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<span class="kw">set </span><font color="Maroon" title="c2">o</font> =  <a href="hurwitz2.html#K2" title="HURWITZ2:func.2">odd_part</a> <font color="Maroon" title="c1">p</font>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="50_2_1_1"><span class="kw">now </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">  for <font color="Olive" title="b1">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <span class="p1">(<span class="default"><a href="hurwitz2.html#K2" title="HURWITZ2:func.2">odd_part</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b1">i</font> is   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">i</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"> <span class="p1">(<span class="default"><a href="hurwitz2.html#K2" title="HURWITZ2:func.2">odd_part</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">i</font> is   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a></span><br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="50_2_1_1_1"><span class="kw">now </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"> ( ( <font color="Maroon" title="c3">i</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  &amp; <span class="p1">(<span class="default"><a href="hurwitz2.html#K2" title="HURWITZ2:func.2">odd_part</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">i</font> is   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> ) or ( <font color="Maroon" title="c3">i</font> is  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  &amp; <span class="p1">(<span class="default"><a href="hurwitz2.html#K2" title="HURWITZ2:func.2">odd_part</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">i</font> is   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> ) )</span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_2_1_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:50_2_1_1_1_1"/>
( <font color="Maroon" title="c3">i</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  or <font color="Maroon" title="c3">i</font> is  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_2_1_1_1_1_1"><span class="kw">case </span></a><a NAME="E1:50_2_1_1_1_1_1"/>
<font color="Maroon" title="c3">i</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</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"> <span class="p1">(<span class="default"><a href="hurwitz2.html#K2" title="HURWITZ2:func.2">odd_part</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">i</font> is   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a></span><br/><div class="add"><span class="kw">then </span><span class="p1">(<span class="default"><a href="hurwitz2.html#K2" title="HURWITZ2:func.2">odd_part</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">i</font> = 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hurwitz2.html#D2" target="_self" onmouseover="rs('hurwitz2/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
 <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complfld.html#D1" onmouseover="rs('complfld/D1')" onmouseout="rh()">COMPLFLD:def 1</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:50_2_1_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="hurwitz2.html#K2" title="HURWITZ2:func.2">odd_part</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">i</font> is   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_2_1_1_1_1_2"><span class="kw">case </span></a><a NAME="E1:50_2_1_1_1_1_2"/>
<font color="Maroon" title="c3">i</font> is  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</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"> <span class="p1">(<span class="default"><a href="hurwitz2.html#K2" title="HURWITZ2:func.2">odd_part</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">i</font> is   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a></span><br/><div class="add"><a NAME="E2:50_2_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="hurwitz2.html#K2" title="HURWITZ2:func.2">odd_part</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hurwitz2.html#D2" target="_self" onmouseover="rs('hurwitz2/D2')" onmouseout="rh()">Def2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:50_2_1_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="hurwitz2.html#K2" title="HURWITZ2:func.2">odd_part</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">i</font> is   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</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"> 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="E2:50_2_1_1"/>
<span class="p1">(<span class="default"><a href="hurwitz2.html#K2" title="HURWITZ2:func.2">odd_part</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">i</font> is   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</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"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:50_2_1"/>
 <a href="hurwitz2.html#K2" title="HURWITZ2:func.2">odd_part</a> <font color="Maroon" title="c1">p</font> is  <a href="hurwitz2.html#V6" title="HURWITZ2:attr.6">real</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"> verum</span><br/>


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