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<b>let </b><font color="Maroon">F1</font> be  <a href="matrlin.html#V1" target="_self">FinSequence-yielding</a> <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">F2</font> be  <a href="matrlin.html#V1" target="_self">FinSequence-yielding</a> <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:11_1_2"/><i><font color="Green">E54</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">F1</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>
 <b>and </b><br/><a NAME="E2:11_1_2"/><i><font color="Green">E55</font></i>: 
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">F1</font> holds <br/>for <font color="Olive">f</font>, <font color="Olive">g</font> being  <a href="finseq_1.html#NM1">FinSequence</a>  st <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> &amp; <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> holds <br/><font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="finseq_1.html#K7">^</a> <font color="Olive">g</font>
 <b>and </b><br/><a NAME="E3:11_1_2"/><i><font color="Green">E57</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">F2</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>
 <b>and </b><br/><a NAME="E4:11_1_2"/><i><font color="Green">E58</font></i>: 
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">F2</font> holds <br/>for <font color="Olive">f</font>, <font color="Olive">g</font> being  <a href="finseq_1.html#NM1">FinSequence</a>  st <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> &amp; <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> holds <br/><font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="finseq_1.html#K7">^</a> <font color="Olive">g</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:11_1_2_1"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F1</font>
 ;<br/><a NAME="E2:11_1_2_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font> )
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>, <font color="Maroon">g</font> = <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i/>;<br/><b>thus </b><font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">f</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">g</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , , </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:11_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_1.html#T9">FUNCT_1:9</a></i>;<br/>


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