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

<span class="kw">let </span><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#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">let </span><font color="Maroon" title="c5">f</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>









<span class="kw">assume </span><a NAME="E1:35"/>
( <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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E2:35"/><span class="kw">then </span>
( <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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#T28" target="_self" onmouseover="rs('partfun1/T28')" onmouseout="rh()">Th28</a>, <a class="ref" href="partfun1.html#T29" target="_self" onmouseover="rs('partfun1/T29')" onmouseout="rh()">Th29</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:35"/>
<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>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
