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<b>let </b><font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c2">g</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a> &amp;  <a href="funct_4.html#K2" title="FUNCT_4:func.2">~</a> <font color="Maroon" title="c1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="funct_4.html#K2" title="FUNCT_4:func.2">~</a> <font color="Maroon" title="c2">g</font> implies <font color="Maroon" title="c1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">g</font> )</span><br/>

<b>assume </b><a NAME="E1:60"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not  <a href="funct_4.html#K2" title="FUNCT_4:func.2">~</a> <font color="Maroon" title="c1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="funct_4.html#K2" title="FUNCT_4:func.2">~</a> <font color="Maroon" title="c2">g</font> or <font color="Maroon" title="c1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">g</font> )</span><br/>

<b>then reconsider </b><font color="Maroon" title="c3">R</font> =  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> as   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a> ;<br/>
<a NAME="E3:60"/>
<font color="Maroon" title="c3">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">R</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c3">R</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T21" title="RELAT_1:th.21">RELAT_1:21</a></i>;<br/>
<a NAME="E4:60"/><b>then </b><i><font color="Green" title="E33">A1</font></i>: 
(  <a href="funct_4.html#K2" title="FUNCT_4:func.2">~</a> <span class="p1">(<span class="default"><a href="funct_4.html#K2" title="FUNCT_4:func.2">~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">f</font> &amp;  <a href="funct_4.html#K2" title="FUNCT_4:func.2">~</a> <span class="p1">(<span class="default"><a href="funct_4.html#K2" title="FUNCT_4:func.2">~</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">g</font> )
 
<b>by </b><i><a class="ref" href="funct_4.html#T52" title="FUNCT_4:th.52">FUNCT_4:52</a>, <a class="ref" href="funct_4.html#T53" title="FUNCT_4:th.53">FUNCT_4:53</a></i>;<br/>
<b>assume </b><a NAME="E5:60"/>
 <a href="funct_4.html#K2" title="FUNCT_4:func.2">~</a> <font color="Maroon" title="c1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="funct_4.html#K2" title="FUNCT_4:func.2">~</a> <font color="Maroon" title="c2">g</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">g</font></span><br/>

<a NAME="E6:60"/><b>then </b>
<font color="Maroon" title="c1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="funct_4.html#K2" title="FUNCT_4:func.2">~</a> <span class="p1">(<span class="default"><a href="funct_4.html#K2" title="FUNCT_4:func.2">~</a> <font color="Maroon" title="c2">g</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E4:60"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="yellow20.html#T45" target="_self" title="YELLOW20:th.45">Th45</a></i>;<br/>
<b>hence </b><a NAME="E7:60"/>
<font color="Maroon" title="c1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">g</font>
 <b>by </b><i><a class="txt" href="#E4:60"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</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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