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<b>let </b><font color="Maroon" title="c1">a</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c2">s</font> be   <a href="prepower.html#NM1" title="PREPOWER:NM.1">Rational_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:90"/><i><font color="Green" title="E72">A1</font></i>: 
( <font color="Maroon" title="c2">s</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp; <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:90_1"/>
( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 or <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_1_1"><b>suppose </b></a><a NAME="E1:90_1_1"/>
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:90_1_1"/>
<font color="Maroon" title="c1">a</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c2">s</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 <b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="prepower.html#E93"><i><font color="Green" title="E70">Lm6</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_1_2"><b>suppose </b></a><a NAME="E1:90_1_2"/><i><font color="Green" title="E73">A2</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1
 ;<br/><div class="add"><a NAME="E2:90_1_2"/><b>then </b>
<font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font>
 <b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="real_1.html#T73" title="REAL_1:th.73">REAL_1:73</a></i>;<br/><a NAME="E3:90_1_2"/><b>then </b>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font>
 <b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a></i>;<br/><a NAME="E4:90_1_2"/><b>then </b><i><font color="Green" title="E74">A3</font></i>: 
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c2">s</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 <b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="prepower.html#E93"><i><font color="Green" title="E70">Lm6</font></i></a></i>;<br/><a NAME="E5:90_1_2"/>
<font color="Maroon" title="c2">s</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 <b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="seq_2.html#T27" title="SEQ_2:th.27">SEQ_2:27</a></i>;<br/><b>then consider </b><font color="Maroon" title="c3">d</font> being  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><br/><a NAME="E7:90_1_2"/><i><font color="Green" title="E75">A4</font></i>: 
( 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c3">d</font> &amp; ( for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   holds  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c3">d</font> ) )
 <b>by </b><i><a class="ref" href="seq_2.html#T15" title="SEQ_2:th.15">SEQ_2:15</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c4">d</font> = <font color="Maroon" title="c3">d</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/><b>consider </b><font color="Maroon" title="c5">m1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E10:90_1_2"/><i><font color="Green" title="E76">A5</font></i>: 
2 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c4">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">m1</font>
 <b>by </b><i><a class="ref" href="seq_4.html#T10" title="SEQ_4:th.10">SEQ_4:10</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c6">m1</font> = <font color="Maroon" title="c5">m1</font> as   <a href="rat_1.html#NM1" title="RAT_1:NM.1">Rational</a> ;<br/><a NAME="E12:90_1_2"/><i><font color="Green" title="E77">A6</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <font color="Maroon" title="c6">m1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="prepower.html#T63" target="_self" title="PREPOWER:th.63">Th63</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">c</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>assume </b><a NAME="E1:90_1_2_1"/><i><font color="Green" title="E78">A7</font></i>: 
<font color="Maroon" title="c7">c</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/><a NAME="E2:90_1_2_1"/><b>then </b>
<font color="Maroon" title="c7">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <font color="Maroon" title="c6">m1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="prepower.html#E12:90_1_2"><i><font color="Green" title="E77">A6</font></i></a>, <a class="ref" href="xreal_1.html#T131" title="XREAL_1:th.131">XREAL_1:131</a></i>;<br/><b>then consider </b><font color="Maroon" title="c8">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E4:90_1_2_1"/><i><font color="Green" title="E79">A8</font></i>: 
for <font color="Olive" title="b1">m</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon" title="c8">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">m</font> holds <br/> <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">m</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c7">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <font color="Maroon" title="c6">m1</font></span>)</span>
 <b>by </b><i><a class="txt" href="prepower.html#E4:90_1_2"><i><font color="Green" title="E74">A3</font></i></a>, <a class="ref" href="seq_4.html#T58" title="SEQ_4:th.58">SEQ_4:58</a></i>;<br/><b>take </b><font color="Maroon" title="c9">n</font> = <font color="Maroon" title="c8">n</font>;<br/><b>let </b><font color="Maroon" title="c10">m</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E5:90_1_2_1"/>
<font color="Maroon" title="c10">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c9">n</font>
 ;<br/><a NAME="E6:90_1_2_1"/><b>then </b><i><font color="Green" title="E80">A9</font></i>: 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c7">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <font color="Maroon" title="c6">m1</font></span>)</span>
 <b>by </b><i><a class="txt" href="prepower.html#E4:90_1_2_1"><i><font color="Green" title="E79">A8</font></i></a></i>;<br/><a NAME="E7:90_1_2_1"/><i><font color="Green" title="E81">A10</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="prepower.html#T63" target="_self" title="PREPOWER:th.63">Th63</a></i>;<br/><a NAME="E8:90_1_2_1"/><i><font color="Green" title="E82">A11</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="prepower.html#T63" target="_self" title="PREPOWER:th.63">Th63</a></i>;<br/><a NAME="E9:90_1_2_1"/><i><font color="Green" title="E83">A12</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="prepower.html#T63" target="_self" title="PREPOWER:th.63">Th63</a></i>;<br/><a NAME="E10:90_1_2_1"/><i><font color="Green" title="E84">A13</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="prepower.html#T63" target="_self" title="PREPOWER:th.63">Th63</a></i>;<br/> <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> = 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#D7" target="_self" title="PREPOWER:def.7">Def7</a></i>
<br/>.= 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#D7" target="_self" title="PREPOWER:def.7">Def7</a></i>
<br/>.= 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="prepower.html#T68" target="_self" title="PREPOWER:th.68">Th68</a></i>
<br/>.= 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="prepower.html#T68" target="_self" title="PREPOWER:th.68">Th68</a></i>
<br/>.= 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K5" title="XCMPLX_0:func.5">"</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T217" title="XCMPLX_1:th.217">XCMPLX_1:217</a></i>
<br/>.= 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K5" title="XCMPLX_0:func.5">"</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K5" title="XCMPLX_0:func.5">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T217" title="XCMPLX_1:th.217">XCMPLX_1:217</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E7:90_1_2_1"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="prepower.html#E8:90_1_2_1"><i><font color="Green" title="E82">A11</font></i></a>, <a class="ref" href="seq_2.html#T11" title="SEQ_2:th.11">SEQ_2:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T151" title="COMPLEX1:th.151">COMPLEX1:151</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="prepower.html#T64" target="_self" title="PREPOWER:th.64">Th64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E9:90_1_2_1"><i><font color="Green" title="E83">A12</font></i></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></i>
;<br/><a NAME="E12:90_1_2_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <font color="Maroon" title="c6">m1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="prepower.html#E6:90_1_2_1"><i><font color="Green" title="E80">A9</font></i></a>, <a class="txt" href="prepower.html#E9:90_1_2_1"><i><font color="Green" title="E83">A12</font></i></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/><a NAME="E13:90_1_2_1"/><b>then </b><i><font color="Green" title="E85">A14</font></i>: 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <font color="Maroon" title="c6">m1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="prepower.html#E10:90_1_2_1"><i><font color="Green" title="E84">A13</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/><a NAME="E14:90_1_2_1"/><i><font color="Green" title="E86">A15</font></i>: 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c4">d</font>
 <b>by </b><i><a class="txt" href="prepower.html#E7:90_1_2"><i><font color="Green" title="E75">A4</font></i></a></i>;<br/><a NAME="E15:90_1_2_1"/>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c4">d</font>
 <b>by </b><i><a class="txt" href="prepower.html#E7:90_1_2"><i><font color="Green" title="E75">A4</font></i></a></i>;<br/><a NAME="E16:90_1_2_1"/><b>then </b><i><font color="Green" title="E87">A16</font></i>: 
<span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c4">d</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c4">d</font>
 <b>by </b><i><a class="txt" href="prepower.html#E14:90_1_2_1"><i><font color="Green" title="E86">A15</font></i></a>, <a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/><a NAME="E17:90_1_2_1"/>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="complex1.html#T142" title="COMPLEX1:th.142">COMPLEX1:142</a></i>;<br/><a NAME="E18:90_1_2_1"/><b>then </b>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c4">d</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c4">d</font>
 <b>by </b><i><a class="txt" href="prepower.html#E16:90_1_2_1"><i><font color="Green" title="E87">A16</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E19:90_1_2_1"/><b>then </b>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c6">m1</font>
 <b>by </b><i><a class="txt" href="prepower.html#E10:90_1_2"><i><font color="Green" title="E76">A5</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E20:90_1_2_1"/><b>then </b><i><font color="Green" title="E88">A17</font></i>: 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c6">m1</font>
 <b>by </b><i><a class="ref" href="complex1.html#T138" title="COMPLEX1:th.138">COMPLEX1:138</a></i>;<br/><a NAME="E21:90_1_2_1"/>
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="absvalue.html#T11" title="ABSVALUE:th.11">ABSVALUE:11</a></i>;<br/><a NAME="E22:90_1_2_1"/><b>then </b>
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c6">m1</font>
 <b>by </b><i><a class="txt" href="prepower.html#E20:90_1_2_1"><i><font color="Green" title="E88">A17</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E23:90_1_2_1"/><b>then </b><i><font color="Green" title="E89">A18</font></i>: 
<font color="Maroon" title="c6">m1</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T52" title="XREAL_1:th.52">XREAL_1:52</a></i>;<br/><a NAME="E24:90_1_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <font color="Maroon" title="c6">m1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="prepower.html#T64" target="_self" title="PREPOWER:th.64">Th64</a></i>;<br/><a NAME="E25:90_1_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <font color="Maroon" title="c6">m1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1
 <b>by </b><i><a class="txt" href="prepower.html#E1:90"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="prepower.html#E1:90_1_2"><i><font color="Green" title="E73">A2</font></i></a>, <a class="txt" href="prepower.html#E23:90_1_2_1"><i><font color="Green" title="E89">A18</font></i></a>, <a class="ref" href="prepower.html#T76" target="_self" title="PREPOWER:th.76">Th76</a></i>;<br/><a NAME="E26:90_1_2_1"/><b>then </b>
<font color="Maroon" title="c7">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <font color="Maroon" title="c6">m1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c7">c</font>
 <b>by </b><i><a class="txt" href="prepower.html#E1:90_1_2_1"><i><font color="Green" title="E78">A7</font></i></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/><a NAME="E27:90_1_2_1"/><b>then </b>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c7">c</font>
 <b>by </b><i><a class="txt" href="prepower.html#E13:90_1_2_1"><i><font color="Green" title="E85">A14</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E28:90_1_2_1"/><b>then </b>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K8" title="PREPOWER:func.8">#Q</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c7">c</font>
 <b>by </b><i><a class="ref" href="prepower.html#D7" target="_self" title="PREPOWER:def.7">Def7</a></i>;<br/><b>hence </b><a NAME="E29:90_1_2_1"/>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c7">c</font>
 <b>by </b><i><a class="ref" href="prepower.html#D7" target="_self" title="PREPOWER:def.7">Def7</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E14:90_1_2"/>
<font color="Maroon" title="c1">a</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c2">s</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 <b>by </b><i><a class="ref" href="seq_4.html#T58" title="SEQ_4:th.58">SEQ_4:58</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
