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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th22</font></span>: <a NAME="T22"><span class="comment"><font color="firebrick">:: RLVECT_X:22</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">V</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a><br/>  for <font color="Olive" title="b3">v1</font>, <font color="Olive" title="b4">v2</font>, <font color="Olive" title="b5">v3</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b2">V</font> holds <br/> ( <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlvect_x.html#K2" title="RLVECT_X:func.2">Z_Lin</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b3">v1</font>,<font color="Olive" title="b4">v2</font>,<font color="Olive" title="b5">v3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> iff  ex <font color="Olive" title="b6">a</font>, <font color="Olive" title="b7">b</font>, <font color="Olive" title="b8">c</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b3">v1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b7">b</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b4">v2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b8">c</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b5">v3</font></span>)</span> )</div></div>
