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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:29"/>
<font color="Maroon">c<sub>2</sub></font> <a href="o_ring_1.html#NR5" target="_self">is_a_product_of_squares</a> 
 ;<br/>

<a NAME="E2:29"/><b>then </b><i><font color="Green">E21</font></i>: 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="o_ring_1.html#NR6" target="_self">is_a_Sum_of_products_of_squares</a> 
 
<b>by </b><i><a class="txt" href="o_ring_1.html#E22"><i><font color="Green">Lemma19</font></i></a></i>;<br/>
<a NAME="E3:29"/>
(  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="o_ring_1.html#E4"><i><font color="Green">Lemma4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:29"/>
<font color="Maroon">c<sub>2</sub></font> <a href="o_ring_1.html#NR7" target="_self">is_a_sum_of_products_of_squares</a> 
 <b>by </b><i><a class="txt" href="o_ring_1.html#E2:29"><i><font color="Green">E21</font></i></a>, <a class="ref" href="o_ring_1.html#D9" target="_self">Def9</a></i>;<br/>


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