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

<span class="kw">let </span><font color="Maroon" title="c1">H1</font>, <font color="Maroon" title="c2">H2</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</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">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#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c2">H2</font> iff for <font color="Olive" title="b2">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( for <font color="Olive" title="b3">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b3">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">m</font> holds <br/> <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Olive" title="b1">r</font>,<font color="Olive" title="b3">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font> ) holds <br/> <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Olive" title="b1">r</font>,<font color="Olive" title="b2">m</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> )</span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c2">H2</font> iff for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</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">m</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> )</span><br/>





<a NAME="E1:174"/><span class="lab"><font color="Green" title="E140">A1</font></span>: 
( ( for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> ) 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">m</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a>  ) implies for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</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">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="174_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:174_1"/><span class="lab"><font color="Green" title="E141">A2</font></span>: 
for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> ) 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">m</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</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">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</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">m</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font></span><br/>

<a NAME="E2:174_1"/>
for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</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">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="174_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">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"> ( ( 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>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font> ) 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="c4">m</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> )</span><br/>

<a NAME="E1:174_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> <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>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font> ) 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="c4">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="174_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:174_1_1_1"/><span class="lab"><font color="Green" title="E142">A3</font></span>: 
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>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c4">m</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font></span><br/>

<a NAME="E2:174_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> <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#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="174_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">j</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">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">m</font> 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="c5">j</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:174_1_1_1_1"/>
<font color="Maroon" title="c5">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c5">j</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span></span><br/>

<a NAME="E2:174_1_1_1_1"/><span class="kw">then </span>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c5">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:174_1_1_1"><span class="lab"><font color="Green" title="E142">A3</font></span></a></span>;<br/>
<a NAME="E3:174_1_1_1_1"/><span class="kw">then </span>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c5">j</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font></span>)</span>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D65" target="_self" title="MODELC_2:def.65">Def65</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:174_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="c5">j</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T50" target="_self" title="MODELC_2:th.50">Th50</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>
<a NAME="E3:174_1_1_1"/><span class="kw">then </span>
 <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#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:174_1"><span class="lab"><font color="Green" title="E141">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:174_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="c4">m</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D65" target="_self" title="MODELC_2:def.65">Def65</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>
<span class="kw">hence </span><a NAME="E2:174_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> <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>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font> ) 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="c4">m</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:174_1"/>
for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</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">m</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:174"/><span class="lab"><font color="Green" title="E141">A4</font></span>: 
( ( for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</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">m</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> ) implies for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> ) 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">m</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="174_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:174_2"/><span class="lab"><font color="Green" title="E142">A5</font></span>: 
for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</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">m</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> ) 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">m</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span><br/>

<a NAME="E2:174_2"/>
for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> ) 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">m</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="174_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">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"> ( ( 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#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> ) 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="c4">m</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a>  )</span><br/>

<a NAME="E1:174_2_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> <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#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> ) 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="c4">m</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="174_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:174_2_1_1"/><span class="lab"><font color="Green" title="E143">A6</font></span>: 
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#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c4">m</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span><br/>

<a NAME="E2:174_2_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> <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>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="174_2_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">j</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">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">m</font> 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="c5">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:174_2_1_1_1"/>
<font color="Maroon" title="c5">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c5">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font></span><br/>

<a NAME="E2:174_2_1_1_1"/><span class="kw">then </span>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c5">j</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:174_2_1_1"><span class="lab"><font color="Green" title="E143">A6</font></span></a></span>;<br/>
<a NAME="E3:174_2_1_1_1"/><span class="kw">then </span>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c5">j</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font></span>)</span>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T50" target="_self" title="MODELC_2:th.50">Th50</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:174_2_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="c5">j</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D65" target="_self" title="MODELC_2:def.65">Def65</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>
<a NAME="E3:174_2_1_1"/><span class="kw">then </span>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:174_2"><span class="lab"><font color="Green" title="E142">A5</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:174_2_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="c4">m</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D65" target="_self" title="MODELC_2:def.65">Def65</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>
<span class="kw">hence </span><a NAME="E2:174_2_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> <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#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> ) 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="c4">m</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:174_2"/>
for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> ) 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">m</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> 
 ; <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 NAME="E3:174"/>
( <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#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c2">H2</font> iff <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c2">H2</font></span>)</span>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D65" target="_self" title="MODELC_2:def.65">Def65</a></span>;<br/>
<a NAME="E4:174"/><span class="kw">then </span>
( <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#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c2">H2</font> iff <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> <a href="modelc_2.html#K26" title="MODELC_2:func.26">'R'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T55" target="_self" title="MODELC_2:th.55">Th55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:174"/>
( <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#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c2">H2</font> iff for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</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">m</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">H2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:174"><span class="lab"><font color="Green" title="E140">A1</font></span></a>, <a class="txt" href="#E2:174"><span class="lab"><font color="Green" title="E141">A4</font></span></a>, <a class="ref" href="modelc_2.html#T62" target="_self" title="MODELC_2:th.62">Th62</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>
