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<span class="kw">let </span><font color="Maroon" title="c1">R1</font>, <font color="Maroon" title="c2">R2</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">BiModule</a> (<font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font>) is   <a href="vectsp_2.html#NM8" title="VECTSP_2:NM.8">BiMod</a> of <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font></span><br/>



<a NAME="E1:65"/>
 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">R1</font><br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c2">R2</font><br/>  for <font color="Olive" title="b5">v</font>, <font color="Olive" title="b6">w</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp_2.html#K6" title="VECTSP_2:func.6">BiModule</a> (<font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font>)</span>)</span> holds <br/> ( <font color="Olive" title="b1">x</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b6">w</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b5">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b6">w</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b5">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b5">v</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b5">v</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">R1</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">v</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b6">w</font></span>)</span> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Olive" title="b3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">w</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Olive" title="b3">p</font></span>)</span> &amp; <font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b4">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Olive" title="b4">q</font></span>)</span> &amp; <font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">q</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Olive" title="b4">q</font></span>)</span> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Olive" title="b3">p</font> &amp; <font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">R2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">v</font> &amp; <font color="Olive" title="b1">x</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b5">v</font></span>)</span> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Olive" title="b3">p</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="vectsp_2.html#E42"><span class="lab"><font color="Green" title="E26">Lm9</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:65"/>
 <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">BiModule</a> (<font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font>) is   <a href="vectsp_2.html#NM8" title="VECTSP_2:NM.8">BiMod</a> of <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_2.html#D9" target="_self" title="VECTSP_2:def.9">Def23</a>, <a class="ref" href="vectsp_2.html#D10" target="_self" title="VECTSP_2:def.10">Def24</a>, <a class="ref" href="vectsp_1.html#D14" title="VECTSP_1:def.14">VECTSP_1:def 14</a>, <a class="ref" href="vectsp_1.html#D15" title="VECTSP_1:def.15">VECTSP_1:def 15</a>, <a class="ref" href="vectsp_1.html#D16" title="VECTSP_1:def.16">VECTSP_1:def 16</a>, <a class="ref" href="vectsp_1.html#D17" title="VECTSP_1:def.17">VECTSP_1:def 17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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