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<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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being <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/> for <font color="Olive" title="b2">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> holds  <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K11" title="COHSP_1:func.11">LinTrace</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <font color="Olive" title="b2">a</font></span><br/><b>let </b><font color="Maroon" title="c3">f</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> holds  <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K11" title="COHSP_1:func.11">LinTrace</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <font color="Olive" title="b1">a</font></span><br/><b>let </b><font color="Maroon" title="c4">a</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K11" title="COHSP_1:func.11">LinTrace</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <font color="Maroon" title="c4">a</font></span><br/>





<b>set </b><font color="Maroon" title="c5">X</font> =  <a href="cohsp_1.html#K11" title="COHSP_1:func.11">LinTrace</a> <font color="Maroon" title="c3">f</font>;<br/>
<a NAME="E1:111"/><i><font color="Green" title="E63">A1</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> holds <br/>for <font color="Olive" title="b3">y1</font>, <font color="Olive" title="b4">y2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">y1</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> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">y2</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> holds <br/><span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b3">y1</font>,<font color="Olive" title="b4">y2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C2</font>
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T54" target="_self" title="COHSP_1:th.54">Th54</a></i>;<br/>
<a NAME="E2:111"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C1</font> holds <br/>for <font color="Olive" title="b3">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">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> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">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> holds <br/><font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font>
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T55" target="_self" title="COHSP_1:th.55">Th55</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">g</font> being  <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><b> such that </b><br/><a NAME="E4:111"/><i><font color="Green" title="E64">A2</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="c6">g</font> &amp; ( for <font color="Olive" title="b1">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C1</font> holds  <font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K11" title="COHSP_1:func.11">LinTrace</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <font color="Olive" title="b1">a</font> ) )
 <b>by </b><i><a class="txt" href="#E1:111"><i><font color="Green" title="E63">A1</font></i></a>, <a class="txt" href="cohsp_1.html#E83"><i><font color="Green" title="E61">Lm6</font></i></a></i>;<br/>
<a NAME="E5:111"/>
<font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K11" title="COHSP_1:func.11">LinTrace</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <font color="Maroon" title="c4">a</font>
 
<b>by </b><i><a class="txt" href="#E4:111"><i><font color="Green" title="E64">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:111"/>
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K11" title="COHSP_1:func.11">LinTrace</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <font color="Maroon" title="c4">a</font>
 <b>by </b><i><a class="txt" href="#E4:111"><i><font color="Green" title="E64">A2</font></i></a>, <a class="ref" href="cohsp_1.html#T56" target="_self" title="COHSP_1:th.56">Th56</a></i>; <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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