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<span class="kw">take </span><font color="Maroon" title="c4">f</font> = <font color="Maroon" title="c3">n</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a>  the   <a href="nomin_2.html#NM2" title="NOMIN_2:NM.2">SCBinominativeFunction</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>; <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"> ( <font color="Maroon" title="c4">f</font> is <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> <a href="nomin_2.html#V1" title="NOMIN_2:attr.1">-FPrg-yielding</a>  &amp; <font color="Maroon" title="c4">f</font> is <font color="Maroon" title="c3">n</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:51_1_1"/>
<font color="Maroon" title="c4">f</font> is <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> <a href="nomin_2.html#V1" title="NOMIN_2:attr.1">-FPrg-yielding</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"> <font color="Maroon" title="c4">f</font> is <font color="Maroon" title="c3">n</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a> </span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="51_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">a</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="nomin_2.html#D6" target="_self" onmouseover="rs('nomin_2/D6')" onmouseout="rh()">NOMIN_2:def 6</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"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">a</font> &amp; <font color="Maroon" title="c5">a</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="Maroon" title="c4">f</font> implies <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">a</font> is   <a href="nomin_2.html#NM2" title="NOMIN_2:NM.2">SCBinominativeFunction</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> )</span><br/>

<a NAME="E1:51_1_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">n</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E2:51_1_1_1"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">a</font> &amp; <font color="Maroon" title="c5">a</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="Maroon" title="c4">f</font> implies <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">a</font> is   <a href="nomin_2.html#NM2" title="NOMIN_2:NM.2">SCBinominativeFunction</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T57" onmouseover="rs('finseq_2/T57')" onmouseout="rh()">FINSEQ_2:57</a>, <a class="ref" href="finseq_3.html#T25" onmouseover="rs('finseq_3/T25')" onmouseout="rh()">FINSEQ_3:25</a></span>; <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/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E2:51_1_1"/>
<font color="Maroon" title="c4">f</font> is <font color="Maroon" title="c3">n</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</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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