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

<b>let </b><font color="Maroon">G</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="lang1.html#L1" target="_self">DTConstrStr</a> ;<br/><b>let </b><font color="Maroon">n</font> be   <a href="lang1.html#NM2">String</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">n1</font> be   <a href="lang1.html#NM2">String</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">n2</font> be   <a href="lang1.html#NM2">String</a> of <font color="Maroon">G</font>;<br/>







<b>given </b><font color="Maroon">m1</font> being   <a href="lang1.html#NM2">String</a> of <font color="Maroon">G</font>, <font color="Maroon">m2</font> being   <a href="lang1.html#NM2">String</a> of <font color="Maroon">G</font>, <font color="Maroon">m3</font> being   <a href="lang1.html#NM2">String</a> of <font color="Maroon">G</font>, <font color="Maroon">s</font> being   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">G</font><b> such that </b><a NAME="E1:17"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">n1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="lang1.html#K1" target="_self">^</a> <span class="p2"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">m2</font> &amp; <font color="Maroon">n2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">m3</font></span>)</span> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">m2</font> &amp; <font color="Maroon">s</font> <a href="lang1.html#R1" target="_self">==&gt;</a> <font color="Maroon">m3</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lang1.html#D4" target="_self">LANG1:def 4</a><br/>

<b>thus </b><a NAME="E2:17"/>
<font color="Maroon">n</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">n1</font> <a href="lang1.html#R2" target="_self">==&gt;</a> <font color="Maroon">n</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">n2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>take </b>
<font color="Maroon">n</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">m1</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="lang1.html#D4" target="_self">LANG1:def 4</a><br/>

<b>take </b>
<font color="Maroon">m2</font>
;<br/>

<b>take </b>
<font color="Maroon">m3</font>
;<br/>

<b>take </b>
<font color="Maroon">s</font>
;<br/>

<b>thus </b><font color="Maroon">n</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">n1</font> = 
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="lang1.html#K1" target="_self">^</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="lang1.html#K1" target="_self">^</a> <span class="p3"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span></span>)</span></span>)</span> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">m2</font>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">m1</font></span>)</span> <a href="lang1.html#K1" target="_self">^</a> <span class="p2"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">m2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
;<br/>

<b>thus </b><font color="Maroon">n</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">n2</font> = 
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="lang1.html#K1" target="_self">^</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">m3</font></span>)</span></span>)</span> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">m2</font>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">m1</font></span>)</span> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">m3</font></span>)</span> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">m2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
;<br/>

<b>thus </b><a NAME="E3:17_1"/>
<font color="Maroon">s</font> <a href="lang1.html#R1" target="_self">==&gt;</a> <font color="Maroon">m3</font>
 <b>by </b><i/>;<br/>


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

<b>take </b>
<font color="Maroon">m1</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="lang1.html#D4" target="_self">LANG1:def 4</a><br/>

<b>take </b>
<font color="Maroon">m2</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">n</font>
;<br/>

<b>take </b>
<font color="Maroon">m3</font>
;<br/>

<b>take </b>
<font color="Maroon">s</font>
;<br/>

<b>thus </b><a NAME="E3:17"/>
( <font color="Maroon">n1</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="lang1.html#K1" target="_self">^</a> <span class="p2"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">n</font></span>)</span> &amp; <font color="Maroon">n2</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">m3</font></span>)</span> <a href="lang1.html#K1" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="lang1.html#K1" target="_self">^</a> <font color="Maroon">n</font></span>)</span> &amp; <font color="Maroon">s</font> <a href="lang1.html#R1" target="_self">==&gt;</a> <font color="Maroon">m3</font> )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/>


</div>
