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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">L</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="vectsp_1.html#V3" title="VECTSP_1:attr.3">right_unital</a>  <a href="algstr_0.html#L5" title="ALGSTR_0:struct.5">multLoopStr_0</a>  holds <br/> ( <span class="p1">(<span class="default"><a href="polynom1.html#K25" title="POLYNOM1:func.25">1_</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font></span>)</span> <a href="polynom1.html#K13" title="POLYNOM1:func.13">.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b1">L</font> &amp; ( for <font color="Olive" title="b2">b</font> being  <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">EmptyBag</a> <font color="Maroon" title="c1">n</font> holds <br/><span class="p1">(<span class="default"><a href="polynom1.html#K25" title="POLYNOM1:func.25">1_</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font></span>)</span> <a href="polynom1.html#K13" title="POLYNOM1:func.13">.</a> <font color="Olive" title="b2">b</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="Olive" title="b1">L</font> ) )</span><br/><b>let </b><font color="Maroon" title="c2">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="vectsp_1.html#V3" title="VECTSP_1:attr.3">right_unital</a>  <a href="algstr_0.html#L5" title="ALGSTR_0:struct.5">multLoopStr_0</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="polynom1.html#K25" title="POLYNOM1:func.25">1_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K13" title="POLYNOM1:func.13">.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c2">L</font> &amp; ( for <font color="Olive" title="b1">b</font> being  <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b1">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">EmptyBag</a> <font color="Maroon" title="c1">n</font> holds <br/><span class="p1">(<span class="default"><a href="polynom1.html#K25" title="POLYNOM1:func.25">1_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K13" title="POLYNOM1:func.13">.</a> <font color="Olive" title="b1">b</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/>



<b>set </b><font color="Maroon" title="c3">Z</font> =  <a href="polynom1.html#K24" title="POLYNOM1:func.24">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font>;<br/>
<a NAME="E1:155"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Bags</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<b>hence </b><a NAME="E2:155"/>
<span class="p1">(<span class="default"><a href="polynom1.html#K25" title="POLYNOM1:func.25">1_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K13" title="POLYNOM1:func.13">.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c2">L</font>
 <b>by </b><i><a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">b</font> being  <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b1">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">EmptyBag</a> <font color="Maroon" title="c1">n</font> holds <br/><span class="p1">(<span class="default"><a href="polynom1.html#K25" title="POLYNOM1:func.25">1_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K13" title="POLYNOM1:func.13">.</a> <font color="Olive" title="b1">b</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/>

<b>let </b><font color="Maroon" title="c4">b</font> be   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">EmptyBag</a> <font color="Maroon" title="c1">n</font> implies <span class="p1">(<span class="default"><a href="polynom1.html#K25" title="POLYNOM1:func.25">1_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K13" title="POLYNOM1:func.13">.</a> <font color="Maroon" title="c4">b</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/>

<b>assume </b><a NAME="E3:155"/><i><font color="Green" title="E93">A1</font></i>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">EmptyBag</a> <font color="Maroon" title="c1">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="polynom1.html#K25" title="POLYNOM1:func.25">1_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K13" title="POLYNOM1:func.13">.</a> <font color="Maroon" title="c4">b</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/>

<a NAME="E4:155"/><i><font color="Green" title="E94">A2</font></i>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Bags</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="ref" href="polynom1.html#D14" target="_self" title="POLYNOM1:def.14">Def14</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="polynom1.html#K25" title="POLYNOM1:func.25">1_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K13" title="POLYNOM1:func.13">.</a> <font color="Maroon" title="c4">b</font> = 
<span class="p1">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K13" title="POLYNOM1:func.13">.</a> <font color="Maroon" title="c4">b</font>
<b>by </b><i><a class="txt" href="#E3:155"><i><font color="Green" title="E93">A1</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
<b>by </b><i><a class="txt" href="#E4:155"><i><font color="Green" title="E94">A2</font></i></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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