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

<b>let </b><font color="Maroon">C1</font> be   <a href="coh_sp.html#NM1">Coherence_Space</a>, <font color="Maroon">C2</font> be   <a href="coh_sp.html#NM1">Coherence_Space</a>;<br/><b>let </b><font color="Maroon">x1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">x2</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y2</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:119_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x2</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K12" target="_self">LinCoh</a> <font color="Maroon">C1</font>,<font color="Maroon">C2</font></span>)</span>
 ;<br/><a NAME="E2:119_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x2</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K12" target="_self">LinCoh</a> <font color="Maroon">C1</font>,<font color="Maroon">C2</font>
 <b>by </b><i><a class="ref" href="coh_sp.html#T5">COH_SP:5</a></i>;<br/><b>then consider </b><font color="Maroon">f</font> being  <a href="cohsp_1.html#V10" target="_self">U-linear</a> <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">C1</font>,<font color="Maroon">C2</font><b> such that </b><br/><a NAME="E4:119_1"/><i><font color="Green">E26</font></i>: 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x2</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R1">=</a>  <a href="cohsp_1.html#K11" target="_self">LinTrace</a> <font color="Maroon">f</font>
 <b>by </b><i/>;<br/><a NAME="E5:119_1"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K11" target="_self">LinTrace</a> <font color="Maroon">f</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x2</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K11" target="_self">LinTrace</a> <font color="Maroon">f</font> )
 <b>by </b><i><a class="ref" href="cohsp_1.html#T17" target="_self">Th17</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E6:119_1"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x1</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K8" target="_self">Trace</a> <font color="Maroon">f</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x2</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K8" target="_self">Trace</a> <font color="Maroon">f</font> )
 <b>by </b><i><a class="ref" href="cohsp_1.html#T12" target="_self">Th12</a></i>;<br/><a NAME="E7:119_1"/><b>then </b><i><font color="Green">E27</font></i>: 
( <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x1</font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x2</font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x1</font></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x2</font></span><a href="tarski.html#K1">}</a></span> &amp; <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x1</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x2</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="cohsp_1.html#K8" target="_self">Trace</a> <font color="Maroon">f</font> &amp;  <a href="cohsp_1.html#K8" target="_self">Trace</a> <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K9" target="_self">StabCoh</a> <font color="Maroon">C1</font>,<font color="Maroon">C2</font> )
 <b>by </b><i><a class="ref" href="cohsp_1.html#T6" target="_self">Th6</a>, <a class="ref" href="cohsp_1.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a>, <a class="ref" href="zfmisc_1.html#T38">ZFMISC_1:38</a></i>;<br/><a NAME="E8:119_1"/><b>then </b>
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C1</font> &amp; <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x1</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x2</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K9" target="_self">StabCoh</a> <font color="Maroon">C1</font>,<font color="Maroon">C2</font> )
 <b>by </b><i><a class="ref" href="classes1.html#D1">CLASSES1:def 1</a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/><a NAME="E9:119_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x1</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x2</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K9" target="_self">StabCoh</a> <font color="Maroon">C1</font>,<font color="Maroon">C2</font></span>)</span>
 <b>by </b><i><a class="ref" href="coh_sp.html#T5">COH_SP:5</a></i>;<br/><a NAME="E10:119_1"/><b>then </b>
( ( not <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x1</font></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x2</font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">y2</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C2</font> ) or ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <font color="Maroon">C2</font> &amp; ( <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> implies <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x1</font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x2</font></span><a href="tarski.html#K1">}</a></span> ) ) )
 <b>by </b><i><a class="ref" href="cohsp_1.html#D10" target="_self">Def10</a>, <a class="ref" href="cohsp_1.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E11:119_1"/><b>then </b>
( ( not <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">y2</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C2</font> ) or ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <font color="Maroon">C2</font> &amp; ( <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> implies <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) ) )
 <b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a>, <a class="ref" href="zfmisc_1.html#T6">ZFMISC_1:6</a></i>;<br/><b>hence </b><a NAME="E12:119_1"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C1</font> &amp; ( ( not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">y2</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C2</font> ) or ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <font color="Maroon">C2</font> &amp; ( <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> implies <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) ) ) )
 <b>by </b><i><a class="ref" href="cohsp_1.html#D10" target="_self">Def10</a>, <a class="ref" href="coh_sp.html#T5">COH_SP:5</a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:119"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C1</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">a</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x1</font></span><a href="tarski.html#K1">}</a></span>, <font color="Maroon">b</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x2</font></span><a href="tarski.html#K1">}</a></span> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <b>by </b><i><a class="ref" href="coh_sp.html#T4">COH_SP:4</a></i>;<br/>
<b>assume </b><a NAME="E4:119"/>
( ( not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">y2</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C2</font> ) or ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <font color="Maroon">C2</font> &amp; ( <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> implies <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) ) )
 ;<br/>

<a NAME="E5:119"/><b>then </b>
( ( not <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">y2</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C2</font> ) or ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <font color="Maroon">C2</font> &amp; ( <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> implies <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) ) )
 
<b>by </b><i><a class="ref" href="coh_sp.html#T5">COH_SP:5</a></i>;<br/>
<a NAME="E6:119"/><b>then </b>
( ( not <font color="Maroon">a</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">y2</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C2</font> ) or ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <font color="Maroon">C2</font> &amp; ( <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> implies <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) ) )
 
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>;<br/>
<a NAME="E7:119"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K9" target="_self">StabCoh</a> <font color="Maroon">C1</font>,<font color="Maroon">C2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E8:119"/><b>then </b>
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K9" target="_self">StabCoh</a> <font color="Maroon">C1</font>,<font color="Maroon">C2</font>
 
<b>by </b><i><a class="ref" href="coh_sp.html#T5">COH_SP:5</a></i>;<br/>
<b>then consider </b><font color="Maroon">f</font> being  <a href="cohsp_1.html#V9" target="_self">U-stable</a> <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">C1</font>,<font color="Maroon">C2</font><b> such that </b><br/><a NAME="E10:119"/><i><font color="Green">E36</font></i>: 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R1">=</a>  <a href="cohsp_1.html#K8" target="_self">Trace</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T6" target="_self">Th6</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="119_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:119_2"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K8" target="_self">Trace</a> <font color="Maroon">f</font>
 ;<br/><a NAME="E2:119_2"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> or <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="cohsp_1.html#T17" target="_self">Th17</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E3:119_2"/><b>then </b>
( <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x1</font></span><a href="tarski.html#K1">}</a></span> or <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x2</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><b>hence </b><a NAME="E4:119_2"/>
 ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">x</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/></div><b>end;</b></div>
<a NAME="E12:119"/><b>then </b>
<font color="Maroon">f</font> is <a href="cohsp_1.html#V10" target="_self">U-linear</a>
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E13:119"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="cohsp_1.html#K11" target="_self">LinTrace</a> <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K12" target="_self">LinCoh</a> <font color="Maroon">C1</font>,<font color="Maroon">C2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E14:119"/>
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x2</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="cohsp_1.html#K11" target="_self">LinTrace</a> <font color="Maroon">f</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="119_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:119_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x2</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<a NAME="E2:119_3"/><b>then </b>
( ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K8" target="_self">Trace</a> <font color="Maroon">f</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x2</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K8" target="_self">Trace</a> <font color="Maroon">f</font> ) )
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T17" target="_self">Th17</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:119_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K11" target="_self">LinTrace</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T12" target="_self">Th12</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E15:119"/><b>then </b>
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x2</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K12" target="_self">LinCoh</a> <font color="Maroon">C1</font>,<font color="Maroon">C2</font>
 
<b>by </b><i><a class="ref" href="cohsp_1.html#D10" target="_self">Def10</a>, <a class="ref" href="classes1.html#D1">CLASSES1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E16:119"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x2</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K12" target="_self">LinCoh</a> <font color="Maroon">C1</font>,<font color="Maroon">C2</font></span>)</span>
 <b>by </b><i><a class="ref" href="coh_sp.html#T5">COH_SP:5</a></i>;<br/>


</div>
