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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="E1:82"/>
<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><br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">c<sub>4</sub></font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E3:82"/><i><font color="Green">E69</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <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> &amp; <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>and </b><br/><a NAME="E4:82"/><i><font color="Green">E70</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="zf_lang.html#NM2">ZF-formula</a> st <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</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="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="zf_lang.html#R1" target="_self">is_immediate_constituent_of</a> <font color="Olive">b<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="zf_lang.html#D40" target="_self">Def40</a></i>;<br/>
<b>assume </b><a NAME="E5:82"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E6:82"/><b>then </b>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="zf_lang.html#E3:82"><i><font color="Green">E69</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/>
<a NAME="E7:82"/><b>then </b>
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E9:82"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/>
<a NAME="E10:82"/>
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<a NAME="E11:82"/><b>then </b>
( 1 <a href="nat_1.html#K1">+</a> <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> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="zf_lang.html#E9:82"><i><font color="Green">E71</font></i></a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> being   <a href="zf_lang.html#NM2">ZF-formula</a><b> such that </b><br/><a NAME="E13:82"/><i><font color="Green">E72</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="zf_lang.html#R1" target="_self">is_immediate_constituent_of</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="txt" href="zf_lang.html#E4:82"><i><font color="Green">E70</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>thus </b><a NAME="E14:82"/>
<font color="Maroon">c<sub>6</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#E3:82"><i><font color="Green">E69</font></i></a>, <a class="txt" href="zf_lang.html#E9:82"><i><font color="Green">E71</font></i></a>, <a class="txt" href="zf_lang.html#E13:82"><i><font color="Green">E72</font></i></a></i>;<br/>


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