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<b>let </b><font color="Maroon" title="c1">R</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font>;<br/>





<b>assume </b><a NAME="E1:150"/><i><font color="Green" title="E101">A1</font></i>: 
( <font color="Maroon" title="c2">x</font> <a href="o_ring_1.html#NR1" title="O_RING_1:NR.1">is_a_square</a>  &amp; <font color="Maroon" title="c3">y</font> <a href="o_ring_1.html#NR7" title="O_RING_1:NR.7">is_a_sum_of_products_of_squares</a>  )
 ;<br/>

<a NAME="E2:150"/><b>then </b><i><font color="Green" title="E102">A2</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="o_ring_1.html#NR13" title="O_RING_1:NR.13">is_generated_from_squares</a> 
 
<b>by </b><i><a class="txt" href="o_ring_1.html#E46"><i><font color="Green" title="E43">Lm31</font></i></a></i>;<br/>
<a NAME="E3:150"/>
<font color="Maroon" title="c3">y</font> <a href="o_ring_1.html#NR13" title="O_RING_1:NR.13">is_generated_from_squares</a> 
 
<b>by </b><i><a class="txt" href="o_ring_1.html#E1:150"><i><font color="Green" title="E101">A1</font></i></a>, <a class="txt" href="o_ring_1.html#E70"><i><font color="Green" title="E67">Lm54</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:150"/>
<font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">y</font> <a href="o_ring_1.html#NR13" title="O_RING_1:NR.13">is_generated_from_squares</a> 
 <b>by </b><i><a class="txt" href="o_ring_1.html#E2:150"><i><font color="Green" title="E102">A2</font></i></a>, <a class="txt" href="o_ring_1.html#E149"><i><font color="Green" title="E100">Lm87</font></i></a></i>;<br/>


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