<?xml version="1.0"?>
<div class="add">

<span class="kw">set </span><font color="Maroon" title="c1">p</font> =  <a href="polynom3.html#K8" title="POLYNOM3:func.8">0_.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="47_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">  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="polynom3.html#K8" title="POLYNOM3:func.8">0_.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a></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="c2">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="polynom3.html#K8" title="POLYNOM3:func.8">0_.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c2">i</font> is   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a></span><br/><span class="p1">(<span class="default"><a href="polynom3.html#K8" title="POLYNOM3:func.8">0_.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c2">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="funcop_1.html#T7" onmouseover="rs('funcop_1/T7')" onmouseout="rh()">FUNCOP_1:7</a>, <a class="ref" href="ordinal1.html#D12" onmouseover="rs('ordinal1/D12')" onmouseout="rh()">ORDINAL1:def 12</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="E2:47_1_1_1"/>
<span class="p1">(<span class="default"><a href="polynom3.html#K8" title="POLYNOM3:func.8">0_.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c2">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="E2:47_1_1"/>
 <a href="polynom3.html#K8" title="POLYNOM3:func.8">0_.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 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">  not  <a href="polynom3.html#K8" title="POLYNOM3:func.8">0_.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> is  <a href="hurwitz2.html#V7" title="HURWITZ2:attr.7">positive</a> </span><br/>

<a NAME="E3:47_1_1"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T6" onmouseover="rs('complex1/T6')" onmouseout="rh()">COMPLEX1:6</a>, <a class="ref" href="complfld.html#D1" onmouseover="rs('complfld/D1')" onmouseout="rh()">COMPLFLD:def 1</a></span>;<br/>
 <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<span class="p1">(<span class="default"><a href="polynom3.html#K8" title="POLYNOM3:func.8">0_.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a></span>)</span>,<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a></span>)</span>) = 
 <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="polynom4.html#T17" onmouseover="rs('polynom4/T17')" onmouseout="rh()">POLYNOM4:17</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="E5:47_1_1"/>
 not  <a href="polynom3.html#K8" title="POLYNOM3:func.8">0_.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> is  <a href="hurwitz2.html#V7" title="HURWITZ2:attr.7">positive</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47_1_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="complex1.html#T4" onmouseover="rs('complex1/T4')" onmouseout="rh()">COMPLEX1:4</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/>


</div>
