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

<b>let </b><font color="Maroon" title="c1">H1</font>, <font color="Maroon" title="c2">H2</font> be   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">r</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a>  holds <br/> ( <font color="Olive" title="b1">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font> iff <font color="Olive" title="b1">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c3">r</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font> iff <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span></span>)</span> )</span><br/>





<a NAME="E1:180"/><i><font color="Green" title="E145">A1</font></i>: 
( <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font> implies <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="180_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:180_1"/>
<font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span></span>)</span></span><br/>

<b>then consider </b><font color="Maroon" title="c4">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E3:180_1"/><i><font color="Green" title="E146">B1</font></i>: 
for <font color="Olive" title="b1">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">m</font> holds <br/> <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Olive" title="b1">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font>
 <b>and </b><br/><a NAME="E4:180_1"/><i><font color="Green" title="E147">B2</font></i>: 
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c4">m</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font>
 <b>by </b><i><a class="ref" href="modelc_2.html#T68" target="_self" title="MODELC_2:th.68">Th23</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="180_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:180_1_1"/>
( <font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c4">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="180_1_1_1"><b>suppose </b></a><a NAME="E1:180_1_1_1"/>
<font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:180_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E129"><i><font color="Green" title="E96">LemShift03</font></i></a>, <a class="txt" href="modelc_2.html#E4:180_1"><i><font color="Green" title="E147">B2</font></i></a></i>;<br/><b>hence </b><a NAME="E3:180_1_1_1"/>
<font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="modelc_2.html#T66" target="_self" title="MODELC_2:th.66">Th21</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="180_1_1_2"><b>suppose </b></a><a NAME="E1:180_1_1_2"/><i><font color="Green" title="E148">B3</font></i>: 
<font color="Maroon" title="c4">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span></span>)</span></span><br/><div class="add"><b>set </b><font color="Maroon" title="c5">G</font> = <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font>;<br/><b>set </b><font color="Maroon" title="c6">k</font> = <font color="Maroon" title="c4">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1;<br/><b>set </b><font color="Maroon" title="c7">r1</font> =  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,1;<br/><b>reconsider </b><font color="Maroon" title="c8">k</font> = <font color="Maroon" title="c4">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <b>by </b><i><a class="txt" href="modelc_2.html#E1:180_1_1_2"><i><font color="Green" title="E148">B3</font></i></a>, <a class="ref" href="nat_1.html#T20" title="NAT_1:th.20">NAT_1:20</a></i>;<br/><a NAME="E3:180_1_1_2"/><i><font color="Green" title="E149">B301</font></i>: 
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E129"><i><font color="Green" title="E96">LemShift03</font></i></a></i>;<br/><a NAME="E4:180_1_1_2"/><i><font color="Green" title="E150">B302</font></i>: 
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,1</span>)</span>,<font color="Maroon" title="c8">k</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E130"><i><font color="Green" title="E97">LemShift04</font></i></a></i>;<br/><a NAME="E5:180_1_1_2"/><i><font color="Green" title="E151">B4</font></i>: 
<font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E3:180_1"><i><font color="Green" title="E146">B1</font></i></a>, <a class="txt" href="modelc_2.html#E1:180_1_1_2"><i><font color="Green" title="E148">B3</font></i></a>, <a class="txt" href="modelc_2.html#E3:180_1_1_2"><i><font color="Green" title="E149">B301</font></i></a></i>;<br/><a NAME="E6:180_1_1_2"/><i><font color="Green" title="E152">B5</font></i>: 
for <font color="Olive" title="b1">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">k</font> holds <br/> <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,1</span>)</span>,<font color="Olive" title="b1">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="180_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c9">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">k</font> implies  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,1</span>)</span>,<font color="Maroon" title="c9">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> )</span><br/>

<b>assume </b><a NAME="E1:180_1_1_2_1"/><i><font color="Green" title="E153">C1</font></i>: 
<font color="Maroon" title="c9">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,1</span>)</span>,<font color="Maroon" title="c9">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font></span><br/>

<a NAME="E2:180_1_1_2_1"/><i><font color="Green" title="E154">C2</font></i>: 
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,1</span>)</span>,<font color="Maroon" title="c9">j</font>
 
<b>by </b><i><a class="txt" href="modelc_2.html#E130"><i><font color="Green" title="E97">LemShift04</font></i></a></i>;<br/>
<a NAME="E3:180_1_1_2_1"/>
<font color="Maroon" title="c9">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="txt" href="modelc_2.html#E1:180_1_1_2_1"><i><font color="Green" title="E153">C1</font></i></a>, <a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/>
<b>hence </b><a NAME="E4:180_1_1_2_1"/>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,1</span>)</span>,<font color="Maroon" title="c9">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E3:180_1"><i><font color="Green" title="E146">B1</font></i></a>, <a class="txt" href="modelc_2.html#E2:180_1_1_2_1"><i><font color="Green" title="E154">C2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E7:180_1_1_2"/>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,1 <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E4:180_1_1_2"><i><font color="Green" title="E150">B302</font></i></a>, <a class="txt" href="modelc_2.html#E4:180_1"><i><font color="Green" title="E147">B2</font></i></a>, <a class="txt" href="modelc_2.html#E6:180_1_1_2"><i><font color="Green" title="E152">B5</font></i></a>, <a class="ref" href="modelc_2.html#T68" target="_self" title="MODELC_2:th.68">Th23</a></i>;<br/><a NAME="E8:180_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span>
 <b>by </b><i><a class="ref" href="modelc_2.html#T67" target="_self" title="MODELC_2:th.67">Th22</a></i>;<br/><a NAME="E9:180_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_2.html#E5:180_1_1_2"><i><font color="Green" title="E151">B4</font></i></a>, <a class="ref" href="modelc_2.html#T65" target="_self" title="MODELC_2:th.65">Th20</a></i>;<br/><b>hence </b><a NAME="E10:180_1_1_2"/>
<font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="modelc_2.html#T66" target="_self" title="MODELC_2:th.66">Th21</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E2:180"/>
( <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span></span>)</span> implies <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="180_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:180_2"/><i><font color="Green" title="E146">A1</font></i>: 
<font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="180_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="180_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:180_2_1_1"/>
( <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> or <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span> )
 </span><b>by </b><i><a class="txt" href="modelc_2.html#E1:180_2"><i><font color="Green" title="E146">A1</font></i></a>, <a class="ref" href="modelc_2.html#T66" target="_self" title="MODELC_2:th.66">Th21</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="180_2_1_1_1"><b>suppose </b></a><a NAME="E1:180_2_1_1_1"/><i><font color="Green" title="E147">B1</font></i>: 
<font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span><br/><div class="add"><a NAME="E2:180_2_1_1_1"/>
 ex <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>( ( for <font color="Olive" title="b2">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b2">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">m</font> holds <br/> <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Olive" title="b2">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> ) &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Olive" title="b1">m</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="180_2_1_1_1_1"><b>proof </b></a><div class="add">

<b>take </b>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Olive" title="b1">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> ) &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> )</span><br/>

<b>thus </b><a NAME="E1:180_2_1_1_1_1"/>
( ( for <font color="Olive" title="b1">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Olive" title="b1">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> ) &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> )
 <b>by </b><i><a class="txt" href="modelc_2.html#E1:180_2_1_1_1"><i><font color="Green" title="E147">B1</font></i></a>, <a class="txt" href="modelc_2.html#E129"><i><font color="Green" title="E96">LemShift03</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:180_2_1_1_1"/>
<font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font>
 <b>by </b><i><a class="ref" href="modelc_2.html#T68" target="_self" title="MODELC_2:th.68">Th23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="180_2_1_1_2"><b>suppose </b></a><a NAME="E1:180_2_1_1_2"/>
<font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span><br/><div class="add"><a NAME="E2:180_2_1_1_2"/><b>then </b><i><font color="Green" title="E147">B1</font></i>: 
( <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> &amp; <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span> )
 <b>by </b><i><a class="ref" href="modelc_2.html#T65" target="_self" title="MODELC_2:th.65">Th20</a></i>;<br/><a NAME="E3:180_2_1_1_2"/><b>then </b><i><font color="Green" title="E148">B2</font></i>: 
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,1 <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font>
 <b>by </b><i><a class="ref" href="modelc_2.html#T67" target="_self" title="MODELC_2:th.67">Th22</a></i>;<br/><b>set </b><font color="Maroon" title="c4">r1</font> =  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,1;<br/><b>consider </b><font color="Maroon" title="c5">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E5:180_2_1_1_2"/><i><font color="Green" title="E149">B3</font></i>: 
for <font color="Olive" title="b1">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">m</font> holds <br/> <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,1</span>)</span>,<font color="Olive" title="b1">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font>
 <b>and </b><br/><a NAME="E6:180_2_1_1_2"/><i><font color="Green" title="E150">B4</font></i>: 
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,1</span>)</span>,<font color="Maroon" title="c5">m</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E3:180_2_1_1_2"><i><font color="Green" title="E148">B2</font></i></a>, <a class="ref" href="modelc_2.html#T68" target="_self" title="MODELC_2:th.68">Th23</a></i>;<br/><b>set </b><font color="Maroon" title="c6">m1</font> = <font color="Maroon" title="c5">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1;<br/><a NAME="E7:180_2_1_1_2"/><i><font color="Green" title="E151">B5</font></i>: 
for <font color="Olive" title="b1">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 holds <br/> <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Olive" title="b1">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="180_2_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 implies  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c7">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> )</span><br/>

<b>assume </b><a NAME="E1:180_2_1_1_2_1"/><i><font color="Green" title="E152">C1</font></i>: 
<font color="Maroon" title="c7">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c7">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="180_2_1_1_2_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="180_2_1_1_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:180_2_1_1_2_1_1_1"/>
( <font color="Maroon" title="c7">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c7">j</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="180_2_1_1_2_1_1_1_1"><b>suppose </b></a><a NAME="E1:180_2_1_1_2_1_1_1_1"/>
<font color="Maroon" title="c7">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c7">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font></span><br/><div class="add"><b>hence </b><a NAME="E2:180_2_1_1_2_1_1_1_1"/>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c7">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E129"><i><font color="Green" title="E96">LemShift03</font></i></a>, <a class="txt" href="modelc_2.html#E2:180_2_1_1_2"><i><font color="Green" title="E147">B1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="180_2_1_1_2_1_1_1_2"><b>suppose </b></a><a NAME="E1:180_2_1_1_2_1_1_1_2"/><i><font color="Green" title="E153">C3</font></i>: 
<font color="Maroon" title="c7">j</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c7">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font></span><br/><div class="add"><b>set </b><font color="Maroon" title="c8">j1</font> = <font color="Maroon" title="c7">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1;<br/><b>reconsider </b><font color="Maroon" title="c9">j1</font> = <font color="Maroon" title="c7">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <b>by </b><i><a class="txt" href="modelc_2.html#E1:180_2_1_1_2_1_1_1_2"><i><font color="Green" title="E153">C3</font></i></a>, <a class="ref" href="nat_1.html#T20" title="NAT_1:th.20">NAT_1:20</a></i>;<br/><a NAME="E3:180_2_1_1_2_1_1_1_2"/>
<font color="Maroon" title="c7">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="txt" href="modelc_2.html#E1:180_2_1_1_2_1"><i><font color="Green" title="E152">C1</font></i></a>, <a class="ref" href="xreal_1.html#T16" title="XREAL_1:th.16">XREAL_1:16</a></i>;<br/><a NAME="E4:180_2_1_1_2_1_1_1_2"/><b>then </b>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,1</span>)</span>,<font color="Maroon" title="c9">j1</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E5:180_2_1_1_2"><i><font color="Green" title="E149">B3</font></i></a></i>;<br/><a NAME="E5:180_2_1_1_2_1_1_1_2"/><b>then </b>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">j1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E130"><i><font color="Green" title="E97">LemShift04</font></i></a></i>;<br/><b>hence </b><a NAME="E6:180_2_1_1_2_1_1_1_2"/>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c7">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:180_2_1_1_2_1"/>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c7">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E8:180_2_1_1_2"/>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E6:180_2_1_1_2"><i><font color="Green" title="E150">B4</font></i></a>, <a class="txt" href="modelc_2.html#E130"><i><font color="Green" title="E97">LemShift04</font></i></a></i>;<br/><b>hence </b><a NAME="E9:180_2_1_1_2"/>
<font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font>
 <b>by </b><i><a class="ref" href="modelc_2.html#T68" target="_self" title="MODELC_2:th.68">Th23</a>, <a class="txt" href="modelc_2.html#E7:180_2_1_1_2"><i><font color="Green" title="E151">B5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:180_2"/>
<font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:180"/>
( <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font> iff <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="modelc_2.html#E1:180"><i><font color="Green" title="E145">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
