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<b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">q1</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>, <font color="Maroon">q2</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>assume </b><a NAME="E1:37"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">q1</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">i</font> &amp; <font color="Maroon">q2</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">i</font> &amp; <font color="Maroon">f</font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a>  &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> )
 ;<br/>

<a NAME="E2:37"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> 1,<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="topreal1.html#T31">TOPREAL1:31</a></i>;<br/>
<b>assume </b><a NAME="E3:37"/><i><font color="Green">E32</font></i>: 
 <a href="jordan5c.html#R1" target="_self">LE</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font>, <a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font>,<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> 1,<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span>
 ;<br/>

<a NAME="E4:37"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2
 
<b>by </b><i><a class="txt" href="jordan5c.html#E1:37"><i><font color="Green">E29</font></i></a>, <a class="ref" href="topreal1.html#D10">TOPREAL1:def 10</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">P</font> =  <a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font>, <font color="Maroon">Q</font> =  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">i</font> as  non <a href="xboole_0.html#V1">empty</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>by </b><i><a class="txt" href="jordan5c.html#E1:37"><i><font color="Green">E29</font></i></a>, <a class="ref" href="topreal1.html#T29">TOPREAL1:29</a></i>;<br/>
<b>consider </b><font color="Maroon">F</font> being   <a href="struct_0.html#NM6">Function</a> of <a href="topmetr.html#K5">I[01]</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> <font color="Maroon">P</font></span>)</span><b> such that </b><br/><a NAME="E7:37"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">F</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a>  &amp; <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> 1 &amp; <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="topreal1.html#D2">TOPREAL1:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon">ppi</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">pi1</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E9:37"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">ppi</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">pi1</font> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">ppi</font> &amp; <font color="Maroon">ppi</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">pi1</font> &amp; <font color="Maroon">pi1</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span><a href="rcomp_1.html#K1">.]</a></span> &amp; <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">ppi</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> &amp; <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">pi1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> )
 <b>by </b><i><a class="txt" href="jordan5c.html#E1:37"><i><font color="Green">E29</font></i></a>, <a class="txt" href="jordan5c.html#E3:37"><i><font color="Green">E32</font></i></a>, <a class="ref" href="jordan5b.html#T7">JORDAN5B:7</a></i>;<br/>
<a NAME="E10:37"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">ppi</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">dd</font> where <font color="Olive">dd</font> is   <a href="real_1.html#NM1">Real</a> : ( <font color="Maroon">ppi</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">dd</font> &amp; <font color="Olive">dd</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">pi1</font> ) </span>}</span>  &amp; <font color="Maroon">pi1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">dd</font> where <font color="Olive">dd</font> is   <a href="real_1.html#NM1">Real</a> : ( <font color="Maroon">ppi</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">dd</font> &amp; <font color="Olive">dd</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">pi1</font> ) </span>}</span>  )
 
<b>by </b><i><a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a></i>;<br/>
<a NAME="E11:37"/><b>then </b><i><font color="Green">E37</font></i>: 
( <font color="Maroon">ppi</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span><a href="rcomp_1.html#K1">.]</a></span> &amp; <font color="Maroon">pi1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span><a href="rcomp_1.html#K1">.]</a></span> )
 
<b>by </b><i><a class="ref" href="rcomp_1.html#D1">RCOMP_1:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">Poz</font> = <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span><a href="rcomp_1.html#K1">.]</a></span> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K5">I[01]</a>  <b>by </b><i><a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a>, , <a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a>, <a class="ref" href="rcomp_1.html#D1">RCOMP_1:def 1</a>, <a class="ref" href="treal_1.html#T1">TREAL_1:1</a></i>;<br/>
<b>consider </b><font color="Maroon">G</font> being   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K5">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">Poz</font></span>)</span>,<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> <font color="Maroon">Q</font></span>)</span><b> such that </b><br/><a NAME="E14:37"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">Poz</font> &amp; <font color="Maroon">G</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a>  )
 <b>by </b><i><a class="txt" href="jordan5c.html#E1:37"><i><font color="Green">E29</font></i></a>, <a class="txt" href="jordan5c.html#E3:37"><i><font color="Green">E32</font></i></a>, <a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a>, <a class="ref" href="jordan5b.html#T8">JORDAN5B:8</a></i>;<br/>
<b>set </b><font color="Maroon">Ex</font> =  <a href="treal_1.html#K3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon">H</font> = <font color="Maroon">G</font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span>;<br/>
<a NAME="E15:37"/><i><font color="Green">E39</font></i>: 
 <a href="treal_1.html#K3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 
<b>by </b><i><a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a>, <a class="ref" href="treal_1.html#T20">TREAL_1:20</a></i>;<br/>
<a NAME="E16:37"/><b>then </b><i><font color="Green">E40</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E17:37"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>
 
;<br/>
<i><font color="Green">E42</font></i>:  <a href="relset_1.html#K4">dom</a> <font color="Maroon">G</font> = 
 <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K5">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">Poz</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan5c.html#E10:37"><i><font color="Green">E36</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>
<br/>.= 
<font color="Maroon">Poz</font>
<b>by </b><i><a class="ref" href="pre_topc.html#D10">PRE_TOPC:def 10</a></i>
<br/>.= 
 <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a>, <a class="ref" href="topmetr.html#T25">TOPMETR:25</a></i>
;<br/>
<b>then </b><i><font color="Green">E43</font></i>:  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span></span>)</span> = 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jordan5c.html#E14:37"><i><font color="Green">E38</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>
<br/>.= 
 <a href="pre_topc.html#K2">[#]</a> <a href="topmetr.html#K5">I[01]</a> 
<b>by </b><i><a class="txt" href="jordan5c.html#E11:37"><i><font color="Green">E37</font></i></a>, <a class="ref" href="topmetr.html#T27">TOPMETR:27</a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> 

;<br/>
<i><font color="Green">E44</font></i>:  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span></span>)</span> = 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">G</font>
<b>by </b><i><a class="txt" href="jordan5c.html#E14:37"><i><font color="Green">E38</font></i></a>, <a class="txt" href="jordan5c.html#E16:37"><i><font color="Green">E40</font></i></a>, <a class="ref" href="relat_1.html#T47">RELAT_1:47</a></i>
<br/>.= 
 <a href="pre_topc.html#K2">[#]</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"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jordan5c.html#E10:37"><i><font color="Green">E36</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>
;<br/>
<b>then reconsider </b><font color="Maroon">H</font> = <font color="Maroon">G</font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> as   <a href="struct_0.html#NM6">Function</a> of <a href="topmetr.html#K5">I[01]</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> <font color="Maroon">Q</font></span>)</span> <b>by </b><i><a class="txt" href="jordan5c.html#E17:37"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funct_2.html#T4">FUNCT_2:4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">K1</font> =  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font>, <font color="Maroon">K2</font> = <a href="topmetr.html#K5">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">Poz</font> as    <a href="pre_topc.html#M1">SubSpace</a> of  <a href="topmetr.html#K5">I[01]</a>  <b>by </b><i><a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a>, <a class="ref" href="topmetr.html#T27">TOPMETR:27</a>, <a class="ref" href="treal_1.html#T6">TREAL_1:6</a></i>;<br/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K1</font> = 
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span><a href="rcomp_1.html#K1">.]</a></span>
<b>by </b><i><a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a>, <a class="ref" href="topmetr.html#T25">TOPMETR:25</a></i>
<br/>.= 
 <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K5">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">Poz</font></span>)</span>
<b>by </b><i><a class="ref" href="pre_topc.html#D10">PRE_TOPC:def 10</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K2</font>

;<br/>
<a NAME="E24:37"/><b>then </b>
(  <a href="topmetr.html#K5">I[01]</a>  <a href="hidden.html#R1">=</a>  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1 &amp; <a href="topmetr.html#K5">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">Poz</font> <a href="hidden.html#R1">=</a>  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> )
 
<b>by </b><i><a class="ref" href="topmetr.html#T27">TOPMETR:27</a>, <a class="ref" href="tsep_1.html#T5">TSEP_1:5</a></i>;<br/>
<a NAME="E25:37"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">H</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 
<b>by </b><i><a class="txt" href="jordan5c.html#E10:37"><i><font color="Green">E36</font></i></a>, <a class="txt" href="jordan5c.html#E11:37"><i><font color="Green">E37</font></i></a>, <a class="ref" href="tops_2.html#T71">TOPS_2:71</a></i>;<br/>
<i><font color="Green">E46</font></i>: <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 0 = 
<span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span>
<b>by </b><i><a class="ref" href="treal_1.html#D1">TREAL_1:def 1</a></i>
<br/>.= 
 <a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font>
<b>by </b><i><a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a>, <a class="ref" href="treal_1.html#T12">TREAL_1:12</a></i>
<br/>.= 
<font color="Maroon">ppi</font>
<b>by </b><i><a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a>, <a class="ref" href="treal_1.html#D1">TREAL_1:def 1</a></i>
;<br/>
<a NAME="E27:37"/>
0 <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">H</font>
 
<b>by </b><i><a class="txt" href="jordan5c.html#E17:37"><i><font color="Green">E41</font></i></a>, <a class="ref" href="borsuk_1.html#T86">BORSUK_1:86</a></i>;<br/>
<b>then </b><i><font color="Green">E47</font></i>: <font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> 0 = 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">ppi</font>
<b>by </b><i><a class="txt" href="jordan5c.html#E20:37"><i><font color="Green">E44</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a>, <a class="txt" href="jordan5c.html#E9:37"><i><font color="Green">E35</font></i></a>, <a class="txt" href="jordan5c.html#E10:37"><i><font color="Green">E36</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>
<i><font color="Green">E48</font></i>: <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 = 
<span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span>
<b>by </b><i><a class="ref" href="treal_1.html#D2">TREAL_1:def 2</a></i>
<br/>.= 
<font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> 
<b>by </b><i><a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a>, <a class="ref" href="treal_1.html#T12">TREAL_1:12</a></i>
<br/>.= 
<font color="Maroon">pi1</font>
<b>by </b><i><a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a>, <a class="ref" href="treal_1.html#D2">TREAL_1:def 2</a></i>
;<br/>
<a NAME="E30:37"/>
1 <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">H</font>
 
<b>by </b><i><a class="txt" href="jordan5c.html#E17:37"><i><font color="Green">E41</font></i></a>, <a class="ref" href="borsuk_1.html#T86">BORSUK_1:86</a></i>;<br/>
<b>then </b><i><font color="Green">E49</font></i>: <font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">pi1</font>
<b>by </b><i><a class="txt" href="jordan5c.html#E26:37"><i><font color="Green">E46</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a>, <a class="txt" href="jordan5c.html#E9:37"><i><font color="Green">E35</font></i></a>, <a class="txt" href="jordan5c.html#E10:37"><i><font color="Green">E36</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>
<a NAME="E32:37"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">Q</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>,<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="jordan5c.html#E1:37"><i><font color="Green">E29</font></i></a>, <a class="ref" href="jordan5b.html#T15">JORDAN5B:15</a></i>;<br/>
<a NAME="E33:37"/>
<font color="Maroon">q1</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">H</font>
 
<b>by </b><i><a class="txt" href="jordan5c.html#E1:37"><i><font color="Green">E29</font></i></a>, <a class="txt" href="jordan5c.html#E18:37"><i><font color="Green">E42</font></i></a>, <a class="ref" href="pre_topc.html#D10">PRE_TOPC:def 10</a></i>;<br/>
<b>then consider </b><font color="Maroon">x1'</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E35:37"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">x1'</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">H</font> &amp; <font color="Maroon">q1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1'</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E36:37"/>
<font color="Maroon">q2</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">H</font>
 
<b>by </b><i><a class="txt" href="jordan5c.html#E1:37"><i><font color="Green">E29</font></i></a>, <a class="txt" href="jordan5c.html#E18:37"><i><font color="Green">E42</font></i></a>, <a class="ref" href="pre_topc.html#D10">PRE_TOPC:def 10</a></i>;<br/>
<b>then consider </b><font color="Maroon">x2'</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E38:37"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">x2'</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">H</font> &amp; <font color="Maroon">q2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2'</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E39:37"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">x1'</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">l</font> where <font color="Olive">l</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">l</font> &amp; <font color="Olive">l</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span>  &amp; <font color="Maroon">x2'</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">l</font> where <font color="Olive">l</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">l</font> &amp; <font color="Olive">l</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span>  )
 
<b>by </b><i><a class="txt" href="jordan5c.html#E17:37"><i><font color="Green">E41</font></i></a>, <a class="txt" href="jordan5c.html#E31:37"><i><font color="Green">E49</font></i></a>, <a class="txt" href="jordan5c.html#E32:37"><i><font color="Green">E50</font></i></a>, <a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a>, <a class="ref" href="rcomp_1.html#D1">RCOMP_1:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">x1</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E41:37"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1'</font> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">x1</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 ;<br/>
<b>consider </b><font color="Maroon">x2</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E43:37"/><i><font color="Green">E99</font></i>: 
( <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2'</font> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">x2</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 <b>by </b><i/>;<br/>
<a NAME="E44:37"/><i><font color="Green">E100</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a>  &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a>  )
 
<b>by </b><i>, <a class="txt" href="jordan5c.html#E35:37"><i><font color="Green">E53</font></i></a>, <a class="ref" href="borsuk_1.html#T86">BORSUK_1:86</a></i>;<br/>
<b>reconsider </b><font color="Maroon">X1</font> = <font color="Maroon">x1</font>, <font color="Maroon">X2</font> = <font color="Maroon">x2</font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span> <b>by </b><i>, <a class="txt" href="jordan5c.html#E35:37"><i><font color="Green">E53</font></i></a>, <a class="ref" href="borsuk_1.html#T86">BORSUK_1:86</a>, <a class="ref" href="topmetr.html#T27">TOPMETR:27</a></i>;<br/>
<a NAME="E46:37"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="jordan5c.html#E14:37"><i><font color="Green">E38</font></i></a>, <a class="txt" href="jordan5c.html#E16:37"><i><font color="Green">E40</font></i></a>, <a class="txt" href="jordan5c.html#E17:37"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>
<a NAME="E47:37"/><b>then </b>
( <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <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="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font> <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="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="jordan5c.html#E15:37"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E48:37"/><b>then </b><i><font color="Green">E101</font></i>: 
( <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Poz</font> &amp; <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Poz</font> )
 
<b>by </b><i><a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a>, <a class="ref" href="topmetr.html#T25">TOPMETR:25</a></i>;<br/>
<i><font color="Green">E102</font></i>: <font color="Maroon">q1</font> = 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan5c.html#E31:37"><i><font color="Green">E49</font></i></a>, , <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan5c.html#E10:37"><i><font color="Green">E36</font></i></a>, <a class="txt" href="jordan5c.html#E38:37"><i><font color="Green">E55</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>
<i><font color="Green">E103</font></i>: <font color="Maroon">q2</font> = 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan5c.html#E32:37"><i><font color="Green">E50</font></i></a>, <a class="txt" href="jordan5c.html#E35:37"><i><font color="Green">E53</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan5c.html#E10:37"><i><font color="Green">E36</font></i></a>, <a class="txt" href="jordan5c.html#E38:37"><i><font color="Green">E55</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>
<b>reconsider </b><font color="Maroon">E1</font> = <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">X1</font>, <font color="Maroon">E2</font> = <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">X2</font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="txt" href="jordan5c.html#E38:37"><i><font color="Green">E55</font></i></a></i>;<br/>
<a NAME="E52:37"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">E1</font> &amp; <font color="Maroon">E1</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">E2</font> &amp; <font color="Maroon">E2</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 
<b>by </b><i><a class="txt" href="jordan5c.html#E38:37"><i><font color="Green">E55</font></i></a>, <a class="ref" href="borsuk_1.html#T86">BORSUK_1:86</a></i>;<br/>
<a NAME="E53:37"/><b>then </b><i><font color="Green">E104</font></i>: 
<font color="Maroon">E1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">E2</font>
 
<b>by </b><i><a class="txt" href="jordan5c.html#E2:37"><i><font color="Green">E31</font></i></a>, <a class="txt" href="jordan5c.html#E3:37"><i><font color="Green">E32</font></i></a>, <a class="txt" href="jordan5c.html#E39:37"><i><font color="Green">E56</font></i></a>, <a class="txt" href="jordan5c.html#E41:37"><i><font color="Green">E57</font></i></a>, </i>;<br/>
<a NAME="E54:37"/>
(  <a href="treal_1.html#K3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="treal_1.html#K3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> <a href="treal_1.html#K2">(#)</a> </span>)</span> is <a href="pre_topc.html#V5">continuous</a> )
 
<b>by </b><i><a class="txt" href="jordan5c.html#E11:37"><i><font color="Green">E37</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E55:37"/><b>then </b>
<font color="Maroon">x1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x2</font>
 
<b>by </b><i><a class="txt" href="jordan5c.html#E7:37"><i><font color="Green">E33</font></i></a>, <a class="txt" href="jordan5c.html#E20:37"><i><font color="Green">E44</font></i></a>, <a class="txt" href="jordan5c.html#E26:37"><i><font color="Green">E46</font></i></a>, <a class="ref" href="jordan5c.html#D1" target="_self">Def1</a>, <a class="ref" href="jordan5a.html#T16">JORDAN5A:16</a></i>;<br/>
<b>hence </b><a NAME="E56:37"/>
 <a href="jordan5c.html#R1" target="_self">LE</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font>, <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">i</font>,<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>,<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="jordan5c.html#E19:37"><i><font color="Green">E43</font></i></a>, <a class="txt" href="jordan5c.html#E25:37"><i><font color="Green">E45</font></i></a>, <a class="txt" href="jordan5c.html#E28:37"><i><font color="Green">E47</font></i></a>, <a class="txt" href="jordan5c.html#E29:37"><i><font color="Green">E48</font></i></a>, <a class="txt" href="jordan5c.html#E31:37"><i><font color="Green">E49</font></i></a>, <a class="txt" href="jordan5c.html#E32:37"><i><font color="Green">E50</font></i></a>, , <a class="txt" href="jordan5c.html#E35:37"><i><font color="Green">E53</font></i></a>, </i>;<br/>


</div>
