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<b>let </b><font color="Maroon">x</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">M</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">m</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">m'</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="zf_lang.html#K1">VAR</a> ,<font color="Maroon">M</font>;<br/>











<b>assume </b><a NAME="E1:64"/>
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 ;<br/>

<b>then </b><i><font color="Green">E46</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">y</font>,<font color="Maroon">m'</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">m</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">m</font>
<b>by </b><i/>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">z</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>assume </b><a NAME="E1:64_2"/><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">y</font>,<font color="Maroon">m'</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">y</font>,<font color="Maroon">m'</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font>
 ;<br/><a NAME="E2:64_2"/>
( <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> or <font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> )
 ;<br/><a NAME="E3:64_2"/><b>then </b>
( ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">y</font>,<font color="Maroon">m'</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m'</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">y</font>,<font color="Maroon">m'</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m'</font> ) or ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">y</font>,<font color="Maroon">m'</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">m</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">y</font>,<font color="Maroon">m'</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> ) )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:64_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:64"/>
<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">y</font>,<font color="Maroon">m'</font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">y</font>,<font color="Maroon">m'</font></span>)</span> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">m</font>
 <b>by </b><i>, </i>;<br/>


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