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<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <span class="kw">means </span><font color="Maroon" title="c2">t</font> is $1 <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">TT</font> =  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">T</font> = <font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K28" title="FOMODEL1:func.28">-termsOfMaxDepth</a> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">TF</font> = <font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K28" title="FOMODEL1:func.28">-termsOfMaxDepth</a>  as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ;<br/>
<a NAME="E2:102_1_1"/>
<font color="Maroon" title="c2">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D32" target="_self" title="FOMODEL1:def.32">DefTermal2</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">mm</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E4:102_1_1"/><span class="lab"><font color="Green" title="E33">B0</font></span>: 
<font color="Maroon" title="c2">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">TF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">mm</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel1.html#E39"><span class="lab"><font color="Green" title="E20">Lm26</font></span></a></span>;<br/>
<a NAME="E5:102_1_1"/>
<font color="Maroon" title="c2">t</font> is <font color="Maroon" title="c6">mm</font> <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D33" target="_self" title="FOMODEL1:def.33">DefTermal</a>, <a class="txt" href="#E4:102_1_1"><span class="lab"><font color="Green" title="E33">B0</font></span></a></span>;<br/>
<a NAME="E6:102_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">B1</font></span>: 
 ex <font color="Olive" title="b1">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">IT</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E8:102_1_1"/><span class="lab"><font color="Green" title="E35">B2</font></span>: 
( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">IT</font>] &amp; (  for <font color="Olive" title="b1">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>] holds <br/><font color="Maroon" title="c7">IT</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> ) )
 <span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S5" title="NAT_1:sch.5">NAT_1:sch 5</a>(<a class="txt" href="#E6:102_1_1"><span class="lab"><font color="Green" title="E34">B1</font></span></a>);<br/></span>
<span class="kw">take </span>
<font color="Maroon" title="c7">IT</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="c2">t</font> is <font color="Maroon" title="c7">IT</font> <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a>  &amp; (  for <font color="Olive" title="b1">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon" title="c2">t</font> is <font color="Olive" title="b1">n</font> <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a>  holds <br/><font color="Maroon" title="c7">IT</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> ) )</span><br/>

<span class="kw">thus </span><a NAME="E9:102_1_1"/>
( <font color="Maroon" title="c2">t</font> is <font color="Maroon" title="c7">IT</font> <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a>  &amp; (  for <font color="Olive" title="b1">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon" title="c2">t</font> is <font color="Olive" title="b1">n</font> <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a>  holds <br/><font color="Maroon" title="c7">IT</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:102_1_1"><span class="lab"><font color="Green" title="E35">B2</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/>


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