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<div><span class="kw">theorem </span><a NAME="T1"><span class="comment"><font color="firebrick">:: LEXBFS:1</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b3">X</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="b4">F</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <font color="Olive" title="b3">X</font>  st <font color="Olive" title="b4">F</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  holds <br/> <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b4">F</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b5">w</font></span>)</span> where <font color="Olive" title="b5">w</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  : ( <font color="Olive" title="b1">A</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b5">w</font> &amp; <font color="Olive" title="b5">w</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">A</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b2">B</font> ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">B</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</div></div>
