<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>22</sub></font> be   <a href="topreal2.html#NM1">Simple_closed_curve</a>;<br/>

<b>assume </b><a NAME="E1:152"/><i><font color="Green">E175</font></i>: 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,0</span><a href="euclid.html#K23">]|</a></span>,<span class="p1"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span> <a href="jordan24.html#R1">realize-max-dist-in</a> <font color="Maroon">c<sub>22</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>23</sub></font>, <font color="Maroon">c<sub>24</sub></font> being  <a href="compts_1.html#V6">compact</a> <a href="jordan21.html#V1">with_the_max_arc</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E3:152"/><i><font color="Green">E176</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="topreal1.html#R1">is_an_arc_of</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,0</span><a href="euclid.html#K23">]|</a></span>,<span class="p1"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span>
 <b>and </b><br/><a NAME="E4:152"/><i><font color="Green">E177</font></i>: 
<font color="Maroon">c<sub>24</sub></font> <a href="topreal1.html#R1">is_an_arc_of</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,0</span><a href="euclid.html#K23">]|</a></span>,<span class="p1"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span>
 <b>and </b><br/><a NAME="E5:152"/><i><font color="Green">E178</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>24</sub></font>
 <b>and </b><br/><a NAME="E6:152"/><i><font color="Green">E179</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,0</span><a href="euclid.html#K23">]|</a></span>,<span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span><a href="domain_1.html#K7">}</a></span>
 <b>and </b><br/><a NAME="E7:152"/><i><font color="Green">E180</font></i>: 
 <a href="jordan21.html#K1">UMP</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 <b>and </b><br/><a NAME="E8:152"/><i><font color="Green">E181</font></i>: 
 <a href="jordan21.html#K2">LMP</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font>
 <b>and </b><br/><a NAME="E9:152"/><i><font color="Green">E182</font></i>: 
 <a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">c<sub>23</sub></font>
 <b>and </b><br/><a NAME="E10:152"/><i><font color="Green">E183</font></i>: 
 <a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="jordan.html#E196"><i><font color="Green">Lemma171</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>25</sub></font> =  <a href="jordan21.html#K2">LMP</a> <font color="Maroon">c<sub>23</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>26</sub></font> = <span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><a href="jordan21.html#K2">LMP</a> <font color="Maroon">c<sub>23</sub></font></span>)</span>,<span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 3</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>24</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>27</sub></font> =  <a href="jordan21.html#K1">UMP</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p3">(<span class="default"><a href="jordan21.html#K2">LMP</a> <font color="Maroon">c<sub>23</sub></font></span>)</span>,<span class="p3"><a href="euclid.html#K23">|[</a><span class="default">0,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> 3</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>24</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>28</sub></font> = <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan21.html#K1">UMP</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p5">(<span class="default"><a href="jordan21.html#K2">LMP</a> <font color="Maroon">c<sub>23</sub></font></span>)</span>,<span class="p5"><a href="euclid.html#K23">|[</a><span class="default">0,<span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> 3</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>24</sub></font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><a href="jordan21.html#K2">LMP</a> <font color="Maroon">c<sub>23</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E11:152"/><i><font color="Green">E184</font></i>: 
 <a href="connsp_1.html#K1">skl</a> <span class="p1">(<span class="default"><a href="connsp_3.html#K2">Down</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan21.html#K1">UMP</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="jordan21.html#K2">LMP</a> <font color="Maroon">c<sub>23</sub></font></span>)</span>,<span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 3</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>24</sub></font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><a href="jordan21.html#K2">LMP</a> <font color="Maroon">c<sub>23</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="connsp_1.html#R3">is_a_component_of</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="connsp_1.html#T43">CONNSP_1:43</a></i>;<br/>
<a NAME="E12:152"/><i><font color="Green">E185</font></i>: 
 <a href="connsp_1.html#K1">skl</a> <span class="p1">(<span class="default"><a href="connsp_3.html#K2">Down</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan21.html#K1">UMP</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="jordan21.html#K2">LMP</a> <font color="Maroon">c<sub>23</sub></font></span>)</span>,<span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 3</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>24</sub></font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><a href="jordan21.html#K2">LMP</a> <font color="Maroon">c<sub>23</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="jordan2c.html#K1">BDD</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E1:152"><i><font color="Green">E175</font></i></a>, <a class="txt" href="jordan.html#E3:152"><i><font color="Green">E176</font></i></a>, <a class="txt" href="jordan.html#E4:152"><i><font color="Green">E177</font></i></a>, <a class="txt" href="jordan.html#E5:152"><i><font color="Green">E178</font></i></a>, <a class="txt" href="jordan.html#E6:152"><i><font color="Green">E179</font></i></a>, <a class="txt" href="jordan.html#E7:152"><i><font color="Green">E180</font></i></a>, <a class="txt" href="jordan.html#E8:152"><i><font color="Green">E181</font></i></a>, <a class="txt" href="jordan.html#E9:152"><i><font color="Green">E182</font></i></a>, <a class="txt" href="jordan.html#E10:152"><i><font color="Green">E183</font></i></a>, <a class="ref" href="jordan.html#T96" target="_self">Th96</a></i>;<br/>
<b>thus </b><a NAME="E13:152"/>
<font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="jordan1.html#D2">JORDAN1:def 2</a><br/>

<b>take </b><font color="Maroon">c<sub>29</sub></font> =  <a href="jordan2c.html#K2">UBD</a> <font color="Maroon">c<sub>22</sub></font>;<br/>

<b>take </b><font color="Maroon">c<sub>30</sub></font> =  <a href="jordan2c.html#K1">BDD</a> <font color="Maroon">c<sub>22</sub></font>;<br/>

<b>thus </b><a NAME="E14:152"/>
<font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>30</sub></font>
 <b>by </b><i><a class="ref" href="jordan2c.html#T31">JORDAN2C:31</a></i>;<br/>

<b>thus </b><a NAME="E15:152"/>
<font color="Maroon">c<sub>29</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>30</sub></font>
 <b>by </b><i><a class="ref" href="jordan2c.html#T28">JORDAN2C:28</a></i>;<br/>

<a NAME="E16:152"/><i><font color="Green">E186</font></i>: 
 <a href="connsp_1.html#K1">skl</a> <span class="p1">(<span class="default"><a href="connsp_3.html#K2">Down</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan21.html#K1">UMP</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="jordan21.html#K2">LMP</a> <font color="Maroon">c<sub>23</sub></font></span>)</span>,<span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 3</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>24</sub></font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><a href="jordan21.html#K2">LMP</a> <font color="Maroon">c<sub>23</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pre_topc.html#K1">{}</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan.html#E11:152"><i><font color="Green">E184</font></i></a>, <a class="ref" href="connsp_1.html#T34">CONNSP_1:34</a></i>;<br/>
<a NAME="E17:152"/>
<font color="Maroon">c<sub>29</sub></font> <a href="connsp_1.html#R4">is_a_component_of</a> <font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="jordan2c.html#T132">JORDAN2C:132</a></i>;<br/>
<a NAME="E18:152"/><b>then </b><i><font color="Green">E187</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>29</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="connsp_1.html#R3">is_a_component_of</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="connsp_1.html#D6">CONNSP_1:def 6</a></i>;<br/>
<b>then </b><font color="Maroon">c<sub>22</sub></font> = 
 <a href="tops_1.html#K2">Fr</a> <font color="Maroon">c<sub>29</sub></font>
<b>by </b><i><a class="txt" href="jordan.html#E12:152"><i><font color="Green">E185</font></i></a>, <a class="txt" href="jordan.html#E16:152"><i><font color="Green">E186</font></i></a>, <a class="txt" href="jordan.html#E94"><i><font color="Green">Lemma81</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>29</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span>

;<br/>
<a NAME="E20:152"/><b>then </b><i><font color="Green">E188</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<font color="Maroon">c<sub>22</sub></font> = 
 <a href="tops_1.html#K2">Fr</a> <font color="Maroon">c<sub>30</sub></font>
<b>by </b><i><a class="txt" href="jordan.html#E12:152"><i><font color="Green">E185</font></i></a>, <a class="txt" href="jordan.html#E11:152"><i><font color="Green">E184</font></i></a>, <a class="txt" href="jordan.html#E16:152"><i><font color="Green">E186</font></i></a>, <a class="txt" href="jordan.html#E94"><i><font color="Green">Lemma81</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>30</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span>

;<br/>
<a NAME="E22:152"/><b>then </b><i><font color="Green">E189</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>30</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E23:152"/>
<font color="Maroon">c<sub>30</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="jordan2c.html#T29">JORDAN2C:29</a></i>;<br/>
<a NAME="E24:152"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>30</sub></font>
 
<b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/>
<a NAME="E25:152"/><b>then </b><i><font color="Green">E190</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>30</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">c<sub>30</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E22:152"><i><font color="Green">E189</font></i></a>, <a class="ref" href="xboole_1.html#T86">XBOOLE_1:86</a></i>;<br/>
<a NAME="E26:152"/><i><font color="Green">E191</font></i>: 
<font color="Maroon">c<sub>29</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>30</sub></font>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T28">JORDAN2C:28</a></i>;<br/>
<a NAME="E27:152"/><b>then </b>
<font color="Maroon">c<sub>30</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/>
<a NAME="E28:152"/><b>then </b><i><font color="Green">E192</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>30</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="tops_1.html#T31">TOPS_1:31</a></i>;<br/>
<a NAME="E29:152"/>
<font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>30</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="jordan2c.html#T31">JORDAN2C:31</a></i>;<br/>
<a NAME="E30:152"/><b>then </b>
<font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>30</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/>
<a NAME="E31:152"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#R1">misses</a> <font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T70">XBOOLE_1:70</a></i>;<br/>
<a NAME="E32:152"/><b>then </b><i><font color="Green">E193</font></i>: 
<font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>22</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E26:152"><i><font color="Green">E191</font></i></a>, <a class="ref" href="xboole_1.html#T70">XBOOLE_1:70</a></i>;<br/>
<a NAME="E33:152"/>
<font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>29</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="jordan2c.html#T31">JORDAN2C:31</a></i>;<br/>
<a NAME="E34:152"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>29</sub></font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/>
<a NAME="E35:152"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>29</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E36:152"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>29</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T53">XBOOLE_1:53</a></i>;<br/>
<a NAME="E37:152"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>29</sub></font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>;<br/>
<a NAME="E38:152"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T53">XBOOLE_1:53</a></i>;<br/>
<a NAME="E39:152"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E40:152"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>30</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E28:152"><i><font color="Green">E192</font></i></a>, <a class="txt" href="jordan.html#E32:152"><i><font color="Green">E193</font></i></a>, <a class="ref" href="subset_1.html#T46">SUBSET_1:46</a></i>;<br/>
<a NAME="E41:152"/><b>then </b><i><font color="Green">E194</font></i>: 
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>30</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">c<sub>30</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T43">XBOOLE_1:43</a></i>;<br/>
<a NAME="E42:152"/>
<font color="Maroon">c<sub>29</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="jordan2c.html#T30">JORDAN2C:30</a></i>;<br/>
<a NAME="E43:152"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#R1">misses</a> <font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/>
<a NAME="E44:152"/><b>then </b><i><font color="Green">E195</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>29</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E20:152"><i><font color="Green">E188</font></i></a>, <a class="ref" href="xboole_1.html#T86">XBOOLE_1:86</a></i>;<br/>
<a NAME="E45:152"/>
<font color="Maroon">c<sub>29</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="txt" href="jordan.html#E26:152"><i><font color="Green">E191</font></i></a>, <a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/>
<a NAME="E46:152"/><b>then </b><i><font color="Green">E196</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>29</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="tops_1.html#T31">TOPS_1:31</a></i>;<br/>
<a NAME="E47:152"/>
<font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>29</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="jordan2c.html#T31">JORDAN2C:31</a></i>;<br/>
<a NAME="E48:152"/><b>then </b>
<font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>29</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/>
<a NAME="E49:152"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>30</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T70">XBOOLE_1:70</a></i>;<br/>
<a NAME="E50:152"/><b>then </b><i><font color="Green">E197</font></i>: 
<font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>22</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>30</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E26:152"><i><font color="Green">E191</font></i></a>, <a class="ref" href="xboole_1.html#T70">XBOOLE_1:70</a></i>;<br/>
<a NAME="E51:152"/>
<font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>30</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="jordan2c.html#T31">JORDAN2C:31</a></i>;<br/>
<a NAME="E52:152"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>30</sub></font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/>
<a NAME="E53:152"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>30</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E54:152"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>30</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T53">XBOOLE_1:53</a></i>;<br/>
<a NAME="E55:152"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>30</sub></font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>;<br/>
<a NAME="E56:152"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T53">XBOOLE_1:53</a></i>;<br/>
<a NAME="E57:152"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>30</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E58:152"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>29</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>29</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E46:152"><i><font color="Green">E196</font></i></a>, <a class="txt" href="jordan.html#E50:152"><i><font color="Green">E197</font></i></a>, <a class="ref" href="subset_1.html#T46">SUBSET_1:46</a></i>;<br/>
<a NAME="E59:152"/><b>then </b>
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>29</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">c<sub>29</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T43">XBOOLE_1:43</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>29</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">c<sub>29</sub></font> = 
<font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="jordan.html#E44:152"><i><font color="Green">E195</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>30</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">c<sub>30</sub></font>
<b>by </b><i><a class="txt" href="jordan.html#E25:152"><i><font color="Green">E190</font></i></a>, <a class="txt" href="jordan.html#E41:152"><i><font color="Green">E194</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>
;<br/><br/>

<b>thus </b><a NAME="E61:152"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>29</sub></font> or  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>30</sub></font> or ( <font color="Olive">b<sub>1</sub></font> <a href="connsp_1.html#R3">is_a_component_of</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="connsp_1.html#R3">is_a_component_of</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>22</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jordan.html#E12:152"><i><font color="Green">E185</font></i></a>, <a class="txt" href="jordan.html#E18:152"><i><font color="Green">E187</font></i></a>, <a class="ref" href="connsp_1.html#T43">CONNSP_1:43</a></i>;<br/>


</div>
