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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th15</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: MOD_4:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</font>, <font color="Olive" title="b2">L</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b3">V</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">ModuleStr</a> over <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b4">W</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="vectsp_2.html#L1" title="VECTSP_2:struct.1">RightModStr</a> over <font color="Olive" title="b2">L</font><br/>  for <font color="Olive" title="b5">x</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b6">y</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Olive" title="b2">L</font><br/>  for <font color="Olive" title="b7">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b3">V</font><br/>  for <font color="Olive" title="b8">w</font> being   <a href="vectsp_2.html#NM4" title="VECTSP_2:NM.4">Vector</a> of <font color="Olive" title="b4">W</font>  st <font color="Olive" title="b3">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_4.html#K4" title="MOD_4:func.4">opp</a> <font color="Olive" title="b4">W</font> &amp; <font color="Olive" title="b5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">y</font> &amp; <font color="Olive" title="b7">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">w</font> holds <br/><font color="Olive" title="b8">w</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <font color="Olive" title="b6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">x</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b7">v</font></div></div>
