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<b>let </b><font color="Maroon">f</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font></span>)</span>, <font color="Maroon">h</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:57_3_2"/><i><font color="Green">E75</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font></span>)</span> holds  <font color="Maroon">f</font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="prvect_1.html#K17" target="_self">.</a> <font color="Olive">i</font></span>)</span>
 <b>and </b><br/><a NAME="E2:57_3_2"/><i><font color="Green">E76</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font></span>)</span> holds  <font color="Maroon">h</font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="prvect_1.html#K17" target="_self">.</a> <font color="Olive">i</font></span>)</span>
 ;<br/>

<b>reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f</font>, <font color="Maroon">h'</font> = <font color="Maroon">h</font> as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<a NAME="E4:57_3_2"/><i><font color="Green">E77</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f'</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font></span>)</span> &amp;  <a href="relat_1.html#K1">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"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="card_3.html#T18">CARD_3:18</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_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="E1:57_3_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">i</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font></span>)</span> ;<br/><b>thus </b><font color="Maroon">f'</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
the <a href="struct_0.html#U2">Zero</a> of <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="prvect_1.html#K17" target="_self">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">h'</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="txt" href="prvect_1.html#E9"><i><font color="Green">Lemma34</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:57_3_2"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font>
 <b>by </b><i><a class="ref" href="prvect_1.html#T11" target="_self">Th11</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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