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<b>let </b><font color="Maroon">K</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">K</font>, <font color="Maroon">y</font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">K</font>, <font color="Maroon">z</font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">K</font>, <font color="Maroon">u</font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K2" target="_self">opp</a> <font color="Maroon">K</font></span>)</span>, <font color="Maroon">b</font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K2" target="_self">opp</a> <font color="Maroon">K</font></span>)</span>, <font color="Maroon">c</font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K2" target="_self">opp</a> <font color="Maroon">K</font></span>)</span>, <font color="Maroon">d</font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K2" target="_self">opp</a> <font color="Maroon">K</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:12"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/>

<a NAME="E2:12"/><b>then </b>
( <font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c</font> &amp; <font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="group_1.html#K1">*</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font> &amp; <font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="group_1.html#K1">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font> &amp; <font color="Maroon">z</font> <a href="group_1.html#K1">*</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:12"/>
( <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">y</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c</font> &amp; <font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">y</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="group_1.html#K1">*</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font> &amp; <font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">y</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="group_1.html#K1">*</a> <font color="Maroon">u</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span> )
 <b>by </b><i>, </i>;<br/>


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