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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/>



<b>assume </b><a NAME="E1:80"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#R1" target="_self">is_immediate_constituent_of</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>thus </b><a NAME="E2:80"/>
<font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">c<sub>2</sub></font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="zf_lang.html#D41" target="_self">ZF_LANG:def 41</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1"><b>proof </b></a><div class="add">

<b>take </b><font color="Maroon">c<sub>3</sub></font> = 2; <i><font color="Red">:: according to </font></i><a class="ref" href="zf_lang.html#D40" target="_self">ZF_LANG:def 40</a><br/>

<b>take </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>;<br/>

<b>thus </b><a NAME="E1:80_1"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>thus </b><a NAME="E2:80_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/>

<b>thus </b><a NAME="E3:80_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E4:80_1"/><i><font color="Green">E68</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E5:80_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<a NAME="E6:80_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E7:80_1"/><b>then </b><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="zf_lang.html#E4:80_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>1</sub></font>
;<br/>

<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<b>thus </b><a NAME="E8:80_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="zf_lang.html#E7:80_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/>

<b>thus </b><a NAME="E9:80_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#R1" target="_self">is_immediate_constituent_of</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E1:80"><i><font color="Green">E67</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E3:80"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E4:80"/><b>then </b>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="zf_lang.html#E1:80"><i><font color="Green">E67</font></i></a>, <a class="ref" href="zf_lang.html#T81" target="_self">Th81</a></i>;<br/>
<b>hence </b><a NAME="E5:80"/>
contradiction
 ;<br/>


</div>
