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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E3">Th2</font></span>: <a NAME="T2"><span class="comment"><font color="firebrick">:: RUSUB_4:2</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a><br/>  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font>  st  <a href="bhsp_1.html#G1" title="BHSP_1:aggr.1">UNITSTR</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">V</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Olive" title="b1">V</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b1">V</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Olive" title="b1">V</font>, the <a href="bhsp_1.html#U1" title="BHSP_1:sel.1">scalar</a> of <font color="Olive" title="b1">V</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rusub_3.html#K1" title="RUSUB_3:func.1">Lin</a> <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b3">B</font> is  <a href="rlvect_3.html#V1" title="RLVECT_3:attr.1">linearly-independent</a>  holds <br/>(  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b3">B</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b2">A</font> &amp;  ex <font color="Olive" title="b4">C</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font> st <br/>( <font color="Olive" title="b4">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">A</font> &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b2">A</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b3">B</font></span>)</span> &amp;  <a href="bhsp_1.html#G1" title="BHSP_1:aggr.1">UNITSTR</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">V</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Olive" title="b1">V</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b1">V</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Olive" title="b1">V</font>, the <a href="bhsp_1.html#U1" title="BHSP_1:sel.1">scalar</a> of <font color="Olive" title="b1">V</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rusub_3.html#K1" title="RUSUB_3:func.1">Lin</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">B</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b4">C</font></span>)</span> ) )</div></div>
