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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:56_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>1</sub></font>, <a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>3</sub></font>()]
 <b>and </b><br/><a NAME="E2:56_1"/><i><font color="Green">E44</font></i>: 
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">c<sub>1</sub></font>, <a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>2</sub></font>()
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow16.html#D6" target="_self">YELLOW16:def 6</a><br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>2</sub></font>()</span>)</span>;<br/>
<a NAME="E3:56_1"/>
 <a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>3</sub></font>() is    <a href="yellow_0.html#M1">SubRelStr</a> of  <a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>2</sub></font>()
 
<b>by </b><i><a class="txt" href="yellow16.html#E2:56"><i><font color="Green">E41</font></i></a>, <a class="ref" href="yellow16.html#T39" target="_self">Th39</a></i>;<br/>
<a NAME="E4:56_1"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>2</sub></font>()</span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>2</sub></font>()</span>)</span> <b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E6:56_1"/><i><font color="Green">E45</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>2</sub></font>()</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>()
 
<b>by </b><i><a class="ref" href="waybel_3.html#T27">WAYBEL_3:27</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><a NAME="E1:56_1_1"/>
<font color="Maroon">P<sub>1</sub></font>[ <a href="waybel_3.html#K5">pi</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">F<sub>3</sub></font>() <a href="yellow16.html#K2" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font>]
 <b>by </b><i><a class="txt" href="yellow16.html#E1:56"><i><font color="Green">E40</font></i></a>, <a class="txt" href="yellow16.html#E1:56_1"><i><font color="Green">E43</font></i></a></i>;<br/><a NAME="E2:56_1_1"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">F<sub>3</sub></font>() <a href="yellow16.html#K2" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="yellow16.html#R5" target="_self">inherits_sup_of</a>  <a href="waybel_3.html#K5">pi</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">F<sub>2</sub></font>() <a href="yellow16.html#K2" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="yellow16.html#E3:56"><i><font color="Green">E42</font></i></a></i>;<br/><a NAME="E3:56_1_1"/>
 <a href="yellow_0.html#R1">ex_sup_of</a>  <a href="waybel_3.html#K5">pi</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">F<sub>2</sub></font>() <a href="yellow16.html#K2" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="yellow16.html#E2:56_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="yellow16.html#T33" target="_self">Th33</a></i>;<br/><a NAME="E4:56_1_1"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K5">pi</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">F<sub>3</sub></font>() <a href="yellow16.html#K2" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow16.html#E2:56_1_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="yellow16.html#D6" target="_self">Def6</a></i>;<br/><b>hence </b><a NAME="E5:56_1_1"/>
<span class="p1">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>2</sub></font>()</span>)</span></span>)</span> <a href="waybel_3.html#K7">.</a> <font color="Maroon">c<sub>4</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">F<sub>3</sub></font>() <a href="yellow16.html#K2" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow16.html#E2:56_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="yellow16.html#T35" target="_self">Th35</a></i>;<br/></div><b>end;</b></div>
<a NAME="E8:56_1"/><b>then </b>
 <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>2</sub></font>()</span>)</span> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span>
 
<b>by </b><i><a class="txt" href="yellow16.html#E6:56_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="waybel_3.html#T27">WAYBEL_3:27</a></i>;<br/>
<b>hence </b><a NAME="E9:56_1"/>
 <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>2</sub></font>()</span>)</span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span>
 ;<br/>


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