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<span class="kw">let </span><font color="Maroon" title="c1">n</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"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</font> being  <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b1">p</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Olive" title="b2">q</font> &amp; <font color="Olive" title="b2">q</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Olive" title="b3">r</font> holds <br/><font color="Olive" title="b1">p</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Olive" title="b3">r</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">r</font> be   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</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">p</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c3">q</font> &amp; <font color="Maroon" title="c3">q</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c4">r</font> implies <font color="Maroon" title="c2">p</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c4">r</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:107"/><span class="lab"><font color="Green" title="E41">A1</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c3">q</font>
 <span class="kw">and </span><br/><a NAME="E2:107"/><span class="lab"><font color="Green" title="E42">A2</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c4">r</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">p</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c4">r</font></span><br/>

<a NAME="E3:107"/><span class="lab"><font color="Green" title="E43">A3</font></span>: 
( <font color="Maroon" title="c3">q</font> <a href="pre_poly.html#R1" title="PRE_POLY:pred.1">&lt;</a> <font color="Maroon" title="c4">r</font> or <font color="Maroon" title="c3">q</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">r</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:107"><span class="lab"><font color="Green" title="E42">A2</font></span></a>, <a class="ref" href="pre_poly.html#D10" target="_self" title="PRE_POLY:def.10">Def12</a></span>;<br/>
<a NAME="E4:107"/>
( <font color="Maroon" title="c2">p</font> <a href="pre_poly.html#R1" title="PRE_POLY:pred.1">&lt;</a> <font color="Maroon" title="c3">q</font> or <font color="Maroon" title="c2">p</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">q</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:107"><span class="lab"><font color="Green" title="E41">A1</font></span></a>, <a class="ref" href="pre_poly.html#D10" target="_self" title="PRE_POLY:def.10">Def12</a></span>;<br/>
<a NAME="E5:107"/><span class="kw">then </span>
( <font color="Maroon" title="c2">p</font> <a href="pre_poly.html#R1" title="PRE_POLY:pred.1">&lt;</a> <font color="Maroon" title="c4">r</font> or <font color="Maroon" title="c2">p</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c4">r</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:107"><span class="lab"><font color="Green" title="E43">A3</font></span></a>, <a class="ref" href="pre_poly.html#T41" target="_self" title="PRE_POLY:th.41">Th45</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:107"/>
<font color="Maroon" title="c2">p</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c4">r</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D10" target="_self" title="PRE_POLY:def.10">Def12</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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