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

<span class="kw">let </span><font color="Maroon" title="c1">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">phi1</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="c1">S</font> holds   <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">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="Olive" title="b1">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Olive" title="b2">phi2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Olive" title="b1">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Olive" title="b2">phi2</font></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span><br/><span class="kw">let </span><font color="Maroon" title="c2">phi1</font>, <font color="Maroon" title="c3">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="c1">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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">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="c2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">nor</font> =  <a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">phi</font> = <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="c1">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="c2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">m1</font> =  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">m2</font> =  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">m</font> =  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font></span>)</span>,<span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font></span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c9">M</font> =  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">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="c2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi2</font></span>)</span>;<br/>
<a NAME="E1:143"/>
(  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">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="c2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi2</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">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="c2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi2</font></span>)</span> &amp;  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">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="c2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi2</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font> &amp;  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">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="c2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi2</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel2.html#E78"><span class="lab"><font color="Green" title="E61">Lm39</font></span></a></span>;<br/>
<a NAME="E2:143"/><span class="kw">then </span>
 <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">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="c2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi2</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font></span>)</span>,<span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#D10" title="XXREAL_0:def.10">XXREAL_0:def 10</a></span>;<br/>
<a NAME="E3:143"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">B1</font></span>: 
<span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">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="c2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">d1</font> = <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font></span>)</span>)</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font></span>)</span>, <font color="Maroon" title="c11">d2</font> = <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font></span>)</span>)</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font></span>)</span> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> ;<br/>
<a NAME="E5:143"/>
( <font color="Maroon" title="c2">phi1</font> is <span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c10">d1</font></span>)</span> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  &amp; <font color="Maroon" title="c3">phi2</font> is <span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c11">d2</font></span>)</span> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D31" target="_self" title="FOMODEL2:def.31">DefDepth</a></span>;<br/>
<a NAME="E6:143"/><span class="kw">then </span>
( <font color="Maroon" title="c2">phi1</font> is <span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c10">d1</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  &amp; <font color="Maroon" title="c3">phi2</font> is <span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c11">d2</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  )
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">phi11</font> = <font color="Maroon" title="c2">phi1</font>, <font color="Maroon" title="c13">phi22</font> = <font color="Maroon" title="c3">phi2</font> as   <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font></span>)</span>,<span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font></span>)</span>) <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="c1">S</font> ;<br/>
<a NAME="E8:143"/><span class="lab"><font color="Green" title="E64">Z0</font></span>: 
<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="c1">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="c2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi2</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="c1">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="c12">phi11</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c13">phi22</font>
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="143_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c14">n</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"> ( <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="c1">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="c2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi2</font> is <font color="Maroon" title="c14">n</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  implies <font color="Maroon" title="c14">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )</span><br/><span class="kw">assume </span><a NAME="E1:143_1"/>
<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="c1">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="c2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi2</font> is <font color="Maroon" title="c14">n</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</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="c14">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span><br/><a NAME="E2:143_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">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="c2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D31" target="_self" title="FOMODEL2:def.31">DefDepth</a></span>;<br/><span class="kw">hence </span><a NAME="E3:143_1"/>
<font color="Maroon" title="c14">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:143"><span class="lab"><font color="Green" title="E63">B1</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</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">hence </span><a NAME="E10:143"/>
 <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">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="c2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c2">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi2</font></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:143"><span class="lab"><font color="Green" title="E64">Z0</font></span></a>, <a class="ref" href="fomodel2.html#D31" target="_self" title="FOMODEL2:def.31">DefDepth</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/>


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