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

<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">BASSIGN</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span><br/>  for <font color="Olive" title="b2">t</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> <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b3">f</font> being   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K42" title="MODELC_2:func.42">Inf_seqModel</a> (<font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">BASSIGN</font>)</span>)</span> holds <br/> ( <font color="Olive" title="b2">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K22" title="MODELC_2:func.22">'X'</a> <font color="Olive" title="b3">f</font> iff  <a href="modelc_2.html#K29" title="MODELC_2:func.29">Shift</a> (<font color="Olive" title="b2">t</font>,1) <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Olive" title="b3">f</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">BASSIGN</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</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">  for <font color="Olive" title="b1">t</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> <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">f</font> being   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K42" title="MODELC_2:func.42">Inf_seqModel</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">BASSIGN</font>)</span>)</span> holds <br/> ( <font color="Olive" title="b1">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K22" title="MODELC_2:func.22">'X'</a> <font color="Olive" title="b2">f</font> iff  <a href="modelc_2.html#K29" title="MODELC_2:func.29">Shift</a> (<font color="Olive" title="b1">t</font>,1) <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Olive" title="b2">f</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">t</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> <font color="Maroon" title="c1">S</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">f</font> being   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K42" title="MODELC_2:func.42">Inf_seqModel</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">BASSIGN</font>)</span>)</span> holds <br/> ( <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K22" title="MODELC_2:func.22">'X'</a> <font color="Olive" title="b1">f</font> iff  <a href="modelc_2.html#K29" title="MODELC_2:func.29">Shift</a> (<font color="Maroon" title="c3">t</font>,1) <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Olive" title="b1">f</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K42" title="MODELC_2:func.42">Inf_seqModel</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">BASSIGN</font>)</span>)</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"> ( <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K22" title="MODELC_2:func.22">'X'</a> <font color="Maroon" title="c4">f</font> iff  <a href="modelc_2.html#K29" title="MODELC_2:func.29">Shift</a> (<font color="Maroon" title="c3">t</font>,1) <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Maroon" title="c4">f</font> )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">S1</font> =  <a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">t1</font> =  <a href="modelc_2.html#K29" title="MODELC_2:func.29">Shift</a> (<font color="Maroon" title="c3">t</font>,1);<br/>
<span class="kw">set </span><font color="Maroon" title="c7">t1p</font> =  <a href="modelc_2.html#K28" title="MODELC_2:func.28">Shift</a> (<font color="Maroon" title="c3">t</font>,1,<font color="Maroon" title="c1">S</font>);<br/>
<a NAME="E1:148"/><span class="lab"><font color="Green" title="E105">A1</font></span>: 
 <a href="modelc_2.html#K22" title="MODELC_2:func.22">'X'</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K33" title="MODELC_2:func.33">Next_0</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">S</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D48" target="_self" onmouseover="rs('modelc_2/D48')" onmouseout="rh()">Def48</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:148"/>
( <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K22" title="MODELC_2:func.22">'X'</a> <font color="Maroon" title="c4">f</font> implies  <a href="modelc_2.html#K29" title="MODELC_2:func.29">Shift</a> (<font color="Maroon" title="c3">t</font>,1) <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Maroon" title="c4">f</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"> (  <a href="modelc_2.html#K29" title="MODELC_2:func.29">Shift</a> (<font color="Maroon" title="c3">t</font>,1) <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Maroon" title="c4">f</font> implies <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K22" title="MODELC_2:func.22">'X'</a> <font color="Maroon" title="c4">f</font> )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="148_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:148_1"/>
<font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K22" title="MODELC_2:func.22">'X'</a> <font color="Maroon" title="c4">f</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">  <a href="modelc_2.html#K29" title="MODELC_2:func.29">Shift</a> (<font color="Maroon" title="c3">t</font>,1) <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Maroon" title="c4">f</font></span><br/>

<a NAME="E2:148_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">Fid</a> (<span class="p2">(<span class="default"><a href="modelc_2.html#K33" title="MODELC_2:func.33">Next_0</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">S</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:148"><span class="lab"><font color="Green" title="E105">A1</font></span></a></span>;<br/>
<a NAME="E3:148_1"/><span class="kw">then </span>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Next_univ</a> (<font color="Maroon" title="c3">t</font>,<span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">Fid</a> (<font color="Maroon" title="c4">f</font>,<span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D47" target="_self" onmouseover="rs('modelc_2/D47')" onmouseout="rh()">Def47</a></span>;<br/>
<a NAME="E4:148_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">Fid</a> (<font color="Maroon" title="c4">f</font>,<span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K28" title="MODELC_2:func.28">Shift</a> (<font color="Maroon" title="c3">t</font>,1,<font color="Maroon" title="c1">S</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D46" target="_self" onmouseover="rs('modelc_2/D46')" onmouseout="rh()">Def46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:148_1"/>
 <a href="modelc_2.html#K29" title="MODELC_2:func.29">Shift</a> (<font color="Maroon" title="c3">t</font>,1) <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Maroon" title="c4">f</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"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E3:148"/>
 <a href="modelc_2.html#K29" title="MODELC_2:func.29">Shift</a> (<font color="Maroon" title="c3">t</font>,1) <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Maroon" title="c4">f</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"> <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K22" title="MODELC_2:func.22">'X'</a> <font color="Maroon" title="c4">f</font></span><br/>

<a NAME="E4:148"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">Fid</a> (<font color="Maroon" title="c4">f</font>,<span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K29" title="MODELC_2:func.29">Shift</a> (<font color="Maroon" title="c3">t</font>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 
;<br/>
<a NAME="E5:148"/><span class="kw">then </span>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Next_univ</a> (<font color="Maroon" title="c3">t</font>,<span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">Fid</a> (<font color="Maroon" title="c4">f</font>,<span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D46" target="_self" onmouseover="rs('modelc_2/D46')" onmouseout="rh()">Def46</a></span>;<br/>
<a NAME="E6:148"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">Fid</a> (<span class="p2">(<span class="default"><a href="modelc_2.html#K22" title="MODELC_2:func.22">'X'</a> <font color="Maroon" title="c4">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:148"><span class="lab"><font color="Green" title="E105">A1</font></span></a>, <a class="ref" href="modelc_2.html#D47" target="_self" onmouseover="rs('modelc_2/D47')" onmouseout="rh()">Def47</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:148"/>
<font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K22" title="MODELC_2:func.22">'X'</a> <font color="Maroon" title="c4">f</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"> verum</span><br/>


</div>
