<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/>





<b>thus </b><a NAME="E1:170"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="zf_lang.html#V6">universal</a> implies <font color="Maroon">c<sub>1</sub></font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> is <a href="zf_lang.html#V6">universal</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="170_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon">c<sub>4</sub></font> being   <a href="zf_lang.html#NM1">Variable</a>, <font color="Maroon">c<sub>5</sub></font> being   <a href="zf_lang.html#NM2">ZF-formula</a><b> such that </b><a NAME="E1:170_1"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="zf_lang.html#K8">All</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="zf_lang.html#D14">ZF_LANG:def 14</a><br/>

<a NAME="E2:170_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> )
 
;<br/>
<b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="zf_lang.html#NM1">Variable</a><b> such that </b><br/><a NAME="E4:170_1"/><i><font color="Green">E73</font></i>: 
( ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> ) )
 ;<br/>
<a NAME="E5:170_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="zf_lang.html#K8">All</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E1:170_1"><i><font color="Green">E72</font></i></a>, <a class="txt" href="zf_lang1.html#E4:170_1"><i><font color="Green">E73</font></i></a>, <a class="ref" href="zf_lang1.html#T173" target="_self">Th173</a>, <a class="ref" href="zf_lang1.html#T174" target="_self">Th174</a></i>;<br/>
<b>hence </b><a NAME="E6:170_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> is <a href="zf_lang.html#V6">universal</a>
 <b>by </b><i><a class="ref" href="zf_lang.html#T16">ZF_LANG:16</a></i>;<br/>


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

<b>assume </b><a NAME="E2:170"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> is <a href="zf_lang.html#V6">universal</a>
 ;<br/>

<a NAME="E3:170"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> 3 &amp; 3 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="zf_lang.html#T29">ZF_LANG:29</a></i>;<br/>
<a NAME="E4:170"/><b>then </b>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E5:170"/><b>then </b><i><font color="Green">E73</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 4 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 &amp; 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E2:170"><i><font color="Green">E72</font></i></a>, <a class="ref" href="zf_lang1.html#T148" target="_self">Th148</a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a>, <a class="ref" href="zf_lang.html#T39">ZF_LANG:39</a></i>;<br/>
<a NAME="E6:170"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="zf_lang1.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E7:170"/><b>then </b>
4 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> 1
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E5:170"><i><font color="Green">E73</font></i></a>, <a class="ref" href="zf_lang1.html#D4" target="_self">Def4</a></i>;<br/>
<b>hence </b><a NAME="E8:170"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="zf_lang.html#V6">universal</a>
 <b>by </b><i><a class="ref" href="zf_lang.html#T45">ZF_LANG:45</a></i>;<br/>


</div>
