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<b>let </b><font color="Maroon">D</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="vectsp_1.html#L3" target="_self">doubleLoopStr</a> ;<br/>

<b>assume </b><a NAME="E1:26_2_1"/>
( ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">D</font> holds  <span class="p1">(<span class="default"><font color="Olive">b</font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">c</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b</font> <a href="group_1.html#K1">*</a> <font color="Olive">a</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">c</font> <a href="group_1.html#K1">*</a> <font color="Olive">a</font></span>)</span> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">D</font> holds  <font color="Olive">a</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Olive">b</font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">c</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">c</font></span>)</span> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_1.html#D11" target="_self">VECTSP_1:def 11</a>,<a class="ref" href="vectsp_1.html#D12" target="_self">VECTSP_1:def 12</a><br/>

<b>hence </b><a NAME="E2:26_2_1"/>
for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">D</font> holds <br/> ( <font color="Olive">x</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Olive">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">z</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="group_1.html#K1">*</a> <font color="Olive">y</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="group_1.html#K1">*</a> <font color="Olive">z</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">z</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">y</font> <a href="group_1.html#K1">*</a> <font color="Olive">x</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">z</font> <a href="group_1.html#K1">*</a> <font color="Olive">x</font></span>)</span> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_1.html#D18" target="_self">VECTSP_1:def 18</a><br/>


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