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<b>let </b><font color="Maroon" title="c1">p1</font>, <font color="Maroon" title="c2">p3</font>, <font color="Maroon" title="c3">p2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>





<b>assume </b><a NAME="E1:29"/><i><font color="Green" title="E26">A1</font></i>: 
( <font color="Maroon" title="c1">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p3</font> &amp; <font color="Maroon" title="c3">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p3</font> )
 ;<br/>

<a NAME="E2:29"/>
3 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p3</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>;<br/>
<a NAME="E3:29"/><b>then </b><i><font color="Green" title="E27">A2</font></i>: 
3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p3</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E4:29"/><i><font color="Green" title="E28">A3</font></i>: 
<span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p3</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p3</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>;<br/>
<a NAME="E5:29"/><i><font color="Green" title="E29">A4</font></i>: 
( <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p3</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p2</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p3</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p1</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:29_1"/><i><font color="Green" title="E30">A5</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">i</font>
 ;<br/><b>assume </b><a NAME="E2:29_1"/>
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><a NAME="E3:29_1"/><b>then </b>
( <font color="Maroon" title="c4">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 2 )
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:29_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>hence </b><a NAME="E4:29_1"/>
<span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p3</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p3</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:29"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="finseq_6.html#E4:29"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="finseq_6.html#E5:29"><i><font color="Green" title="E29">A4</font></i></a>, <a class="ref" href="nat_1.html#T27" title="NAT_1:th.27">NAT_1:27</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:29"/>
<font color="Maroon" title="c2">p3</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p3</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 <b>by </b><i><a class="txt" href="finseq_6.html#E3:29"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="finseq_6.html#E4:29"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="finseq_6.html#T4" target="_self" title="FINSEQ_6:th.4">Th4</a></i>;<br/>


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