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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">R</font> being   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a>  holds   <a href="ratfunc1.html#NK3" title="RATFUNC1:NK.3">LC</a> <span class="p1">(<span class="default"><a href="ring_5.html#K3" title="RING_5:func.3">npoly</a> (<font color="Olive" title="b1">R</font>,<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">R</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">R</font> be   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="ratfunc1.html#NK3" title="RATFUNC1:NK.3">LC</a> <span class="p1">(<span class="default"><a href="ring_5.html#K3" title="RING_5:func.3">npoly</a> (<font color="Maroon" title="c2">R</font>,<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">R</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">q</font> =  <a href="ring_5.html#K3" title="RING_5:func.3">npoly</a> (<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c1">n</font>);<br/>
<span class="lab"><font color="Green" title="E45">A</font></span>: <font color="Maroon" title="c1">n</font> = 
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <span class="p1">(<span class="default"><a href="ring_5.html#K3" title="RING_5:func.3">npoly</a> (<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="ring_5.html#E57"><span class="lab"><font color="Green" title="E44">lem6</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="ring_5.html#K3" title="RING_5:func.3">npoly</a> (<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="hurwitz.html#D2" onmouseover="rs('hurwitz/D2')" onmouseout="rh()">HURWITZ:def 2</a></span>
;<br/>
<a NAME="E2:95"/><span class="kw">then </span>
<font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="ring_5.html#K3" title="RING_5:func.3">npoly</a> (<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>
 
;<br/>
<a NAME="E3:95"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="ring_5.html#K3" title="RING_5:func.3">npoly</a> (<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95"><span class="lab"><font color="Green" title="E45">A</font></span></a>, <a class="ref" href="xreal_1.html#T233" onmouseover="rs('xreal_1/T233')" onmouseout="rh()">XREAL_1:233</a>, <a class="ref" href="nat_1.html#T11" onmouseover="rs('nat_1/T11')" onmouseout="rh()">NAT_1:11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:95"/>
 <a href="ratfunc1.html#NK3" title="RATFUNC1:NK.3">LC</a> <span class="p1">(<span class="default"><a href="ring_5.html#K3" title="RING_5:func.3">npoly</a> (<font color="Maroon" title="c2">R</font>,<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">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="ring_5.html#E54"><span class="lab"><font color="Green" title="E42">Lm10</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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