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<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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">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  ex <font color="Olive" title="b2">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( (  for <font color="Olive" title="b3">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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> <font color="Maroon" title="c1">H1</font> ) &amp;  <a href="modelc_2.html#K29" title="MODELC_2:func.29">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#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">H2</font> iff  ex <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( (  for <font color="Olive" title="b2">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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#K29" title="MODELC_2:func.29">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="E1:168"/><span class="lab"><font color="Green" title="E118">A1</font></span>: 
(  ex <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( (  for <font color="Olive" title="b2">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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">Evaluate</a> (<font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>) ) &amp;  <a href="modelc_2.html#K29" title="MODELC_2:func.29">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#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>) ) implies  ex <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( (  for <font color="Olive" title="b2">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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#K29" title="MODELC_2:func.29">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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="168_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:168_1"/>
 ex <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( (  for <font color="Olive" title="b2">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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">Evaluate</a> (<font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>) ) &amp;  <a href="modelc_2.html#K29" title="MODELC_2:func.29">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#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>) )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( (  for <font color="Olive" title="b2">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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#K29" title="MODELC_2:func.29">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/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:168_1"/><span class="lab"><font color="Green" title="E119">A2</font></span>: 
 for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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">Evaluate</a> (<font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>)
 <span class="kw">and </span><br/><a NAME="E4:168_1"/><span class="lab"><font color="Green" title="E120">A3</font></span>: 
 <a href="modelc_2.html#K29" title="MODELC_2:func.29">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#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>)
 ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">m</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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#K29" title="MODELC_2:func.29">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="E5:168_1"/>
 for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:168_1"><span class="lab"><font color="Green" title="E119">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:168_1"/>
( (  for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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#K29" title="MODELC_2:func.29">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="#E4:168_1"><span class="lab"><font color="Green" title="E120">A3</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>
<a NAME="E2:168"/><span class="lab"><font color="Green" title="E119">A4</font></span>: 
(  ex <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( (  for <font color="Olive" title="b2">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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#K29" title="MODELC_2:func.29">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  ex <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( (  for <font color="Olive" title="b2">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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">Evaluate</a> (<font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>) ) &amp;  <a href="modelc_2.html#K29" title="MODELC_2:func.29">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#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>) ) )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="168_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:168_2"/>
 ex <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( (  for <font color="Olive" title="b2">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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#K29" title="MODELC_2:func.29">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( (  for <font color="Olive" title="b2">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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">Evaluate</a> (<font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>) ) &amp;  <a href="modelc_2.html#K29" title="MODELC_2:func.29">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#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>) )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:168_2"/><span class="lab"><font color="Green" title="E120">A5</font></span>: 
 for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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>
 <span class="kw">and </span><br/><a NAME="E4:168_2"/><span class="lab"><font color="Green" title="E121">A6</font></span>: 
 <a href="modelc_2.html#K29" title="MODELC_2:func.29">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>
 ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">m</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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">Evaluate</a> (<font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>) ) &amp;  <a href="modelc_2.html#K29" title="MODELC_2:func.29">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#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>) )</span><br/>

<a NAME="E5:168_2"/>
 for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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">Evaluate</a> (<font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:168_2"><span class="lab"><font color="Green" title="E120">A5</font></span></a>, <a class="ref" href="modelc_2.html#D63" target="_self" onmouseover="rs('modelc_2/D63')" onmouseout="rh()">Def63</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:168_2"/>
( (  for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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">Evaluate</a> (<font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>) ) &amp;  <a href="modelc_2.html#K29" title="MODELC_2:func.29">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#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:168_2"><span class="lab"><font color="Green" title="E121">A6</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>
<a NAME="E3:168"/>
( <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#R6" title="MODELC_2:pred.6">|=</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>)</span>)</span> <a href="modelc_2.html#K23" title="MODELC_2:func.23">'U'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>)</span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T54" target="_self" onmouseover="rs('modelc_2/T54')" onmouseout="rh()">Th54</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:168"/>
( <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  ex <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( (  for <font color="Olive" title="b2">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K29" title="MODELC_2:func.29">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#K29" title="MODELC_2:func.29">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="#E1:168"><span class="lab"><font color="Green" title="E118">A1</font></span></a>, <a class="txt" href="#E2:168"><span class="lab"><font color="Green" title="E119">A4</font></span></a>, <a class="ref" href="modelc_2.html#T60" target="_self" onmouseover="rs('modelc_2/T60')" onmouseout="rh()">Th60</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
