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<div><span class="kw">theorem </span><a NAME="T12"><span class="comment"><font color="firebrick">:: VFUNCT_1:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">vector-distributive</a>   <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">scalar-distributive</a>   <a href="rlvect_1.html#V7" title="RLVECT_1:attr.7">scalar-associative</a>   <a href="rlvect_1.html#V8" title="RLVECT_1:attr.8">scalar-unital</a>   <a href="rlvect_1.html#L1" title="RLVECT_1:struct.1">RLSStruct</a> <br/>  for <font color="Olive" title="b3">f1</font>, <font color="Olive" title="b4">f2</font> being   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">PartFunc</a> of <font color="Olive" title="b1">C</font>,<font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b5">f3</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Olive" title="b1">C</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b5">f3</font> <a href="vfunct_1.html#K3" title="VFUNCT_1:func.3">(#)</a> <font color="Olive" title="b3">f1</font></span>)</span> <a href="vfunct_1.html#K2" title="VFUNCT_1:func.2">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">f3</font> <a href="vfunct_1.html#K3" title="VFUNCT_1:func.3">(#)</a> <font color="Olive" title="b4">f2</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b5">f3</font> <a href="vfunct_1.html#K3" title="VFUNCT_1:func.3">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f1</font> <a href="vfunct_1.html#K2" title="VFUNCT_1:func.2">-</a> <font color="Olive" title="b4">f2</font></span>)</span></div></div>
