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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E51">Th56</font></span>: <a NAME="T57"><span class="comment"><font color="firebrick">:: AFINSQ_2:57</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">rF1</font>, <font color="Olive" title="b2">rF2</font> being   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a>  st  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Olive" title="b1">rF1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Olive" title="b2">rF2</font> &amp; (  for <font color="Olive" title="b3">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b1">rF1</font> holds <br/><font color="Olive" title="b1">rF1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">rF2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">i</font> ) holds <br/> <a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Olive" title="b1">rF1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Olive" title="b2">rF2</font></div></div>
