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<b>let </b><font color="Maroon">R1</font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">R2</font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/>



<a NAME="E1:76"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">R1</font><br/> for <font color="Olive">p</font>, <font color="Olive">q</font> being  <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">R2</font><br/> for <font color="Olive">v</font>, <font color="Olive">w</font> being  <a href="vectsp_2.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp_2.html#K9" target="_self">BiModule</a> <font color="Maroon">R1</font>,<font color="Maroon">R2</font></span>)</span> holds <br/> ( <font color="Olive">x</font> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Olive">v</font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">w</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">v</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">w</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">y</font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Olive">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">v</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">y</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">v</font></span>)</span> &amp; <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="vectsp_1.html#K6">*</a> <font color="Olive">v</font> <a href="hidden.html#R1">=</a> <font color="Olive">x</font> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Olive">y</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">v</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R1</font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Olive">v</font> <a href="hidden.html#R1">=</a> <font color="Olive">v</font> &amp; <span class="p1">(<span class="default"><font color="Olive">v</font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">w</font></span>)</span> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">v</font> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">p</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">w</font> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">p</font></span>)</span> &amp; <font color="Olive">v</font> <a href="vectsp_2.html#K6" target="_self">*</a> <span class="p1">(<span class="default"><font color="Olive">p</font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">q</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">v</font> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">p</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">v</font> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">q</font></span>)</span> &amp; <font color="Olive">v</font> <a href="vectsp_2.html#K6" target="_self">*</a> <span class="p1">(<span class="default"><font color="Olive">q</font> <a href="group_1.html#K1">*</a> <font color="Olive">p</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">v</font> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">q</font></span>)</span> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">p</font> &amp; <font color="Olive">v</font> <a href="vectsp_2.html#K6" target="_self">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">v</font> &amp; <font color="Olive">x</font> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Olive">v</font> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">p</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">v</font></span>)</span> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">p</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:76"/>
 <a href="vectsp_2.html#K9" target="_self">BiModule</a> <font color="Maroon">R1</font>,<font color="Maroon">R2</font> is   <a href="vectsp_2.html#NM8">BiMod</a> of <font color="Maroon">R1</font>,<font color="Maroon">R2</font>
 <b>by </b><i>, <a class="txt" href="vectsp_2.html#E24"><i><font color="Green">Lemma30</font></i></a>, <a class="ref" href="vectsp_1.html#D26">VECTSP_1:def 26</a></i>;<br/>


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