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

<b>let </b><font color="Maroon" title="c1">G</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="lang1.html#L1" title="LANG1:struct.1">DTConstrStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b2">n</font>, <font color="Olive" title="b3">n1</font>, <font color="Olive" title="b4">n2</font> being  <a href="lang1.html#NM2" title="LANG1:NM.2">String</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Olive" title="b2">n</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b3">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Olive" title="b1">s</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Olive" title="b4">n2</font> <a href="lang1.html#R2" title="LANG1:pred.2">==&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Olive" title="b4">n2</font></span><br/><b>let </b><font color="Maroon" title="c2">s</font> be   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">n1</font>, <font color="Olive" title="b3">n2</font> being  <a href="lang1.html#NM2" title="LANG1:NM.2">String</a> of <font color="Maroon" title="c1">G</font>  st <font color="Maroon" title="c2">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Olive" title="b1">n</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">s</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Olive" title="b3">n2</font> <a href="lang1.html#R2" title="LANG1:pred.2">==&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Olive" title="b3">n2</font></span><br/><b>let </b><font color="Maroon" title="c3">n</font>, <font color="Maroon" title="c4">n1</font>, <font color="Maroon" title="c5">n2</font> be   <a href="lang1.html#NM2" title="LANG1:NM.2">String</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c3">n</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">s</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> <a href="lang1.html#R2" title="LANG1:pred.2">==&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> )</span><br/>









<b>assume </b><a NAME="E1:14"/><i><font color="Green" title="E2">A1</font></i>: 
<font color="Maroon" title="c2">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c3">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">s</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> <a href="lang1.html#R2" title="LANG1:pred.2">==&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font></span><br/>

<b>take </b>
<font color="Maroon" title="c4">n1</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="lang1.html#D4" target="_self" title="LANG1:def.4">LANG1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">n2</font>, <font color="Olive" title="b2">n3</font> being  <a href="lang1.html#NM2" title="LANG1:NM.2">String</a> of <font color="Maroon" title="c1">G</font> ex <font color="Olive" title="b3">s</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c1">G</font> st <br/>( <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">s</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Olive" title="b3">s</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Olive" title="b1">n2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Olive" title="b2">n3</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Olive" title="b1">n2</font> &amp; <font color="Olive" title="b3">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Olive" title="b2">n3</font> )</span><br/>

<b>take </b>
<font color="Maroon" title="c5">n2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">n3</font> being  <a href="lang1.html#NM2" title="LANG1:NM.2">String</a> of <font color="Maroon" title="c1">G</font> ex <font color="Olive" title="b2">s</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c1">G</font> st <br/>( <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">s</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">s</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Olive" title="b1">n3</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> &amp; <font color="Olive" title="b2">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Olive" title="b1">n3</font> )</span><br/>

<b>take </b>
<font color="Maroon" title="c3">n</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">s</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c1">G</font> st <br/>( <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">s</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Olive" title="b1">s</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> &amp; <font color="Olive" title="b1">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c3">n</font> )</span><br/>

<b>take </b>
<font color="Maroon" title="c2">s</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">s</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">s</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> &amp; <font color="Maroon" title="c2">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c3">n</font> )</span><br/>

<b>thus </b><a NAME="E2:14"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">s</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">s</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c5">n2</font> &amp; <font color="Maroon" title="c2">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c3">n</font> )
 <b>by </b><i><a class="txt" href="#E1:14"><i><font color="Green" title="E2">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
