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

<b>let </b><font color="Maroon">Y</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">Y</font>,<font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">x1</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">x2</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>;<br/>











<b>assume </b><a NAME="E1:78"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">F</font> is <a href="binop_1.html#V2">associative</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funcop_1.html#K7" target="_self">[:]</a> <font color="Maroon">f</font>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x1</font>,<font color="Maroon">x2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> = 
<font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x1</font>,<font color="Maroon">x2</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span>,<font color="Maroon">x1</font></span>)</span>,<font color="Maroon">x2</font>
<b>by </b><i>, <a class="ref" href="binop_1.html#D3">BINOP_1:def 3</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="funcop_1.html#K7" target="_self">[:]</a> <font color="Maroon">f</font>,<font color="Maroon">x1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span>,<font color="Maroon">x2</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:78"/>
<font color="Maroon">F</font> <a href="funcop_1.html#K7" target="_self">[:]</a> <font color="Maroon">f</font>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x1</font>,<font color="Maroon">x2</font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">F</font> <a href="funcop_1.html#K7" target="_self">[:]</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funcop_1.html#K7" target="_self">[:]</a> <font color="Maroon">f</font>,<font color="Maroon">x1</font></span>)</span>,<font color="Maroon">x2</font>
 <b>by </b><i/>;<br/>


</div>
