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<a NAME="E1:25_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="card_3.html#K1" title="CARD_3:func.1">Card</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:25_1_1_1"/>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="card_3.html#K1" title="CARD_3:func.1">Card</a> <font color="Maroon" title="c2">F</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:25_1_1_1"/><i><font color="Green" title="E9">A1</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K1" title="CARD_3:func.1">Card</a> <font color="Maroon" title="c2">F</font></span>)</span> &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_3.html#K1" title="CARD_3:func.1">Card</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E4:25_1_1_1"/><i><font color="Green" title="E10">A2</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">F</font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E3:25_1_1_1"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="card_3.html#D2" title="CARD_3:def.2">CARD_3:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">Fx</font> = <font color="Maroon" title="c2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> as  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<a NAME="E6:25_1_1_1"/>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">Fx</font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E3:25_1_1_1"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="polynom1.html#E4:25_1_1_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="card_3.html#D2" title="CARD_3:def.2">CARD_3:def 2</a></i>;<br/>
<b>hence </b><a NAME="E7:25_1_1_1"/>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:25_1_1"/>
 <a href="card_3.html#K1" title="CARD_3:func.1">Card</a> <font color="Maroon" title="c2">F</font> is  <a href="card_3.html#V1" title="CARD_3:attr.1">Cardinal-yielding</a>  <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></i>;<br/>


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