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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">Th13</font></span>: <a NAME="T14"><span class="comment"><font color="firebrick">:: EUCLID_7:14</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">h</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b1">h</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  holds <br/> ex <font color="Olive" title="b2">h3</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b1">h</font></span>)</span> ex <font color="Olive" title="b3">h2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <br/>( <font color="Olive" title="b3">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b2">h3</font> &amp; <font color="Olive" title="b3">h2</font> is  <a href="valued_0.html#V5" title="VALUED_0:attr.5">increasing</a>  &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b3">h2</font> &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b3">h2</font> )</div></div>
