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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">a</font>, <font color="Olive" title="b2">b</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="b2">b</font> <a href="pre_poly.html#R3" title="PRE_POLY:pred.3">divides</a> <font color="Olive" title="b1">a</font> holds <br/> <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="pre_poly.html#K13" title="PRE_POLY:func.13">-'</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b2">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</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="c3">b</font> <a href="pre_poly.html#R3" title="PRE_POLY:pred.3">divides</a> <font color="Maroon" title="c2">a</font> implies  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K13" title="PRE_POLY:func.13">-'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c3">b</font></span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E1:23"/>
<font color="Maroon" title="c3">b</font> <a href="pre_poly.html#R3" title="PRE_POLY:pred.3">divides</a> <font color="Maroon" title="c2">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K13" title="PRE_POLY:func.13">-'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c3">b</font></span>)</span></span><br/>

<a NAME="E2:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K13" title="PRE_POLY:func.13">-'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#T47" title="PRE_POLY:th.47">PRE_POLY:47</a></span>;<br/>
<a NAME="E3:23"/>
 <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K13" title="PRE_POLY:func.13">-'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K13" title="PRE_POLY:func.13">-'</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c3">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bagorder.html#T14" target="_self" title="BAGORDER:th.14">Th14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:23"/>
 <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K13" title="PRE_POLY:func.13">-'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c3">b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E16">A1</font></span></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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