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<div><span class="kw">theorem </span><a NAME="T43"><span class="comment"><font color="firebrick">:: ZMODLAT1:43</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font>, <font color="Olive" title="b2">W</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="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a><br/>  for <font color="Olive" title="b5">f</font> being   <a href="zmodlat1.html#NM3" title="ZMODLAT1:NM.3">FrForm</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">W</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b4">b</font></span>)</span> <a href="zmodlat1.html#K6" title="ZMODLAT1:func.6">*</a> <font color="Olive" title="b5">f</font> <a href="binop_1.html#R8" title="BINOP_1:pred.8">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="zmodlat1.html#K6" title="ZMODLAT1:func.6">*</a> <font color="Olive" title="b5">f</font></span>)</span> <a href="zmodlat1.html#K9" title="ZMODLAT1:func.9">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">b</font> <a href="zmodlat1.html#K6" title="ZMODLAT1:func.6">*</a> <font color="Olive" title="b5">f</font></span>)</span></div></div>
