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<b>let </b><font color="Maroon">c<sub>21</sub></font> be   <a href="realset2.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">c<sub>22</sub></font>, <font color="Maroon">c<sub>23</sub></font>, <font color="Maroon">c<sub>24</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2" target="_self">suppf</a> <font color="Maroon">c<sub>21</sub></font>;<br/>



<a NAME="E1:51"/>
<span class="p1">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font></span><a href="tarski.html#K4">]</a></span> is    <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2" target="_self">suppf</a> <font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="ref" href="realset2.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E2:51"/><b>then </b><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K7" target="_self">compf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p4"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a>  <a href="realset2.html#K4" target="_self">ndf</a> <font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="ref" href="realset2.html#D14" target="_self">Def14</a></i>;<br/>
<i><font color="Green">E71</font></i>: <span class="p1">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K7" target="_self">compf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>24</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>24</sub></font> = 
<span class="p1">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K7" target="_self">compf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>24</sub></font></span>)</span>,<font color="Maroon">c<sub>24</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#T4" target="_self">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>24</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K7" target="_self">compf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>24</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#T5" target="_self">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>,<span class="p1">(<span class="default"><a href="realset2.html#K4" target="_self">ndf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#D14" target="_self">Def14</a></i>
<br/>.= 
<font color="Maroon">c<sub>23</sub></font>
<b>by </b><i><a class="ref" href="realset2.html#T6" target="_self">Th6</a></i>
;<br/>
<span class="p1">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K7" target="_self">compf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>24</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="realset2.html#K7" target="_self">compf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>24</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K7" target="_self">compf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="realset2.html#E2:51"><i><font color="Green">E70</font></i></a>, <a class="ref" href="realset2.html#T6" target="_self">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="realset2.html#K7" target="_self">compf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>24</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K7" target="_self">compf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#T4" target="_self">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>23</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K7" target="_self">compf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p4"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="realset2.html#E3:51"><i><font color="Green">E71</font></i></a>, <a class="ref" href="realset2.html#T3" target="_self">Th3</a></i>
;<br/>
<b>hence </b><a NAME="E5:51"/>
<span class="p1">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>23</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="realset2.html#K7" target="_self">compf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>24</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K3" target="_self">odf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>23</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K7" target="_self">compf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="realset2.html#K5" target="_self">omf</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p4"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
 ;<br/>


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