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<span class="kw">let </span><font color="Maroon" title="c1">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="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">phi</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  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Olive" title="b2">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp;  not <font color="Olive" title="b2">phi</font> is  <a href="fomodel2.html#V5" title="FOMODEL2:attr.5">exal</a>  holds <br/> ex <font color="Olive" title="b3">phi2</font> being  <font color="Maroon" title="c1">m</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Olive" title="b1">S</font> st  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Olive" title="b2">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">phi2</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">phi</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  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Olive" title="b1">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp;  not <font color="Olive" title="b1">phi</font> is  <a href="fomodel2.html#V5" title="FOMODEL2:attr.5">exal</a>  holds <br/> ex <font color="Olive" title="b2">phi2</font> being  <font color="Maroon" title="c1">m</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c2">S</font> st  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Olive" title="b1">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">phi2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">phi</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"> (  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp;  not <font color="Maroon" title="c3">phi</font> is  <a href="fomodel2.html#V5" title="FOMODEL2:attr.5">exal</a>  implies  ex <font color="Olive" title="b1">phi2</font> being  <font color="Maroon" title="c1">m</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c2">S</font> st  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Maroon" title="c3">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">phi2</font> )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">d</font> =  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">Phim</font> = <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">N</font> =  <a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">assume </span><a NAME="E1:174"/>
(  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp;  not <font color="Maroon" title="c3">phi</font> is  <a href="fomodel2.html#V5" title="FOMODEL2:attr.5">exal</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">phi2</font> being  <font color="Maroon" title="c1">m</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c2">S</font> st  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Maroon" title="c3">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">phi2</font></span><br/>

<a NAME="E2:174"/><span class="kw">then </span>
<font color="Maroon" title="c3">phi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">m</font> <a href="fomodel2.html#K35" title="FOMODEL2:func.35">-NorFormulasOf</a> <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel2.html#E76"><span class="lab"><font color="Green" title="E59">Lm13</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">phi1</font>, <font color="Maroon" title="c8">phi2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font><span class="kw"> such that </span><br/><a NAME="E4:174"/><span class="lab"><font color="Green" title="E76">B0</font></span>: 
<font color="Maroon" title="c3">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"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">S</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="c7">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c8">phi2</font>
 ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">phi11</font> = <font color="Maroon" title="c7">phi1</font>, <font color="Maroon" title="c10">phi22</font> = <font color="Maroon" title="c8">phi2</font> as  <font color="Maroon" title="c1">m</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D24" target="_self" title="FOMODEL2:def.24">DefWff1</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">d1</font> =  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c9">phi11</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">d2</font> =  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c10">phi22</font>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c10">phi22</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Maroon" title="c3">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">phi22</font></span><br/>

<a NAME="E6:174"/>
<font color="Maroon" title="c3">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"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">S</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="c9">phi11</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c10">phi22</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:174"><span class="lab"><font color="Green" title="E76">B0</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:174"/>
<font color="Maroon" title="c10">phi22</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="c3">phi</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#T23" target="_self" title="FOMODEL2:th.23">Th23</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/>

<span class="kw">thus </span><a NAME="E8:174"/>
verum
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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