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<span class="kw">set </span><font color="Maroon" title="c6">D</font> =  <a href="fomodel2.html#K29" title="FOMODEL2:func.29">Depth</a> <font color="Maroon" title="c5">phi</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">e</font> = <font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">d</font> = <font color="Maroon" title="c4">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="fomodel2.html#K29" title="FOMODEL2:func.29">Depth</a> <font color="Maroon" title="c5">phi</font></span>)</span> as   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">psi</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><span class="kw"> such that </span><br/><a NAME="E3:109_1_1"/><span class="lab"><font color="Green" title="E46">A1</font></span>: 
(  <a href="fomodel2.html#K29" title="FOMODEL2:func.29">Depth</a> <font color="Maroon" title="c9">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K29" title="FOMODEL2:func.29">Depth</a> <font color="Maroon" title="c5">phi</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">psi</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel3.html#E56"><span class="lab"><font color="Green" title="E45">Lm33</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">DD</font> =  <a href="fomodel2.html#K29" title="FOMODEL2:func.29">Depth</a> <font color="Maroon" title="c9">psi</font>;<br/>
<a NAME="E4:109_1_1"/>
<font color="Maroon" title="c9">psi</font> <a href="fomodel3.html#K25" title="FOMODEL3:func.25">null</a> <font color="Maroon" title="c8">d</font> is <span class="p1">(<span class="default"><a href="fomodel2.html#K29" title="FOMODEL2:func.29">Depth</a> <font color="Maroon" title="c9">psi</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">d</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E5:109_1_1"/>
 for <font color="Olive">b<sub>1</sub></font> being   <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c5">phi</font> holds <br/><font color="Olive">b<sub>1</sub></font> is <font color="Maroon" title="c4">m</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:109_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="fomodel0.html#D22" onmouseover="rs('fomodel0/D22')" onmouseout="rh()">FOMODEL0:def 22</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/>


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