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<b>consider </b><font color="Maroon" title="c4">l1</font>, <font color="Maroon" title="c5">l2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">IL</font><b> such that </b><br/><a NAME="E2:45_1_1"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c4">l1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">l2</font>
 <b>by </b><i><a class="ref" href="yellow_8.html#D1" title="YELLOW_8:def.1">YELLOW_8:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">l1</font> = <font color="Maroon" title="c4">l1</font>, <font color="Maroon" title="c7">l2</font> = <font color="Maroon" title="c5">l2</font> as    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of <font color="Maroon" title="c3">S</font> <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">I</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <font color="Maroon" title="c3">S</font>;<br/>
<b>take </b><font color="Maroon" title="c9">f</font> = <font color="Maroon" title="c6">l1</font>,<font color="Maroon" title="c7">l2</font> <a href="amistd_2.html#K1" title="AMISTD_2:func.1">--&gt;</a> <font color="Maroon" title="c8">I</font>,<font color="Maroon" title="c8">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c9">f</font> is <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> &amp; <font color="Maroon" title="c9">f</font> is <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> )</span><br/>

<b>thus </b><a NAME="E5:45_1_1"/>
not <font color="Maroon" title="c9">f</font> is <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">f</font> is <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:45_1_1_1"/>
<font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">l1</font>,<font color="Maroon" title="c8">I</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">l2</font>,<font color="Maroon" title="c8">I</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="txt" href="#E2:45_1_1"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="funct_4.html#T71" title="FUNCT_4:th.71">FUNCT_4:71</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">x</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">l1</font>,<font color="Maroon" title="c8">I</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>, <font color="Maroon" title="c11">y</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">l2</font>,<font color="Maroon" title="c8">I</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c9">f</font> <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c10">x</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_8.html#D1" title="YELLOW_8:def.1">YELLOW_8:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c9">f</font> holds  <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font></span><br/>

<b>take </b>
<font color="Maroon" title="c11">y</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">y</font></span><br/>

<b>thus </b><a NAME="E3:45_1_1_1"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">y</font>
 <b>by </b><i><a class="txt" href="#E2:45_1_1"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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

<b>let </b><font color="Maroon" title="c10">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="ami_1.html#D40" title="AMI_1:def.40">AMI_1:def 40</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">f</font> or <font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">IL</font> )</span><br/>

<b>assume </b><a NAME="E6:45_1_1"/>
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">IL</font></span><br/>

<a NAME="E7:45_1_1"/><b>then </b>
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c6">l1</font>,<font color="Maroon" title="c7">l2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>;<br/>
<a NAME="E8:45_1_1"/><b>then </b>
( <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">l1</font> or <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">l2</font> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E9:45_1_1"/>
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">IL</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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