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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th17</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: HAHNBAN1:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> <br/>  for <font color="Olive" title="b2">V</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">ModuleStr</a> over <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b3">r</font>, <font color="Olive" title="b4">s</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b5">f</font> being   <a href="hahnban1.html#NM1" title="HAHNBAN1:NM.1">Functional</a> of <font color="Olive" title="b2">V</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">r</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b4">s</font></span>)</span> <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <font color="Olive" title="b5">f</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">r</font> <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">s</font> <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <font color="Olive" title="b5">f</font></span>)</span></div></div>
