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<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">p</font> being  <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</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"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">pn</font> = <font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_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="E1:34_1_1"/>
(  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> or <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_1_1"><span class="kw">case </span></a><a NAME="E1:34_1_1_1"/><span class="lab"><font color="Green" title="E22">A1</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">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"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font></span><br/><div class="add"><a NAME="E2:34_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A2</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T56" title="AFINSQ_1:th.56">AFINSQ_1:56</a></span>;<br/><a NAME="E3:34_1_1_1"/>
<font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="#E1:34_1_1_1"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="afinsq_2.html#T15" target="_self" title="AFINSQ_2:th.15">Th15</a></span>;<br/><span class="kw">hence </span><a NAME="E4:34_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:34_1_1_1"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="ref" href="afinsq_1.html#T32" title="AFINSQ_1:th.32">AFINSQ_1:32</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="34_1_1_2"><span class="kw">case </span></a><a NAME="E1:34_1_1_2"/><span class="lab"><font color="Green" title="E22">A3</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</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"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font></span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c4">g</font> = <font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font>;<br/><a NAME="E2:34_1_1_2"/><span class="lab"><font color="Green" title="E23">A4</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></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="#E1:34_1_1_2"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="ref" href="afinsq_1.html#T58" title="AFINSQ_1:th.58">AFINSQ_1:58</a></span>;<br/><a NAME="E3:34_1_1_2"/><span class="lab"><font color="Green" title="E24">A5</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</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="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34_1_1_2"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="ref" href="afinsq_2.html#T16" target="_self" title="AFINSQ_2:th.16">Th16</a></span>;<br/><div><span class="lab"><font color="Green" title="E25">A6</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">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="c5">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> )</span><br/><span class="kw">assume </span><a NAME="E1:34_1_1_2_1"/><span class="lab"><font color="Green" title="E26">A7</font></span>: 
<font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_1_2_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_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="E1:34_1_1_2_1_1_1"/>
( <font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">n</font> or <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">m</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_1_2_1_1_1_1"><span class="kw">case </span></a><a NAME="E1:34_1_1_2_1_1_1_1"/>
<font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font></span><br/><div class="add"><a NAME="E2:34_1_1_2_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A8</font></span>: 
<font color="Maroon" title="c5">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T45" title="NAT_1:th.45">NAT_1:45</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:34_1_1_2"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="ref" href="afinsq_1.html#D4" title="AFINSQ_1:def.4">AFINSQ_1:def 4</a></span>
<br/>.= 
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34_1_1_2"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="txt" href="#E2:34_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E27">A8</font></span></a>, <a class="ref" href="afinsq_1.html#T57" title="AFINSQ_1:th.57">AFINSQ_1:57</a></span>
;<br/> <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="34_1_1_2_1_1_1_2"><span class="kw">case </span></a><a NAME="E1:34_1_1_2_1_1_1_2"/>
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">m</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font></span><br/><div class="add"><a NAME="E2:34_1_1_2_1_1_1_2"/><span class="kw">then </span>
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p1">(<span class="default"><font color="Maroon" title="c5">m</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T4" title="FINSEQ_2:th.4">FINSEQ_2:4</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">k</font> = <font color="Maroon" title="c5">m</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <font color="Maroon" title="c1">n</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T5" title="FINSEQ_2:th.5">FINSEQ_2:5</a></span>;<br/><a NAME="E4:34_1_1_2_1_1_1_2"/>
<font color="Maroon" title="c6">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34_1_1_2"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E1:34_1_1_2_1"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></span>;<br/><a NAME="E5:34_1_1_2_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A9</font></span>: 
<font color="Maroon" title="c6">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T45" title="NAT_1:th.45">NAT_1:45</a></span>;<br/><a NAME="E6:34_1_1_2_1_1_1_2"/>
<font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:34_1_1_2"><span class="lab"><font color="Green" title="E23">A4</font></span></a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:34_1_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="ref" href="afinsq_1.html#D4" title="AFINSQ_1:def.4">AFINSQ_1:def 4</a></span>
<br/>.= 
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <font color="Maroon" title="c1">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:34_1_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="ref" href="afinsq_2.html#D2" target="_self" title="AFINSQ_2:def.2">Def2</a></span>
<br/>.= 
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>

;<br/> <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="E3:34_1_1_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">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> <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c1">n</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <font color="Maroon" title="c1">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34_1_1_2"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E2:34_1_1_2"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="ref" href="afinsq_1.html#T20" title="AFINSQ_1:th.20">AFINSQ_1:20</a></span>
<br/>.= 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font>

;<br/><span class="kw">hence </span><a NAME="E6:34_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:34_1_1_2"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="ref" href="afinsq_1.html#T11" title="AFINSQ_1:th.11">AFINSQ_1:11</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="E2:34"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="afinsq_2.html#K2" title="AFINSQ_2:func.2">/^</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</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>
