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

<span class="kw">set </span><font color="Maroon" title="c5">f</font> =  <a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>);<br/>
<span class="kw">let </span><font color="Maroon" title="c6">n1</font>, <font color="Maroon" title="c7">n2</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="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">n1</font> holds <br/>(  not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  &amp;  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) ) ) &amp;  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Maroon" title="c6">n1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  &amp; (  for <font color="Olive" title="b1">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">n1</font> holds <br/><font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>)</span>)</span> ) &amp; (  for <font color="Olive" title="b1">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">n2</font> holds <br/>(  not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  &amp;  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) ) ) &amp;  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Maroon" title="c7">n2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  &amp; (  for <font color="Olive" title="b1">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">n2</font> holds <br/><font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>)</span>)</span> ) implies <font color="Maroon" title="c6">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">n2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:148_1_2"/><span class="lab"><font color="Green" title="E119">A4</font></span>: 
 for <font color="Olive" title="b1">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">n1</font> holds <br/>(  not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  &amp;  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) )
 <span class="kw">and </span><br/><a NAME="E2:148_1_2"/><span class="lab"><font color="Green" title="E120">A5</font></span>: 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Maroon" title="c6">n1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> 
 <span class="kw">and </span><br/><a NAME="E3:148_1_2"/>
 for <font color="Olive" title="b1">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">n1</font> holds <br/><font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:148_1_2"/><span class="lab"><font color="Green" title="E121">A6</font></span>: 
 for <font color="Olive" title="b1">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">n2</font> holds <br/>(  not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  &amp;  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) )
 <span class="kw">and </span><br/><a NAME="E5:148_1_2"/><span class="lab"><font color="Green" title="E122">A7</font></span>: 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Maroon" title="c7">n2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> 
 <span class="kw">and </span><br/><a NAME="E6:148_1_2"/>
 for <font color="Olive" title="b1">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">n2</font> holds <br/><font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> (<font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>)</span>)</span> <a href="modelc_1.html#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">n2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="148_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:148_1_2_1"/><span class="lab"><font color="Green" title="E123">A8</font></span>: 
<font color="Maroon" title="c6">n1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">n2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="148_1_2_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="148_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="E1:148_1_2_1_1_1"/>
( <font color="Maroon" title="c6">n1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">n2</font> or <font color="Maroon" title="c7">n2</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">n1</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:148_1_2_1"><span class="lab"><font color="Green" title="E123">A8</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="148_1_2_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:148_1_2_1_1_1_1"/>
<font color="Maroon" title="c6">n1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">n2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:148_1_2_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:148_1_2"><span class="lab"><font color="Green" title="E120">A5</font></span></a>, <a class="txt" href="#E4:148_1_2"><span class="lab"><font color="Green" title="E121">A6</font></span></a></span>; <a class="txt" 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="148_1_2_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:148_1_2_1_1_1_2"/>
<font color="Maroon" title="c7">n2</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">n1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:148_1_2_1_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:148_1_2"><span class="lab"><font color="Green" title="E119">A4</font></span></a>, <a class="txt" href="#E5:148_1_2"><span class="lab"><font color="Green" title="E122">A7</font></span></a></span>; <a class="txt" 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></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:148_1_2_1"/>
contradiction
 ; <a class="txt" 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>
<span class="kw">hence </span><a NAME="E8:148_1_2"/>
<font color="Maroon" title="c6">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">n2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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