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<span class="kw">let </span><font color="Maroon" title="c4">b1</font>, <font color="Maroon" title="c5">b2</font> be   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">X</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">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c4">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font> or (  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">EmptyBag</a> <font color="Maroon" title="c1">X</font> ) ) &amp; ( <font color="Maroon" title="c3">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c5">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font> or (  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c5">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">EmptyBag</a> <font color="Maroon" title="c1">X</font> ) ) implies <font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:20_1_2"/><span class="lab"><font color="Green" title="E7">A3</font></span>: 
( <font color="Maroon" title="c3">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c4">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font> or (  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">EmptyBag</a> <font color="Maroon" title="c1">X</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( not <font color="Maroon" title="c3">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c5">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font> &amp; not <!--HUMANRECFAILED-->(  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c5">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">EmptyBag</a> <font color="Maroon" title="c1">X</font> ) ) or <font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c6">b</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E3:20_1_2"/><span class="lab"><font color="Green" title="E8">A4</font></span>: 
for <font color="Olive" title="b1">b9</font> being  <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">b9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b</font> holds <br/><font color="Maroon" title="c3">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Olive" title="b1">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D4" target="_self" title="POLYNOM7:def.4">Def4</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:20_1_2"/><span class="lab"><font color="Green" title="E9">A5</font></span>: 
( <font color="Maroon" title="c3">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c5">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font> or (  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c5">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">EmptyBag</a> <font color="Maroon" title="c1">X</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="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:20_1_2_1_1"/>
( <font color="Maroon" title="c3">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c4">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font> or <font color="Maroon" title="c3">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_1_1_1"><span class="kw">case </span></a><a NAME="E1:20_1_2_1_1_1"/><span class="lab"><font color="Green" title="E10">A6</font></span>: 
<font color="Maroon" title="c3">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c4">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</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="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font></span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c7">b19</font> = <font color="Maroon" title="c4">b1</font> as    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D12" title="PRE_POLY:def.12">PRE_POLY:def 12</a></span>;<br/><a NAME="E3:20_1_2_1_1_1"/><span class="lab"><font color="Green" title="E11">A7</font></span>: 
<font color="Maroon" title="c7">b19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c3">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1_2_1_1_1"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c4">b1</font> = 
<font color="Maroon" title="c6">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:20_1_2"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E1:20_1_2_1_1_1"><span class="lab"><font color="Green" title="E10">A6</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c5">b2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:20_1_2"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="txt" href="#E3:20_1_2"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E3:20_1_2_1_1_1"><span class="lab"><font color="Green" title="E11">A7</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_1_1_2"><span class="kw">case </span></a><a NAME="E1:20_1_2_1_1_2"/><span class="lab"><font color="Green" title="E10">A8</font></span>: 
<font color="Maroon" title="c3">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</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="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font></span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_2_1_1_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_1_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:20_1_2_1_1_2_1_1"/>
( <font color="Maroon" title="c3">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c5">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font> or (  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c5">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">EmptyBag</a> <font color="Maroon" title="c1">X</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:20_1_2"><span class="lab"><font color="Green" title="E9">A5</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_1_1_2_1_1_1"><span class="kw">case </span></a><a NAME="E1:20_1_2_1_1_2_1_1_1"/><span class="lab"><font color="Green" title="E11">A9</font></span>: 
<font color="Maroon" title="c3">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c5">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</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="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font></span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c7">b29</font> = <font color="Maroon" title="c5">b2</font> as    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D12" title="PRE_POLY:def.12">PRE_POLY:def 12</a></span>;<br/><a NAME="E3:20_1_2_1_1_2_1_1_1"/>
<font color="Maroon" title="c7">b29</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c3">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1_2_1_1_2_1_1_1"><span class="lab"><font color="Green" title="E11">A9</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E4:20_1_2_1_1_2_1_1_1"/>
<font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1_2"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E1:20_1_2_1_1_2"><span class="lab"><font color="Green" title="E10">A8</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_1_1_2_1_1_2"><span class="kw">case </span></a><a NAME="E1:20_1_2_1_1_2_1_1_2"/>
(  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c5">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">EmptyBag</a> <font color="Maroon" title="c1">X</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="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:20_1_2_1_1_2_1_1_2"/>
<font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1_2"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E1:20_1_2_1_1_2"><span class="lab"><font color="Green" title="E10">A8</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:20_1_2_1_1_2"/>
<font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:20_1_2"/>
<font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
