<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">F</font> be   <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">F</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  implies <font color="Maroon" title="c3">F</font> is  <a href="amistd_1.html#V11" title="AMISTD_1:attr.11">unique-halt</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:52_1_1"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<font color="Maroon" title="c3">F</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">F</font> is  <a href="amistd_1.html#V11" title="AMISTD_1:attr.11">unique-halt</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">f</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> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="amistd_1.html#D23" title="AMISTD_1:def.23">AMISTD_1:def 23</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font> or  not <font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c3">F</font> or <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <font color="Maroon" title="c3">F</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:52_1_1"/>
<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font>
 <span class="kw">and </span><br/><a NAME="E3:52_1_1"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
<font color="Maroon" title="c4">f</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="c3">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <font color="Maroon" title="c3">F</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c5">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E5:52_1_1"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
<font color="Maroon" title="c3">F</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="c5">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="realset1.html#D4" title="REALSET1:def.4">REALSET1:def 4</a></span>;<br/>
<a NAME="E6:52_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:52_1_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E8:52_1_1"/><span class="lab"><font color="Green" title="E22">A4</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D1" title="RELAT_1:def.1">RELAT_1:def 1</a></span>;<br/>
<a NAME="E9:52_1_1"/><span class="lab"><font color="Green" title="E23">A5</font></span>: 
 <a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <font color="Maroon" title="c3">F</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="c3">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#T51" title="AMISTD_1:th.51">AMISTD_1:51</a></span>;<br/>
<a NAME="E10:52_1_1"/><span class="lab"><font color="Green" title="E24">A6</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">F</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="c6">a</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:52_1_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E8:52_1_1"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="relat_1.html#T23" title="RELAT_1:th.23">RELAT_1:23</a></span>;<br/>
<span class="kw">hence </span><font color="Maroon" title="c4">f</font> = 
<font color="Maroon" title="c6">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:52_1_1"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>
<br/>.= 
 <a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <font color="Maroon" title="c3">F</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:52_1_1"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="txt" href="#E10:52_1_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
