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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font>  st <font color="Olive" title="b1">x</font> is <a href="o_ring_1.html#V9" title="O_RING_1:attr.9">being_an_amalgam_of_squares</a> &amp; <font color="Olive" title="b2">y</font> is <a href="o_ring_1.html#V13" title="O_RING_1:attr.13">generated_from_squares</a> holds <br/><font color="Olive" title="b1">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b2">y</font> is <a href="o_ring_1.html#V13" title="O_RING_1:attr.13">generated_from_squares</a></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> is <a href="o_ring_1.html#V9" title="O_RING_1:attr.9">being_an_amalgam_of_squares</a> &amp; <font color="Maroon" title="c3">y</font> is <a href="o_ring_1.html#V13" title="O_RING_1:attr.13">generated_from_squares</a> implies <font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c3">y</font> is <a href="o_ring_1.html#V13" title="O_RING_1:attr.13">generated_from_squares</a> )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:107"/><i><font color="Green" title="E89">A1</font></i>: 
<font color="Maroon" title="c2">x</font> is <a href="o_ring_1.html#V9" title="O_RING_1:attr.9">being_an_amalgam_of_squares</a>
 <b>and </b><br/><a NAME="E2:107"/><i><font color="Green" title="E90">A2</font></i>: 
<font color="Maroon" title="c3">y</font> is <a href="o_ring_1.html#V13" title="O_RING_1:attr.13">generated_from_squares</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c3">y</font> is <a href="o_ring_1.html#V13" title="O_RING_1:attr.13">generated_from_squares</a></span><br/>

<a NAME="E3:107"/>
<font color="Maroon" title="c2">x</font> is <a href="o_ring_1.html#V13" title="O_RING_1:attr.13">generated_from_squares</a>
 
<b>by </b><i><a class="txt" href="#E1:107"><i><font color="Green" title="E89">A1</font></i></a>, <a class="txt" href="o_ring_1.html#E55"><i><font color="Green" title="E52">Lm40</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:107"/>
<font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c3">y</font> is <a href="o_ring_1.html#V13" title="O_RING_1:attr.13">generated_from_squares</a>
 <b>by </b><i><a class="txt" href="#E2:107"><i><font color="Green" title="E90">A2</font></i></a>, <a class="txt" href="o_ring_1.html#E85"><i><font color="Green" title="E77">Lm64</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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