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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th19</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: HAHNBAN1:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="vectsp_1.html#V8" title="VECTSP_1:attr.8">vector-distributive</a>   <a href="vectsp_1.html#V9" title="VECTSP_1:attr.9">scalar-distributive</a>   <a href="vectsp_1.html#V10" title="VECTSP_1:attr.10">scalar-associative</a>   <a href="vectsp_1.html#V11" title="VECTSP_1:attr.11">scalar-unital</a>   <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">ModuleStr</a> over  <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> <br/>  for <font color="Olive" title="b2">F</font> being   <a href="hahnban1.html#NM3" title="HAHNBAN1:NM.3">RFunctional</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b2">F</font> is  <a href="hahnban1.html#V5" title="HAHNBAN1:attr.5">Real_homogeneous</a>  holds <br/> for <font color="Olive" title="b3">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b4">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds  <font color="Olive" title="b2">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Olive" title="b4">r</font></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b3">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">r</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b3">v</font></span>)</span></span>)</span></div></div>
