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<b>let </b><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">X2</font>, <font color="Maroon" title="c3">Y1</font>, <font color="Maroon" title="c4">Y2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Maroon" title="c1">X1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">X2</font> &amp; <font color="Maroon" title="c3">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">Y2</font> holds <br/><span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Olive" title="b1">f</font>,<font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">Y1</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Olive" title="b1">f</font>,<font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c4">Y2</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c5">f</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"> ( <font color="Maroon" title="c1">X1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">X2</font> &amp; <font color="Maroon" title="c3">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">Y2</font> implies <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">Y1</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c4">Y2</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span> )</span><br/>









<b>assume </b><a NAME="E1:48"/>
( <font color="Maroon" title="c1">X1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">X2</font> &amp; <font color="Maroon" title="c3">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">Y2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">Y1</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c4">Y2</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span></span><br/>

<a NAME="E2:48"/><b>then </b>
( <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">Y1</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c3">Y1</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span> &amp; <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c3">Y1</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c4">Y2</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="partfun1.html#T82" target="_self" title="PARTFUN1:th.82">Th82</a>, <a class="ref" href="partfun1.html#T83" target="_self" title="PARTFUN1:th.83">Th83</a></i>;<br/>
<b>hence </b><a NAME="E3:48"/>
<span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">Y1</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c4">Y2</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span>
 <b>by </b><i><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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