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<div><span class="kw">theorem </span><a NAME="T23"><span class="comment"><font color="firebrick">:: ZMODUL06:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a><br/>  for <font color="Olive" title="b2">A1</font>, <font color="Olive" title="b3">A2</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b2">A1</font> is  <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  &amp; <font color="Olive" title="b3">A2</font> is  <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  &amp; <font color="Olive" title="b2">A1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b3">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b2">A1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">A2</font> is  <a href="vectsp_7.html#NV2" title="VECTSP_7:NV.2">linearly-dependent</a>  holds <br/><span class="p1">(<span class="default"><a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <font color="Olive" title="b2">A1</font></span>)</span> <a href="vectsp_5.html#K2" title="VECTSP_5:func.2">/\</a> <span class="p1">(<span class="default"><a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <font color="Olive" title="b3">A2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a> <font color="Olive" title="b1">V</font></div></div>
