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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/>







<b>assume </b><a NAME="E1:50"/><i><font color="Green">E32</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_1.html#K2" target="_self">Indices</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K11" target="_self">0.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:50"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25" target="_self">Th25</a></i>;<br/>
<a NAME="E3:50"/><b>then </b><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E4:50"/><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><a href="matrix_1.html#K11" target="_self">0.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="matrix_1.html#E3:50"><i><font color="Green">E33</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<a NAME="E5:50"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="matrix_1.html#E3:50"><i><font color="Green">E33</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<b>hence </b><a NAME="E6:50"/>
<span class="p1">(<span class="default"><a href="matrix_1.html#K11" target="_self">0.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="matrix_1.html#K3" target="_self">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="matrix_1.html#E1:50"><i><font color="Green">E32</font></i></a>, <a class="txt" href="matrix_1.html#E4:50"><i><font color="Green">E34</font></i></a>, <a class="ref" href="matrix_1.html#D6" target="_self">Def6</a></i>;<br/>


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