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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>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM8">FinSequence</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="E1:57"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="sprect_2.html#R1">is_in_the_area_of</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:57"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="sprect_2.html#D1">SPRECT_2:def 1</a><br/>

<b>assume </b><a NAME="E3:57"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="matrix_2.html#K4">*&gt;</a></span>
 ;<br/>

<a NAME="E4:57"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#T55">FINSEQ_1:55</a></i>;<br/>
<a NAME="E5:57"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="sprect_3.html#E3:57"><i><font color="Green">E36</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:57"/><b>then </b>
<span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_4.html#T25">FINSEQ_4:25</a></i>;<br/>
<b>hence </b><a NAME="E7:57"/>
( not <span class="p1">(<span class="default"><span class="p2"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K15">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; not  <a href="pscomp_1.html#K17">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; not <span class="p1">(<span class="default"><span class="p2"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K18">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; not  <a href="pscomp_1.html#K16">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  )
 <b>by </b><i><a class="txt" href="sprect_3.html#E1:57"><i><font color="Green">E34</font></i></a>, <a class="txt" href="sprect_3.html#E2:57"><i><font color="Green">E35</font></i></a>, <a class="ref" href="sprect_2.html#D1">SPRECT_2:def 1</a></i>;<br/>


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