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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th22</font></span>: <a NAME="T22"><span class="comment"><font color="firebrick">:: LMOD_7:22</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">r</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="b3">V</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</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="b6">W</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b3">V</font> holds <br/> ( <span class="p1">(<span class="default"><font color="Olive" title="b4">a</font> <a href="lmod_7.html#K18" title="LMOD_7:func.18">/</a> <font color="Olive" title="b6">W</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">b</font> <a href="lmod_7.html#K18" title="LMOD_7:func.18">/</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="b4">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b5">b</font></span>)</span> <a href="lmod_7.html#K18" title="LMOD_7:func.18">/</a> <font color="Olive" title="b6">W</font> &amp; <font color="Olive" title="b2">r</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">a</font> <a href="lmod_7.html#K18" title="LMOD_7:func.18">/</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="b2">r</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b4">a</font></span>)</span> <a href="lmod_7.html#K18" title="LMOD_7:func.18">/</a> <font color="Olive" title="b6">W</font> )</div></div>
