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<b>let </b><font color="Maroon" title="c1">R</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Scalar</a> of <font color="Maroon" title="c1">R</font>;<br/>



<b>assume </b><a NAME="E1:39"/>
<font color="Maroon" title="c2">x</font> <a href="o_ring_1.html#NR5" title="O_RING_1:NR.5">is_a_product_of_squares</a> 
 ;<br/>

<a NAME="E2:39"/><b>then </b><i><font color="Green" title="E29">A1</font></i>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="o_ring_1.html#NR8" title="O_RING_1:NR.8">is_an_Amalgam_of_squares</a> 
 
<b>by </b><i><a class="txt" href="o_ring_1.html#E30"><i><font color="Green" title="E27">Lm19</font></i></a></i>;<br/>
<a NAME="E3:39"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> )
 
<b>by </b><i><a class="txt" href="o_ring_1.html#E4"><i><font color="Green" title="E4">Lm4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:39"/>
<font color="Maroon" title="c2">x</font> <a href="o_ring_1.html#NR9" title="O_RING_1:NR.9">is_an_amalgam_of_squares</a> 
 <b>by </b><i><a class="txt" href="o_ring_1.html#E2:39"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="o_ring_1.html#D11" target="_self" title="O_RING_1:def.11">Def11</a></i>;<br/>


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