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<div><span class="kw">theorem </span><a NAME="T47"><span class="comment"><font color="firebrick">:: ZMODLAT1:47</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#L1" title="VECTSP_1:struct.1">ModuleStr</a> over  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> <br/>  for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font>, <font color="Olive" title="b4">h</font> being   <a href="zmodlat1.html#NM4" title="ZMODLAT1:NM.4">FrFunctional</a> of <font color="Olive" title="b1">V</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="zmodlat1.html#K10" title="ZMODLAT1:func.10">+</a> <font color="Olive" title="b3">g</font></span>)</span> <a href="zmodlat1.html#K10" title="ZMODLAT1:func.10">+</a> <font color="Olive" title="b4">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">f</font> <a href="zmodlat1.html#K10" title="ZMODLAT1:func.10">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">g</font> <a href="zmodlat1.html#K10" title="ZMODLAT1:func.10">+</a> <font color="Olive" title="b4">h</font></span>)</span></div></div>
