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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b2">p2</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b3">phi</font>, <font color="Olive" title="b4">phi2</font> being   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Olive" title="b1">S</font>  st  not <font color="Olive" title="b3">phi</font> is  <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  holds <br/>( <font color="Olive" title="b3">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b4">phi2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">p2</font> iff ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">phi</font> &amp; <font color="Olive" title="b4">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K40" title="FOMODEL2:func.40">head</a> <font color="Olive" title="b3">phi</font> &amp; <font color="Olive" title="b2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Olive" title="b3">phi</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p2</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b2">phi</font>, <font color="Olive" title="b3">phi2</font> being   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c2">S</font>  st  not <font color="Olive" title="b2">phi</font> is  <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  holds <br/>( <font color="Olive" title="b2">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b3">phi2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b1">p2</font> iff ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">phi</font> &amp; <font color="Olive" title="b3">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K40" title="FOMODEL2:func.40">head</a> <font color="Olive" title="b2">phi</font> &amp; <font color="Olive" title="b1">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Olive" title="b2">phi</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">p2</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">phi</font>, <font color="Olive" title="b2">phi2</font> being   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c2">S</font>  st  not <font color="Olive" title="b1">phi</font> is  <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  holds <br/>( <font color="Olive" title="b1">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">phi2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">p2</font> iff ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">phi</font> &amp; <font color="Olive" title="b2">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K40" title="FOMODEL2:func.40">head</a> <font color="Olive" title="b1">phi</font> &amp; <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Olive" title="b1">phi</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">phi</font>, <font color="Maroon" title="c5">phi2</font> be   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">phi</font> is  <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  implies ( <font color="Maroon" title="c4">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">phi2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">p2</font> iff ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">phi</font> &amp; <font color="Maroon" title="c5">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K40" title="FOMODEL2:func.40">head</a> <font color="Maroon" title="c4">phi</font> &amp; <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Maroon" title="c4">phi</font> ) ) )</span><br/>









<span class="kw">set </span><font color="Maroon" title="c6">Phi</font> =  <a href="fomodel2.html#K39" title="FOMODEL2:func.39">SubWffsOf</a> <font color="Maroon" title="c4">phi</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">F</font> = <font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">s</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">phi</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">SS</font> =  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">assume </span><a NAME="E1:171"/><span class="lab"><font color="Green" title="E75">B3</font></span>: 
 not <font color="Maroon" title="c4">phi</font> is  <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">phi2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">p2</font> iff ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">phi</font> &amp; <font color="Maroon" title="c5">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K40" title="FOMODEL2:func.40">head</a> <font color="Maroon" title="c4">phi</font> &amp; <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Maroon" title="c4">phi</font> ) )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">phi1</font> being   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c2">S</font>, <font color="Maroon" title="c11">p</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><span class="kw"> such that </span><br/><a NAME="E3:171"/><span class="lab"><font color="Green" title="E76">B0</font></span>: 
( <font color="Maroon" title="c11">p</font> is  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c2">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  &amp;  <a href="fomodel2.html#K39" title="FOMODEL2:func.39">SubWffsOf</a> <font color="Maroon" title="c4">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">phi1</font>,<font color="Maroon" title="c11">p</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c4">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">phi</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c10">phi1</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c11">p</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D35" target="_self" title="FOMODEL2:def.35">DefSub1</a></span>;<br/>
<a NAME="E4:171"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel2.html#K39" title="FOMODEL2:func.39">SubWffsOf</a> <font color="Maroon" title="c4">phi</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c10">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel2.html#K39" title="FOMODEL2:func.39">SubWffsOf</a> <font color="Maroon" title="c4">phi</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c11">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:171"><span class="lab"><font color="Green" title="E76">B0</font></span></a></span>;<br/>
<a NAME="E5:171"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">B4</font></span>: 
( <span class="p1">(<span class="default"><a href="fomodel2.html#K39" title="FOMODEL2:func.39">SubWffsOf</a> <font color="Maroon" title="c4">phi</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">phi1</font> &amp; <span class="p1">(<span class="default"><a href="fomodel2.html#K39" title="FOMODEL2:func.39">SubWffsOf</a> <font color="Maroon" title="c4">phi</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">p</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T29" title="FOMODEL0:th.29">FOMODEL0:29</a></span>;<br/>
<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">phi</font> &amp; <font color="Maroon" title="c5">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K40" title="FOMODEL2:func.40">head</a> <font color="Maroon" title="c4">phi</font> &amp; <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Maroon" title="c4">phi</font> implies <font color="Maroon" title="c4">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">phi2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">p2</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:171_1"/><span class="lab"><font color="Green" title="E78">B1</font></span>: 
<font color="Maroon" title="c4">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">phi2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">p2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">phi</font> &amp; <font color="Maroon" title="c5">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K40" title="FOMODEL2:func.40">head</a> <font color="Maroon" title="c4">phi</font> &amp; <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Maroon" title="c4">phi</font> )</span><br/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">Z0</font></span>: <font color="Maroon" title="c4">phi</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">phi2</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">p2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T32" title="FINSEQ_1:th.32">FINSEQ_1:32</a></span>
<br/>.= 
<font color="Maroon" title="c1">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T41" title="FINSEQ_1:th.41">FINSEQ_1:41</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:171_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">phi</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T6" title="FOMODEL0:th.6">FOMODEL0:6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K40" title="FOMODEL2:func.40">head</a> <font color="Maroon" title="c4">phi</font> &amp; <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Maroon" title="c4">phi</font> )</span><br/><a NAME="E4:171_1"/>
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">p2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">phi</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">phi</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c2">S</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:171_1"><span class="lab"><font color="Green" title="E78">B1</font></span></a>, <a class="ref" href="finseq_1.html#T30" title="FINSEQ_1:th.30">FINSEQ_1:30</a>, <a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/><a NAME="E5:171_1"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">p2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E6:171_1"/><span class="kw">then </span>
( <font color="Maroon" title="c3">p2</font> is  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c2">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">phi2</font>,<font color="Maroon" title="c3">p2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">phi2</font>,<font color="Maroon" title="c3">p2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c4">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">phi</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c5">phi2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">p2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:171_1"><span class="lab"><font color="Green" title="E79">Z0</font></span></a>, <a class="txt" href="#E1:171_1"><span class="lab"><font color="Green" title="E78">B1</font></span></a>, <a class="ref" href="fomodel0.html#T6" title="FOMODEL0:th.6">FOMODEL0:6</a>, <a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/><a NAME="E7:171_1"/><span class="kw">then </span>
 <a href="fomodel2.html#K39" title="FOMODEL2:func.39">SubWffsOf</a> <font color="Maroon" title="c4">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">phi2</font>,<font color="Maroon" title="c3">p2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:171"><span class="lab"><font color="Green" title="E75">B3</font></span></a>, <a class="ref" href="fomodel2.html#D35" target="_self" title="FOMODEL2:def.35">DefSub1</a></span>;<br/><span class="kw">hence </span><a NAME="E8:171_1"/>
( <font color="Maroon" title="c5">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K40" title="FOMODEL2:func.40">head</a> <font color="Maroon" title="c4">phi</font> &amp; <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Maroon" title="c4">phi</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E7:171"/>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">phi</font> &amp; <font color="Maroon" title="c5">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K40" title="FOMODEL2:func.40">head</a> <font color="Maroon" title="c4">phi</font> &amp; <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Maroon" title="c4">phi</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">phi2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">p2</font></span><br/>

<span class="kw">hence </span><a NAME="E8:171"/>
<font color="Maroon" title="c4">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">phi2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">p2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:171"><span class="lab"><font color="Green" title="E77">B4</font></span></a>, <a class="txt" href="#E3:171"><span class="lab"><font color="Green" title="E76">B0</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
