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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">m2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="coh_sp.html#K21" target="_self">MapsT</a> <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">m1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="coh_sp.html#K21" target="_self">MapsT</a> <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">m3</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="coh_sp.html#K21" target="_self">MapsT</a> <font color="Maroon">X</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:75"/><i><font color="Green">E17</font></i>: 
 <a href="coh_sp.html#K22" target="_self">dom</a> <font color="Maroon">m2</font> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K23" target="_self">cod</a> <font color="Maroon">m1</font>
 <b>and </b><br/><a NAME="E2:75"/><i><font color="Green">E18</font></i>: 
 <a href="coh_sp.html#K22" target="_self">dom</a> <font color="Maroon">m3</font> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K23" target="_self">cod</a> <font color="Maroon">m2</font>
 ;<br/>

<a NAME="E3:75"/>
( <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> &amp;  <a href="coh_sp.html#K22" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K22" target="_self">dom</a> <font color="Maroon">m1</font> &amp;  <a href="coh_sp.html#K23" target="_self">cod</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K23" target="_self">cod</a> <font color="Maroon">m2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">m3</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m2</font></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m3</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> &amp;  <a href="coh_sp.html#K22" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">m3</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K22" target="_self">dom</a> <font color="Maroon">m2</font> &amp;  <a href="coh_sp.html#K23" target="_self">cod</a> <span class="p1">(<span class="default"><font color="Maroon">m3</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K23" target="_self">cod</a> <font color="Maroon">m3</font> )
 
<b>by </b><i><a class="ref" href="coh_sp.html#D4" target="_self">Def4</a>, , </i>;<br/>
<a NAME="E4:75"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">m3</font> <a href="coh_sp.html#K25" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">m2</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m3</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m2</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span>)</span> &amp;  <a href="coh_sp.html#K22" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">m3</font> <a href="coh_sp.html#K25" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">m2</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K22" target="_self">dom</a> <font color="Maroon">m1</font> &amp;  <a href="coh_sp.html#K23" target="_self">cod</a> <span class="p1">(<span class="default"><font color="Maroon">m3</font> <a href="coh_sp.html#K25" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">m2</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K23" target="_self">cod</a> <font color="Maroon">m3</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m3</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m2</font></span>)</span> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m3</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">m2</font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> &amp;  <a href="coh_sp.html#K22" target="_self">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m3</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m2</font></span>)</span> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K22" target="_self">dom</a> <font color="Maroon">m1</font> &amp;  <a href="coh_sp.html#K23" target="_self">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m3</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m2</font></span>)</span> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K23" target="_self">cod</a> <font color="Maroon">m3</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">m3</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m2</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m3</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">m2</font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="coh_sp.html#D4" target="_self">Def4</a>, , , <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>;<br/>
<b>hence </b><a NAME="E5:75"/>
<font color="Maroon">m3</font> <a href="coh_sp.html#K25" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m3</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m2</font></span>)</span> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font>
 <b>by </b><i/>;<br/>


</div>
