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

<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font>, <font color="Maroon" title="c3">Z</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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">y</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">Y</font><br/> for <font color="Olive" title="b2">F</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font><br/> for <font color="Olive" title="b3">G</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">Y</font>,<font color="Maroon" title="c3">Z</font> holds  <font color="Olive" title="b2">F</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">y</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">G</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">y</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/><b>let </b><font color="Maroon" title="c4">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">Y</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">F</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font><br/> for <font color="Olive" title="b2">G</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">Y</font>,<font color="Maroon" title="c3">Z</font> holds  <font color="Olive" title="b1">F</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">y</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">G</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/><b>let </b><font color="Maroon" title="c5">F</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</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">G</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">Y</font>,<font color="Maroon" title="c3">Z</font> holds  <font color="Maroon" title="c5">F</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">y</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">G</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/><b>let </b><font color="Maroon" title="c6">G</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">Y</font>,<font color="Maroon" title="c3">Z</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">F</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">y</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/>











<a NAME="E1:12"/>
<font color="Maroon" title="c5">F</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">y</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K11" title="RELAT_1:func.11">Im</a> <font color="Maroon" title="c6">G</font>,<font color="Maroon" title="c4">y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T53" title="FUNCT_2:th.53">FUNCT_2:53</a></i>;<br/>
<b>hence </b><a NAME="E2:12"/>
<font color="Maroon" title="c5">F</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">y</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="setwiseo.html#T13" title="SETWISEO:th.13">SETWISEO:13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
