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<b>let </b><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">p</font> be   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a>;<br/>



<b>thus </b><a NAME="E1:62"/>
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">%&gt;</a></span> implies (  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:62_1"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">%&gt;</a></span>
 ;<br/>

<b>hence </b><a NAME="E2:62_1"/>
 <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="ref" href="afinsq_1.html#D5" target="_self" title="AFINSQ_1:def.5">Def5</a></i>;<br/>

<a NAME="E3:62_1"/>
 <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="afinsq_1.html#E1:62_1"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="afinsq_1.html#D5" target="_self" title="AFINSQ_1:def.5">Def5</a>, <a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a></i>;<br/>
<a NAME="E4:62_1"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_1.html#T14" title="FUNCT_1:th.14">FUNCT_1:14</a></i>;<br/>
<b>hence </b><a NAME="E5:62_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="afinsq_1.html#E1:62_1"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="afinsq_1.html#D5" target="_self" title="AFINSQ_1:def.5">Def5</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:62"/><i><font color="Green" title="E27">A2</font></i>: 
(  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ;<br/>

<a NAME="E3:62"/>
1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
;<br/>
<a NAME="E4:62"/><b>then </b>
0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="txt" href="afinsq_1.html#E2:62"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="afinsq_1.html#T1" target="_self" title="AFINSQ_1:th.1">Th1</a></i>;<br/>
<a NAME="E5:62"/><b>then </b>
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="afinsq_1.html#E2:62"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></i>;<br/>
<a NAME="E6:62"/><b>then </b>
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:62"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">%&gt;</a></span>
 <b>by </b><i><a class="txt" href="afinsq_1.html#E2:62"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="afinsq_1.html#D5" target="_self" title="AFINSQ_1:def.5">Def5</a></i>;<br/>


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