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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">phi</font> is $1 <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c3">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E2:93_1_1"/><span class="lab"><font color="Green" title="E46">B0</font></span>: 
<font color="Maroon" title="c2">phi</font> is <font color="Maroon" title="c3">m</font> <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#D25" target="_self" title="FOMODEL2:def.25">DefWff2</a></span>;<br/>
<a NAME="E3:93_1_1"/><span class="lab"><font color="Green" title="E47">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>]
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:93_1_1"><span class="lab"><font color="Green" title="E46">B0</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">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="E5:93_1_1"/><span class="lab"><font color="Green" title="E48">B2</font></span>: 
( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">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="c4">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="#E3:93_1_1"><span class="lab"><font color="Green" title="E47">B1</font></span></a>);<br/></span>
<span class="kw">take </span>
<font color="Maroon" title="c4">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">phi</font> is <font color="Maroon" title="c4">IT</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</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">phi</font> is <font color="Olive" title="b1">n</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  holds <br/><font color="Maroon" title="c4">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="E6:93_1_1"/>
( <font color="Maroon" title="c2">phi</font> is <font color="Maroon" title="c4">IT</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</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">phi</font> is <font color="Olive" title="b1">n</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  holds <br/><font color="Maroon" title="c4">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="#E5:93_1_1"><span class="lab"><font color="Green" title="E48">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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