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<span class="kw">let </span><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">f</font> where <font color="Olive" title="b1">f</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Maroon" title="c2">k</font></span>)</span> : ( <font color="Olive" title="b1">f</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  &amp; <font color="Olive" title="b1">f</font> is  <a href="stirl2_1.html#V1" title="STIRL2_1:attr.1">"increasing</a>  ) </span> } </span>  is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> </span><br/>



<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Maroon" title="c2">k</font></span>)</span>] <span class="kw">means </span>( $1 is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  &amp; $1 is  <a href="stirl2_1.html#V1" title="STIRL2_1:attr.1">"increasing</a>  );<br/>
<a NAME="E1:29"/>
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">f</font> where <font color="Olive" title="b1">f</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Maroon" title="c2">k</font></span>)</span> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">f</font>] </span> } </span>  is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="stirl2_1.html#S1" target="_self" onmouseover="rs('stirl2_1/S1')" onmouseout="rh()">STIRL2_1:sch 1</a>();<br/></span>
<span class="kw">hence </span><a NAME="E2:29"/>
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">f</font> where <font color="Olive" title="b1">f</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Maroon" title="c2">k</font></span>)</span> : ( <font color="Olive" title="b1">f</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  &amp; <font color="Olive" title="b1">f</font> is  <a href="stirl2_1.html#V1" title="STIRL2_1:attr.1">"increasing</a>  ) </span> } </span>  is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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