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<b>let </b><font color="Maroon">d</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="card_3.html#K4">product</a> <font color="Maroon">a</font>, <font color="Maroon">d'</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="card_3.html#K4">product</a> <font color="Maroon">a</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:46_1_2"/><i><font color="Green">E60</font></i>: 
for <font color="Olive">f</font>, <font color="Olive">g</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K4">product</a> <font color="Maroon">a</font><br/> for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">a</font> holds  <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="prvect_1.html#K13" target="_self">.</a> <font color="Olive">f</font>,<font color="Olive">g</font></span>)</span> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="prvect_1.html#K10" target="_self">.</a> <font color="Olive">i</font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Olive">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive">g</font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Olive">i</font></span>)</span>
 <b>and </b><br/><a NAME="E2:46_1_2"/><i><font color="Green">E61</font></i>: 
for <font color="Olive">f</font>, <font color="Olive">g</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K4">product</a> <font color="Maroon">a</font><br/> for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">a</font> holds  <span class="p1">(<span class="default"><font color="Maroon">d'</font> <a href="prvect_1.html#K13" target="_self">.</a> <font color="Olive">f</font>,<font color="Olive">g</font></span>)</span> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="prvect_1.html#K10" target="_self">.</a> <font color="Olive">i</font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Olive">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive">g</font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Olive">i</font></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1_2_1"><b>now </b></a><div class="add"><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> <font color="Maroon">a</font>, <font color="Maroon">g</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K4">product</a> <font color="Maroon">a</font>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">a</font>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="prvect_1.html#K13" target="_self">.</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="prvect_1.html#K10" target="_self">.</a> <font color="Maroon">i</font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Maroon">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">d'</font> <a href="prvect_1.html#K13" target="_self">.</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Maroon">i</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:46_1_2"/>
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d'</font>
 <b>by </b><i/>;<br/>


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