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<b>let </b><font color="Maroon">m</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">z</font> be   <a href="binarith.html#NM1">Tuple</a> of <font color="Maroon">m</font>,<a href="margrel1.html#K6">BOOLEAN</a> ;<br/><b>let </b><font color="Maroon">d</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="margrel1.html#K6">BOOLEAN</a> ;<br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:17_1"/>
( <font color="Maroon">d</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  or <font color="Maroon">d</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 </span><b>by </b><i><a class="ref" href="margrel1.html#T39">MARGREL1:39</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1"><b>suppose </b></a><a NAME="E1:17_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 ;<br/><div class="add"><a NAME="E2:17_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="binarith.html#K10">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">d</font></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i><a class="ref" href="binarith.html#T3">BINARITH:3</a></i>;<br/><b>then </b><i><font color="Green">E43</font></i>:  <a href="binari_2.html#K4" target="_self">Intval</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="binarith.html#K10">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">d</font></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> = 
 <a href="binarith.html#K7">Absval</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="binarith.html#K10">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">d</font></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K7">Absval</a> <font color="Maroon">z</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K2">IFEQ</a> <font color="Maroon">d</font>,<a href="margrel1.html#K7">FALSE</a> ,0,<span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T46">BINARITH:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K7">Absval</a> <font color="Maroon">z</font></span>)</span> <a href="binop_2.html#K23">+</a> 0
<b>by </b><i>, <a class="ref" href="cqc_lang.html#D1">CQC_LANG:def 1</a></i>
<br/>.= 
 <a href="binarith.html#K7">Absval</a> <font color="Maroon">z</font>

;<br/><span class="p1">(<span class="default"><a href="binarith.html#K7">Absval</a> <font color="Maroon">z</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K2">IFEQ</a> <font color="Maroon">d</font>,<a href="margrel1.html#K7">FALSE</a> ,0,<span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">m</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="binarith.html#K7">Absval</a> <font color="Maroon">z</font></span>)</span> <a href="binop_2.html#K10">-</a> 0
<b>by </b><i>, <a class="ref" href="cqc_lang.html#D1">CQC_LANG:def 1</a></i>
<br/>.= 
 <a href="binarith.html#K7">Absval</a> <font color="Maroon">z</font>

;<br/><b>hence </b><a NAME="E5:17_1_1"/>
 <a href="binari_2.html#K4" target="_self">Intval</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="binarith.html#K10">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">d</font></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K7">Absval</a> <font color="Maroon">z</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K2">IFEQ</a> <font color="Maroon">d</font>,<a href="margrel1.html#K7">FALSE</a> ,0,<span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">m</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_2"><b>suppose </b></a><a NAME="E1:17_1_2"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/><div class="add"><a NAME="E2:17_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="binarith.html#K10">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">d</font></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i><a class="ref" href="binarith.html#T3">BINARITH:3</a></i>;<br/><b>then </b> <a href="binari_2.html#K4" target="_self">Intval</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="binarith.html#K10">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">d</font></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> = 
<span class="p1">(<span class="default"><a href="binarith.html#K7">Absval</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="binarith.html#K10">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">d</font></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K7">Absval</a> <font color="Maroon">z</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K2">IFEQ</a> <font color="Maroon">d</font>,<a href="margrel1.html#K7">FALSE</a> ,0,<span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T46">BINARITH:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K7">Absval</a> <font color="Maroon">z</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="cqc_lang.html#D1">CQC_LANG:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K7">Absval</a> <font color="Maroon">z</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">m</font></span>)</span> <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="power.html#T32">POWER:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K7">Absval</a> <font color="Maroon">z</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p1">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K7">Absval</a> <font color="Maroon">z</font></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">m</font></span>)</span>

;<br/><b>hence </b><a NAME="E4:17_1_2"/>
 <a href="binari_2.html#K4" target="_self">Intval</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="binarith.html#K10">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">d</font></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K7">Absval</a> <font color="Maroon">z</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K2">IFEQ</a> <font color="Maroon">d</font>,<a href="margrel1.html#K7">FALSE</a> ,0,<span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">m</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="cqc_lang.html#D1">CQC_LANG:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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