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<b>let </b><font color="Maroon">F1</font> be   <a href="monoid_1.html#NM1">Function</a> of <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D1</font></span>)</span>,<span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D2</font></span>)</span>, <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D</font>, <font color="Maroon">F2</font> be   <a href="monoid_1.html#NM1">Function</a> of <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D1</font></span>)</span>,<span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D2</font></span>)</span>, <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:72_1_2"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D1</font></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D2</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> holds  <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">x</font> <a href="domain_1.html#K2">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive">x</font> <a href="domain_1.html#K3">`2</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>and </b><br/><a NAME="E2:72_1_2"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D1</font></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D2</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> holds  <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">x</font> <a href="domain_1.html#K2">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive">x</font> <a href="domain_1.html#K3">`2</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D1</font></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D2</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/><b>thus </b><font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="domain_1.html#K2">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="domain_1.html#K3">`2</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:72_1_2"/>
<font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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