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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</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">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Olive" title="b1">n</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</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"> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">mf</font> =  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">fn</font> = <font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">mn</font> =  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span>;<br/>
<a NAME="E1:35"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</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="c1">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfinseq.html#D3" target="_self" title="RFINSEQ:def.3">Def3</a></span>;<br/>
<a NAME="E2:35"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">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="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfinseq.html#D3" target="_self" title="RFINSEQ:def.3">Def3</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_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="E1:35_1_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">R</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">n</font> or <font color="Maroon" title="c2">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="c1">R</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_1"><span class="kw">case </span></a><a NAME="E1:35_1_1_1"/><span class="lab"><font color="Green" title="E18">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">R</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span><br/><div class="add"><a NAME="E2:35_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="rfinseq.html#D2" target="_self" title="RFINSEQ:def.2">Def2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:35_1_1_1"/>
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_1_1_1"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="ref" href="rfinseq.html#D2" target="_self" title="RFINSEQ:def.2">Def2</a>, <a class="ref" href="rfinseq.html#T25" target="_self" title="RFINSEQ:th.25">Th25</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="35_1_1_2"><span class="kw">case </span></a><a NAME="E1:35_1_1_2"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<font color="Maroon" title="c2">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="c1">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span><br/><div class="add"><a NAME="E2:35_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A5</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="rfinseq.html#D2" target="_self" title="RFINSEQ:def.2">Def2</a></span>;<br/><a NAME="E3:35_1_1_2"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">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="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rfinseq.html#D3" target="_self" title="RFINSEQ:def.3">Def3</a></span>;<br/><a NAME="E4:35_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A7</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/><a NAME="E5:35_1_1_2"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">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"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/><a NAME="E6:35_1_1_2"/><span class="lab"><font color="Green" title="E23">A9</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="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_1_1_2"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="rfinseq.html#D2" target="_self" title="RFINSEQ:def.2">Def2</a></span>;<br/><a NAME="E7:35_1_1_2"/><span class="lab"><font color="Green" title="E24">A10</font></span>: 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">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="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">m</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"> ( <font color="Maroon" title="c6">m</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font> )</span><br/><span class="kw">set </span><font color="Maroon" title="c7">r1</font> = <font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span>;<br/><span class="kw">assume </span><a NAME="E1:35_1_1_2_1"/><span class="lab"><font color="Green" title="E25">A11</font></span>: 
<font color="Maroon" title="c6">m</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font></span><br/><a NAME="E2:35_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A12</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:35_1_1_2"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></span>;<br/><a NAME="E3:35_1_1_2_1"/><span class="lab"><font color="Green" title="E27">A13</font></span>: 
<font color="Maroon" title="c6">m</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:35_1_1_2"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E1:35_1_1_2_1"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></span>;<br/><a NAME="E4:35_1_1_2_1"/><span class="lab"><font color="Green" title="E28">A14</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_1_1_2"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E7:35_1_1_2"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E4:35_1_1_2"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E1:35_1_1_2_1"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="ref" href="rfinseq.html#D2" target="_self" title="RFINSEQ:def.2">Def2</a></span>;<br/><a NAME="E5:35_1_1_2_1"/>
<font color="Maroon" title="c6">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E6:35_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A15</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35_1_1_2_1"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1_2_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_2_1_1_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="E1:35_1_1_2_1_1_1"/>
( <font color="Maroon" title="c6">m</font> <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="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span> or <font color="Maroon" title="c6">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_2_1_1_1_1"><span class="kw">case </span></a><a NAME="E1:35_1_1_2_1_1_1_1"/><span class="lab"><font color="Green" title="E30">A16</font></span>: 
<font color="Maroon" title="c6">m</font> <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="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font></span><br/><div class="add"><span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font> = 
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E1:35_1_1_2"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E2:35_1_1_2"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:35_1_1_2"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E5:35_1_1_2"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E4:35_1_1_2"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E1:35_1_1_2_1"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="ref" href="rfinseq.html#D2" target="_self" title="RFINSEQ:def.2">Def2</a></span>
<br/>.= 
<font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E6:35_1_1_2"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E1:35_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="ref" href="rfinseq.html#D3" target="_self" title="RFINSEQ:def.3">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_1_1_2"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E4:35_1_1_2_1"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E1:35_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="ref" href="rfinseq.html#D3" target="_self" title="RFINSEQ:def.3">Def3</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="35_1_1_2_1_1_1_2"><span class="kw">case </span></a><a NAME="E1:35_1_1_2_1_1_1_2"/>
<font color="Maroon" title="c6">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font></span><br/><div class="add"><a NAME="E2:35_1_1_2_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">m</font> <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="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_1_1_2_1"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><a NAME="E3:35_1_1_2_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A17</font></span>: 
<font color="Maroon" title="c6">m</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</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="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E4:35_1_1_2_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A18</font></span>: 
<font color="Maroon" title="c6">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c8">r2</font> = <font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">n</font></span>)</span>;<br/><a NAME="E5:35_1_1_2_1_1_1_2"/><span class="lab"><font color="Green" title="E32">A19</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> 1
 ;<br/><a NAME="E6:35_1_1_2_1_1_1_2"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">m</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E7:35_1_1_2_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">m</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1 <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"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_1_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E30">A17</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/><a NAME="E8:35_1_1_2_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A20</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_1_1_2"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="rfinseq.html#D2" target="_self" title="RFINSEQ:def.2">Def2</a></span>;<br/><a NAME="E9:35_1_1_2_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">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="c1">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:35_1_1_2"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E3:35_1_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E30">A17</font></span></a>, <a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></span>;<br/><a NAME="E10:35_1_1_2_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A21</font></span>: 
<font color="Maroon" title="c6">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:35_1_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E32">A19</font></span></a>, <a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font> = 
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E1:35_1_1_2"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E2:35_1_1_2"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:35_1_1_2"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E5:35_1_1_2"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E4:35_1_1_2"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E1:35_1_1_2_1"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="ref" href="rfinseq.html#D2" target="_self" title="RFINSEQ:def.2">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E6:35_1_1_2_1"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E5:35_1_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E32">A19</font></span></a>, <a class="txt" href="#E10:35_1_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E34">A21</font></span></a>, <a class="ref" href="rfinseq.html#D3" target="_self" title="RFINSEQ:def.3">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E2:35_1_1_2_1"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E4:35_1_1_2_1"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E4:35_1_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E31">A18</font></span></a>, <a class="txt" href="#E8:35_1_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E33">A20</font></span></a>, <a class="ref" href="rfinseq.html#D3" target="_self" title="RFINSEQ:def.3">Def3</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><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E8:35_1_1_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font>
 ; <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><span class="kw">hence </span><a NAME="E9:35_1_1_2"/>
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35_1_1_2"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:35_1_1_2"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E3:35_1_1_2"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:35"/>
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">n</font></span>)</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/>


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