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<div><span class="kw">theorem </span><a NAME="T34"><span class="comment"><font color="firebrick">:: CARDFIL3:34</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</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">L</font> being   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">AbGroup</a><br/>  for <font color="Olive" title="b3">x</font> being   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive">b<sub>2</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b4">J</font>, <font color="Olive" title="b5">e</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Olive" title="b1">I</font>  st <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/>(  <a href="cardfil3.html#K4" title="CARDFIL3:func.4">Sum</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b5">e</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">L</font> &amp; (  for <font color="Olive" title="b6">e</font>, <font color="Olive" title="b7">f</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Olive" title="b1">I</font>  st <font color="Olive" title="b6">e</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b7">f</font> holds <br/> <a href="cardfil3.html#K4" title="CARDFIL3:func.4">Sum</a> (<font color="Olive" title="b3">x</font>,<span class="p1">(<span class="default"><font color="Olive" title="b6">e</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <font color="Olive" title="b7">f</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="cardfil3.html#K4" title="CARDFIL3:func.4">Sum</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b6">e</font>)</span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="cardfil3.html#K4" title="CARDFIL3:func.4">Sum</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b7">f</font>)</span>)</span> ) )</div></div>
