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<b>let </b><font color="Maroon">Ne</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">Ke</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">Ne</font>,<font color="Maroon">Ke</font>;<br/>





<b>assume </b><a NAME="E1:98"/><i><font color="Green">E38</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">F</font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>

<b>let </b><font color="Maroon">I1</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">Ne</font>,<font color="Maroon">Ke</font>, <font color="Maroon">I2</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">Ne</font>,<font color="Maroon">Ke</font>;<br/><b>let </b><font color="Maroon">P1</font> be   <a href="funct_2.html#NM2">Permutation</a> of  <a href="relset_1.html#K5">rng</a> <font color="Maroon">F</font>, <font color="Maroon">P2</font> be   <a href="funct_2.html#NM2">Permutation</a> of  <a href="relset_1.html#K5">rng</a> <font color="Maroon">F</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E2:98"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P1</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">I1</font> &amp; <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P2</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">I2</font> )
 <b>and </b><br/><a NAME="E3:98"/><i><font color="Green">E40</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">I1</font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">I2</font> )
 <b>and </b><br/><a NAME="E4:98"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">I1</font> is <a href="stirl2_1.html#V2" target="_self">"increasing</a> &amp; <font color="Maroon">I2</font> is <a href="stirl2_1.html#V2" target="_self">"increasing</a> )
 ;<br/>

<a NAME="E5:98"/>
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies  <a href="relset_1.html#K5">rng</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
;<br/>
<a NAME="E6:98"/><b>then </b>
(  <a href="relset_1.html#K4">dom</a> <font color="Maroon">P1</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">F</font> &amp;  <a href="relset_1.html#K4">dom</a> <font color="Maroon">P2</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">F</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:98"/>
( <font color="Maroon">P1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P2</font> &amp; <font color="Maroon">I1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I2</font> )
 <b>by </b><i>, , , <a class="ref" href="stirl2_1.html#T20" target="_self">Th20</a>, </i>;<br/>


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