<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">V</font>, <font color="Maroon" title="c2">A</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">  for <font color="Olive" title="b1">D</font> being    <a href="nomin_1.html#M1" title="NOMIN_1:mode.1">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>  ex <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Olive" title="b1">D</font> is   <a href="nomin_1.html#NM2" title="NOMIN_1:NM.2">TypeSSNominativeData</a> of <font color="Maroon" title="c1">V</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K2" title="NOMIN_1:func.2">FNDSC</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">n</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">D</font> be    <a href="nomin_1.html#M1" title="NOMIN_1:mode.1">NonatomicND</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">  ex <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c3">D</font> is   <a href="nomin_1.html#NM2" title="NOMIN_1:NM.2">TypeSSNominativeData</a> of <font color="Maroon" title="c1">V</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K2" title="NOMIN_1:func.2">FNDSC</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span></span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">F</font> =  <a href="nomin_1.html#K2" title="NOMIN_1:func.2">FNDSC</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>);<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">S</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><span class="kw"> such that </span><br/><a NAME="E2:44"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
<font color="Maroon" title="c5">S</font> <a href="nomin_1.html#R2" title="NOMIN_1:pred.2">IsNDRankSeq</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>
 <span class="kw">and </span><br/><a NAME="E3:44"/><span class="lab"><font color="Green" title="E32">A2</font></span>: 
<font color="Maroon" title="c3">D</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Maroon" title="c5">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nomin_1.html#D5" target="_self" onmouseover="rs('nomin_1/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E5:44"/><span class="lab"><font color="Green" title="E33">A3</font></span>: 
<font color="Maroon" title="c6">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="c5">S</font>
 <span class="kw">and </span><br/><a NAME="E6:44"/><span class="lab"><font color="Green" title="E34">A4</font></span>: 
<font color="Maroon" title="c3">D</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="card_5.html#T2" onmouseover="rs('card_5/T2')" onmouseout="rh()">CARD_5:2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">x</font> = <font color="Maroon" title="c6">x</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:44"><span class="lab"><font color="Green" title="E33">A3</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">n</font> = <font color="Maroon" title="c7">x</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 as    <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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:44"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="finseq_3.html#T25" onmouseover="rs('finseq_3/T25')" onmouseout="rh()">FINSEQ_3:25</a>, <a class="ref" href="int_1.html#T5" onmouseover="rs('int_1/T5')" onmouseout="rh()">INT_1:5</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c8">n</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="c3">D</font> is   <a href="nomin_1.html#NM2" title="NOMIN_1:NM.2">TypeSSNominativeData</a> of <font color="Maroon" title="c1">V</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K2" title="NOMIN_1:func.2">FNDSC</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span></span><br/>

<a NAME="E9:44"/><span class="lab"><font color="Green" title="E35">A5</font></span>: 
<span class="p1">(<span class="default"><a href="nomin_1.html#K2" title="NOMIN_1:func.2">FNDSC</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E5:44"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="nomin_1.html#T19" target="_self" onmouseover="rs('nomin_1/T19')" onmouseout="rh()">Th19</a></span>;<br/>
<a NAME="E10:44"/>
<span class="p1">(<span class="default"><a href="nomin_1.html#K2" title="NOMIN_1:func.2">FNDSC</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K2" title="NOMIN_1:func.2">FNDSC</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nomin_1.html#D3" target="_self" onmouseover="rs('nomin_1/D3')" onmouseout="rh()">Def3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:44"/>
<font color="Maroon" title="c3">D</font> is   <a href="nomin_1.html#NM2" title="NOMIN_1:NM.2">TypeSSNominativeData</a> of <font color="Maroon" title="c1">V</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K2" title="NOMIN_1:func.2">FNDSC</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:44"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="txt" href="#E9:44"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="ref" href="nomin_1.html#T4" target="_self" onmouseover="rs('nomin_1/T4')" onmouseout="rh()">Th4</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>
