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<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">S</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">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> holds <br/><font color="Olive" title="b1">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <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><br/><span class="kw">let </span><font color="Maroon" title="c3">S</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</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="c3">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> implies <font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <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><br/>





<span class="kw">assume </span><a NAME="E1:27"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c3">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>
 ; <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">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <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><br/>

<span class="kw">set </span><font color="Maroon" title="c4">S1</font> = <font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>;<br/>
<a NAME="E2:27"/>
<font color="Maroon" title="c3">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E15">A1</font></span></a></span>;<br/>
<a NAME="E3:27"/><span class="kw">then </span>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<a NAME="E4:27"/><span class="kw">then </span>
1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T32" onmouseover="rs('finseq_3/T32')" onmouseout="rh()">FINSEQ_3:32</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:27"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <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>,<font color="Maroon" title="c2">A</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="finseq_1.html#D7" onmouseover="rs('finseq_1/D7')" onmouseout="rh()">FINSEQ_1:def 7</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="nomin_1.html#D4" target="_self" onmouseover="rs('nomin_1/D4')" onmouseout="rh()">NOMIN_1:def 4</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">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> &amp; <font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">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"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p4"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></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">let </span><font color="Maroon" title="c5">n</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"> ( <font color="Maroon" title="c5">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> &amp; <font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">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"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p4"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span>) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E6:27"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon" title="c5">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E7:27"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">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"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p4"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span>)</span><br/>

<a NAME="E8:27"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T39" onmouseover="rs('finseq_1/T39')" onmouseout="rh()">FINSEQ_1:39</a></span>;<br/>
<a NAME="E9:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A4</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T22" onmouseover="rs('finseq_1/T22')" onmouseout="rh()">FINSEQ_1:22</a></span>;<br/>
<a NAME="E10:27"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="finseq_3.html#T25" onmouseover="rs('finseq_3/T25')" onmouseout="rh()">FINSEQ_3:25</a></span>;<br/>
<a NAME="E11:27"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T14" onmouseover="rs('nat_1/T14')" onmouseout="rh()">NAT_1:14</a></span>;<br/>
<a NAME="E12:27"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
<font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <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> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="finseq_3.html#T25" onmouseover="rs('finseq_3/T25')" onmouseout="rh()">FINSEQ_3:25</a></span>;<br/>
<a NAME="E13:27"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:27"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="xreal_1.html#T9" onmouseover="rs('xreal_1/T9')" onmouseout="rh()">XREAL_1:9</a></span>;<br/>
<a NAME="E14:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A8</font></span>: 
<font color="Maroon" title="c5">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:27"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="ref" href="finseq_3.html#T25" onmouseover="rs('finseq_3/T25')" onmouseout="rh()">FINSEQ_3:25</a></span>;<br/>
<a NAME="E15:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A9</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D7" onmouseover="rs('finseq_1/D7')" onmouseout="rh()">FINSEQ_1:def 7</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:27_1"/>
( <font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> or <font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:27"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_1"><span class="kw">suppose </span></a><a NAME="E1:27_1_1"/>
<font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">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"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p4"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span>)</span><br/><div class="add"><a NAME="E2:27_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <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="c3">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:27"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/><a NAME="E3:27_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A10</font></span>: 
<font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:27"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="ref" href="finseq_3.html#T25" onmouseover="rs('finseq_3/T25')" onmouseout="rh()">FINSEQ_3:25</a></span>;<br/><a NAME="E4:27_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">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="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">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="ref" href="finseq_1.html#D7" onmouseover="rs('finseq_1/D7')" onmouseout="rh()">FINSEQ_1:def 7</a></span>;<br/><span class="kw">hence </span><a NAME="E5:27_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">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"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p4"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E14:27"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E15:27"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E3:27_1_1"><span class="lab"><font color="Green" title="E24">A10</font></span></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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_2"><span class="kw">suppose </span></a><a NAME="E1:27_1_2"/>
<font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">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"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p4"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span>)</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:27_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">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"><font color="Maroon" title="c3">S</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p4"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:27"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E15:27"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="ref" href="finseq_1.html#T42" onmouseover="rs('finseq_1/T42')" onmouseout="rh()">FINSEQ_1:42</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></div><span class="kw">end;</span></div>

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