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<b>let </b><font color="Maroon">H1</font> be  <a href="funcop_1.html#V1">Function-yielding</a> <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">H2</font> be  <a href="funcop_1.html#V1">Function-yielding</a> <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:170_1_2"/><i><font color="Green">E27</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H1</font> holds <br/><font color="Maroon">H1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font></span>)</span> ) )
 <b>and </b><br/><a NAME="E2:170_1_2"/><i><font color="Green">E28</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H2</font> holds <br/><font color="Maroon">H2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font></span>)</span> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="170_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:170_1_2_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font></span>)</span>
 ;<br/><b>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> as   <a href="funct_1.html#NM1">Function</a> ;<br/><b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> as   <a href="funct_1.html#NM1">Function</a> ;<br/><a NAME="E4:170_1_2_1"/>
( <font color="Maroon">H1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font> &amp; <font color="Maroon">H2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font> )
 <b>by </b><i><a class="ref" href="pboole.html#T38" target="_self">Th38</a>, <a class="ref" href="pboole.html#T39" target="_self">Th39</a>, <a class="ref" href="pboole.html#T49" target="_self">Th49</a></i>;<br/><b>hence </b><a NAME="E5:170_1_2_1"/>
<font color="Maroon">H1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:170_1_2"/>
<font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H2</font>
 <b>by </b><i><a class="ref" href="pboole.html#T38" target="_self">Th38</a>, <a class="ref" href="pboole.html#T39" target="_self">Th39</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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