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

<b>let </b><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</font> be   <a href="coh_sp.html#NM1" title="COH_SP:NM.1">Coherence_Space</a>;<br/><b>let </b><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font> be  <a href="cohsp_1.html#V10" title="COHSP_1:attr.10">U-linear</a> <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>;<br/>



<b>assume </b><a NAME="E1:108"/><i><font color="Green" title="E61">A1</font></i>: 
 <a href="cohsp_1.html#K11" title="COHSP_1:func.11">LinTrace</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cohsp_1.html#K11" title="COHSP_1:func.11">LinTrace</a> <font color="Maroon" title="c4">g</font>
 ;<br/>

<a NAME="E2:108"/>
 <a href="cohsp_1.html#K8" title="COHSP_1:func.8">Trace</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cohsp_1.html#K8" title="COHSP_1:func.8">Trace</a> <font color="Maroon" title="c4">g</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="108_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">y</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="relat_1.html#D2" title="RELAT_1:def.2">RELAT_1:def 2</a><br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:108_1_1"/><i><font color="Green" title="E62">A2</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cohsp_1.html#K8" title="COHSP_1:func.8">Trace</a> <font color="Maroon" title="c3">f</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c7">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:108_1_1"/><i><font color="Green" title="E63">A3</font></i>: 
<font color="Maroon" title="c5">a</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="c7">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T50" target="_self" title="COHSP_1:th.50">Th50</a></i>;<br/><a NAME="E4:108_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">x</font>,<font color="Maroon" title="c6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cohsp_1.html#K11" title="COHSP_1:func.11">LinTrace</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="txt" href="cohsp_1.html#E1:108_1_1"><i><font color="Green" title="E62">A2</font></i></a>, <a class="txt" href="cohsp_1.html#E3:108_1_1"><i><font color="Green" title="E63">A3</font></i></a>, <a class="ref" href="cohsp_1.html#T51" target="_self" title="COHSP_1:th.51">Th51</a></i>;<br/><b>hence </b><a NAME="E5:108_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cohsp_1.html#K8" title="COHSP_1:func.8">Trace</a> <font color="Maroon" title="c4">g</font>
 <b>by </b><i><a class="txt" href="cohsp_1.html#E1:108"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="cohsp_1.html#E3:108_1_1"><i><font color="Green" title="E63">A3</font></i></a>, <a class="ref" href="cohsp_1.html#T51" target="_self" title="COHSP_1:th.51">Th51</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:108_1"/><i><font color="Green" title="E62">A4</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cohsp_1.html#K8" title="COHSP_1:func.8">Trace</a> <font color="Maroon" title="c4">g</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c7">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:108_1"/><i><font color="Green" title="E63">A5</font></i>: 
<font color="Maroon" title="c5">a</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="c7">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T50" target="_self" title="COHSP_1:th.50">Th50</a></i>;<br/>
<a NAME="E5:108_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">x</font>,<font color="Maroon" title="c6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cohsp_1.html#K11" title="COHSP_1:func.11">LinTrace</a> <font color="Maroon" title="c4">g</font>
 
<b>by </b><i><a class="txt" href="cohsp_1.html#E2:108_1"><i><font color="Green" title="E62">A4</font></i></a>, <a class="txt" href="cohsp_1.html#E4:108_1"><i><font color="Green" title="E63">A5</font></i></a>, <a class="ref" href="cohsp_1.html#T51" target="_self" title="COHSP_1:th.51">Th51</a></i>;<br/>
<b>hence </b><a NAME="E6:108_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cohsp_1.html#K8" title="COHSP_1:func.8">Trace</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="txt" href="cohsp_1.html#E1:108"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="cohsp_1.html#E4:108_1"><i><font color="Green" title="E63">A5</font></i></a>, <a class="ref" href="cohsp_1.html#T51" target="_self" title="COHSP_1:th.51">Th51</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:108"/>
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">g</font>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T38" target="_self" title="COHSP_1:th.38">Th38</a></i>;<br/>


</div>
