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<a NAME="E1:9_1_1"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c6">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E2:9_1_1"/><b>then </b>
<font color="Maroon" title="c5">f</font> <a href="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Maroon" title="c6">g</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="monoid_1.html#K5" title="MONOID_1:func.5">--&gt;</a> <font color="Maroon" title="c7">d</font></span>)</span></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#D4" title="FUNCOP_1:def.4">FUNCOP_1:def 4</a></i>;<br/>
<a NAME="E3:9_1_1"/><b>then </b>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c7">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c7">d</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T12" title="RELSET_1:th.12">RELSET_1:12</a></i>;<br/>
<b>hence </b><a NAME="E4:9_1_1"/>
<font color="Maroon" title="c5">f</font> <a href="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c7">d</font> is    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c4">D</font>
 <b>by </b><i><a class="ref" href="funct_2.html#D2" title="FUNCT_2:def.2">FUNCT_2:def 2</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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