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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E48">Th42</font></span>: <a NAME="T42"><span class="comment"><font color="firebrick">:: TOPALG_6:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> <br/>  for <font color="Olive" title="b2">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="topalg_6.html#K1" title="TOPALG_6:func.1">Curves</a> <font color="Olive" title="b1">T</font>  st (  for <font color="Olive" title="b4">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">i</font> &amp; <font color="Olive" title="b4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">f</font> holds <br/> <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b4">i</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">X</font> ) holds <br/> <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="topalg_6.html#K6" title="TOPALG_6:func.6">Sum</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">X</font></div></div>
