<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T7"><span class="comment"><font color="firebrick">:: O_RING_1:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   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/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Olive" title="b1">R</font>  st ( ( <font color="Olive" title="b2">x</font> is  <a href="o_ring_1.html#V1" title="O_RING_1:attr.1">being_a_square</a>  &amp; <font color="Olive" title="b3">y</font> is  <a href="o_ring_1.html#V1" title="O_RING_1:attr.1">being_a_square</a>  ) or ( <font color="Olive" title="b2">x</font> is  <a href="o_ring_1.html#V3" title="O_RING_1:attr.3">being_a_sum_of_squares</a>  &amp; <font color="Olive" title="b3">y</font> is  <a href="o_ring_1.html#V1" title="O_RING_1:attr.1">being_a_square</a>  ) ) holds <br/><font color="Olive" title="b2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">y</font> is  <a href="o_ring_1.html#V3" title="O_RING_1:attr.3">being_a_sum_of_squares</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="o_ring_1.html#E76"><span class="lab"><font color="Green" title="E57">Lm56</font></span></a>, <a class="txt" href="o_ring_1.html#E82"><span class="lab"><font color="Green" title="E63">Lm62</font></span></a></span>;<br/></div></div>
