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<b>let </b><font color="Maroon">H</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><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>assume </b><a NAME="E1:182"/>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zf_lang1.html#K4" target="_self">variables_in</a> <font color="Maroon">H</font>
 ;<br/>

<a NAME="E2:182"/><b>then </b><i><font color="Green">E46</font></i>: 
( not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">H</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,1,2,3,4</span><a href="enumset1.html#K3">}</a></span> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,1,2,3,4</span><a href="enumset1.html#K3">}</a></span> )
 
<b>by </b><i><a class="ref" href="zf_lang1.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E3:182"/><b>then </b><i><font color="Green">E48</font></i>: 
( not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">H</font> &amp;  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="182_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:182_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">H</font>
 ;<br/><a NAME="E2:182_1"/><b>then </b>
( <font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">H</font> &amp; ( <font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> implies <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> ) )
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>hence </b><a NAME="E3:182_1"/>
<span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:182"/>
<font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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