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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:49"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="topreal1.html#V1">special</a>
 <b>and </b><br/><a NAME="E2:49"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="sppol_1.html#V3" target="_self">alternating</a>
 <b>and </b><br/><a NAME="E3:49"/><i><font color="Green">E37</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E4:49"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E5:49"/><i><font color="Green">E39</font></i>: 
(  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="sppol_1.html#V2" target="_self">vertical</a> &amp; not <!--HUMANRECFAILED-->(  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="sppol_1.html#V2" target="_self">vertical</a> &amp;  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> is <a href="sppol_1.html#V1" target="_self">horizontal</a> ) implies (  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="sppol_1.html#V1" target="_self">horizontal</a> &amp;  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> is <a href="sppol_1.html#V2" target="_self">vertical</a> ) )
 
<b>by </b><i><a class="txt" href="sppol_1.html#E1:49"><i><font color="Green">E35</font></i></a>, <a class="txt" href="sppol_1.html#E2:49"><i><font color="Green">E36</font></i></a>, <a class="txt" href="sppol_1.html#E3:49"><i><font color="Green">E37</font></i></a>, <a class="txt" href="sppol_1.html#E4:49"><i><font color="Green">E38</font></i></a>, <a class="ref" href="sppol_1.html#T55" target="_self">Th55</a></i>;<br/>
<a NAME="E6:49"/>
(  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="sppol_1.html#V1" target="_self">horizontal</a> &amp; not <!--HUMANRECFAILED-->(  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="sppol_1.html#V2" target="_self">vertical</a> &amp;  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> is <a href="sppol_1.html#V1" target="_self">horizontal</a> ) implies (  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="sppol_1.html#V1" target="_self">horizontal</a> &amp;  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> is <a href="sppol_1.html#V2" target="_self">vertical</a> ) )
 
<b>by </b><i><a class="txt" href="sppol_1.html#E1:49"><i><font color="Green">E35</font></i></a>, <a class="txt" href="sppol_1.html#E2:49"><i><font color="Green">E36</font></i></a>, <a class="txt" href="sppol_1.html#E3:49"><i><font color="Green">E37</font></i></a>, <a class="txt" href="sppol_1.html#E4:49"><i><font color="Green">E38</font></i></a>, <a class="ref" href="sppol_1.html#T56" target="_self">Th56</a></i>;<br/>
<b>hence </b><a NAME="E7:49"/>
( (  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="sppol_1.html#V2" target="_self">vertical</a> &amp;  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> is <a href="sppol_1.html#V1" target="_self">horizontal</a> ) or (  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="sppol_1.html#V1" target="_self">horizontal</a> &amp;  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> is <a href="sppol_1.html#V2" target="_self">vertical</a> ) )
 <b>by </b><i><a class="txt" href="sppol_1.html#E1:49"><i><font color="Green">E35</font></i></a>, <a class="txt" href="sppol_1.html#E5:49"><i><font color="Green">E39</font></i></a>, <a class="ref" href="sppol_1.html#T41" target="_self">Th41</a></i>;<br/>


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