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<a NAME="E1:101_1_1"/><i><font color="Green" title="E55">A1</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">g</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K7" title="AMI_1:func.7">sproduct</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T46" target="_self" title="AMI_1:th.46">Th46</a></i>;<br/>
<a NAME="E2:101_1_1"/>
( <font color="Maroon" title="c3">f</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; <font color="Maroon" title="c4">g</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> )
 
<b>by </b><i><a class="ref" href="ami_1.html#D24" target="_self" title="AMI_1:def.24">Def24</a></i>;<br/>
<a NAME="E3:101_1_1"/><b>then </b><i><font color="Green" title="E56">A2</font></i>: 
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">g</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> )
 
<b>by </b><i><a class="ref" href="finset_1.html#T29" title="FINSET_1:th.29">FINSET_1:29</a></i>;<br/>
<a NAME="E4:101_1_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">g</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E5:101_1_1"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">g</font></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="txt" href="ami_1.html#E3:101_1_1"><i><font color="Green" title="E56">A2</font></i></a>, <a class="ref" href="finset_1.html#T14" title="FINSET_1:th.14">FINSET_1:14</a></i>;<br/>
<a NAME="E6:101_1_1"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">g</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="finset_1.html#T29" title="FINSET_1:th.29">FINSET_1:29</a></i>;<br/>
<b>hence </b><a NAME="E7:101_1_1"/>
<font color="Maroon" title="c3">f</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">g</font> is    <a href="ami_1.html#M1" title="AMI_1:mode.1">FinPartState</a> of <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="txt" href="ami_1.html#E1:101_1_1"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="ami_1.html#D24" target="_self" title="AMI_1:def.24">Def24</a></i>;<br/>


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