"><span class="lab"><font color="Green" title="E44">A5</font></span></a>, <a class="ref" href="ordinal1.html#T19" title="ORDINAL1:th.19">ORDINAL1:19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:56"/>
<font color="Maroon" title="c1">U1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">U3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:56"><span class="lab"><font color="Green" title="E45">A6</font></span></a>, <a class="txt" href="#E3:56"><span class="lab"><font color="Green" title="E42">A3</font></span></a>, <a class="ref" href="classes1.html#T42" title="CLASSES1:th.42">CLASSES1:42</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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