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

<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">K</font> being  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a><br/> for <font color="Olive" title="b2">f</font> being   <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>  holds   <a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Olive" title="b1">K</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Olive" title="b1">K</font>,<font color="Olive" title="b2">f</font></span>)</span> <a href="matrixj1.html#K18" title="MATRIXJ1:func.18">|</a> <font color="Maroon" title="c1">n</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being   <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>  holds   <a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Olive" title="b1">f</font></span>)</span> <a href="matrixj1.html#K18" title="MATRIXJ1:func.18">|</a> <font color="Maroon" title="c1">n</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="matrixj1.html#K18" title="MATRIXJ1:func.18">|</a> <font color="Maroon" title="c1">n</font></span><br/>





<a NAME="E1:92"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#D8" target="_self" title="MATRIXJ1:def.8">Def8</a></span>;<br/>
<a NAME="E2:92"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <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">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></span>;<br/>
<a NAME="E3:92"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#D8" target="_self" title="MATRIXJ1:def.8">Def8</a></span>;<br/>
<a NAME="E4:92"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="92_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:92_1"/>
( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">f</font> or <font color="Maroon" title="c1">n</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="c3">f</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="92_1_1"><span class="kw">suppose </span></a><a NAME="E1:92_1_1"/><span class="lab"><font color="Green" title="E62">A3</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="matrixj1.html#K18" title="MATRIXJ1:func.18">|</a> <font color="Maroon" title="c1">n</font></span><br/><div class="add"><a NAME="E2:92_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T79" title="FINSEQ_1:th.79">FINSEQ_1:79</a></span>;<br/><span class="kw">hence </span><a NAME="E3:92_1_1"/>
 <a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="matrixj1.html#K18" title="MATRIXJ1:func.18">|</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:92"><span class="lab"><font color="Green" title="E61">A2</font></span></a>, <a class="txt" href="#E1:92_1_1"><span class="lab"><font color="Green" title="E62">A3</font></span></a>, <a class="ref" href="finseq_1.html#T79" title="FINSEQ_1:th.79">FINSEQ_1:79</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="92_1_2"><span class="kw">suppose </span></a><a NAME="E1:92_1_2"/><span class="lab"><font color="Green" title="E62">A4</font></span>: 
<font color="Maroon" title="c1">n</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="c3">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="matrixj1.html#K18" title="MATRIXJ1:func.18">|</a> <font color="Maroon" title="c1">n</font></span><br/><div class="add"><a NAME="E2:92_1_2"/>
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rfinseq.html#T21" title="RFINSEQ:th.21">RFINSEQ:21</a></span>;<br/><a NAME="E3:92_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A5</font></span>: 
 <a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T58" target="_self" title="MATRIXJ1:th.58">Th58</a></span>;<br/><a NAME="E4:92_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:92"><span class="lab"><font color="Green" title="E60">A1</font></span></a>, <a class="txt" href="#E1:92_1_2"><span class="lab"><font color="Green" title="E62">A4</font></span></a>, <a class="ref" href="finseq_1.html#T80" title="FINSEQ_1:th.80">FINSEQ_1:80</a></span>;<br/><span class="kw">hence </span><a NAME="E5:92_1_2"/>
 <a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="matrixj1.html#K18" title="MATRIXJ1:func.18">|</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:92_1_2"><span class="lab"><font color="Green" title="E63">A5</font></span></a>, <a class="ref" href="finseq_5.html#T26" title="FINSEQ_5:th.26">FINSEQ_5:26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
