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

<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   <a href="topgrp_1.html#NM4" title="TOPGRP_1:NM.4">TopGroup</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b3">W</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span>  ex <font color="Olive" title="b4">A</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b1">a</font> ex <font color="Olive" title="b5">B</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b2">b</font> st <font color="Olive" title="b4">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">B</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">W</font> ) implies <font color="Maroon" title="c1">T</font> is   <a href="topgrp_1.html#NM5" title="TOPGRP_1:NM.5">TopologicalGroup</a> )</span><br/>

<span class="kw">assume </span><a NAME="E1:77"/><span class="lab"><font color="Green" title="E40">A1</font></span>: 
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b3">W</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span>  ex <font color="Olive" title="b4">A</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b1">a</font> ex <font color="Olive" title="b5">B</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b2">b</font> st <font color="Olive" title="b4">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">B</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">W</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">T</font> is   <a href="topgrp_1.html#NM5" title="TOPGRP_1:NM.5">TopologicalGroup</a></span><br/>

<a NAME="E2:77"/><span class="lab"><font color="Green" title="E41">A2</font></span>: 
 for <font color="Olive" title="b1">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b2">W</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b1">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>   ex <font color="Olive" title="b3">A</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b1">a</font> st <font color="Olive" title="b3">A</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">W</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="77_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">W</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>   ex <font color="Olive" title="b2">A</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font> st <font color="Olive" title="b2">A</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">W</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">W</font> be    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">A</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font> st <font color="Olive" title="b1">A</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">W</font></span><br/>



<a NAME="E1:77_1"/>
<font color="Maroon" title="c3">W</font> is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D4" onmouseover="rs('group_1/D4')" onmouseout="rh()">GROUP_1:def 4</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">A</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">T</font>, <font color="Maroon" title="c5">B</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font><span class="kw"> such that </span><br/><a NAME="E3:77_1"/><span class="lab"><font color="Green" title="E42">A3</font></span>: 
<font color="Maroon" title="c4">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">B</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">W</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:77"><span class="lab"><font color="Green" title="E40">A1</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">B</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">B</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">W</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">B</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a>  or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">W</font> )</span><br/>

<span class="kw">assume </span><a NAME="E4:77_1"/><span class="lab"><font color="Green" title="E43">A4</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">B</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">W</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font><span class="kw"> such that </span><br/><a NAME="E6:77_1"/><span class="lab"><font color="Green" title="E44">A5</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> 
 <span class="kw">and </span><br/><a NAME="E7:77_1"/>
<font color="Maroon" title="c7">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">B</font>
 ;<br/>
<a NAME="E8:77_1"/>
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">T</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="connsp_2.html#T4" onmouseover="rs('connsp_2/T4')" onmouseout="rh()">CONNSP_2:4</a></span>;<br/>
<a NAME="E9:77_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">B</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:77_1"><span class="lab"><font color="Green" title="E43">A4</font></span></a>, <a class="txt" href="#E6:77_1"><span class="lab"><font color="Green" title="E44">A5</font></span></a></span>;<br/>
<a NAME="E10:77_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">g</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">B</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D4" onmouseover="rs('group_1/D4')" onmouseout="rh()">GROUP_1:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:77_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">W</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:77_1"><span class="lab"><font color="Green" title="E42">A3</font></span></a>, <a class="txt" href="#E6:77_1"><span class="lab"><font color="Green" title="E44">A5</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E3:77"/>
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b3">W</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">b</font>  ex <font color="Olive" title="b4">A</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b1">a</font> ex <font color="Olive" title="b5">B</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b2">b</font> st <font color="Olive" title="b4">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Olive" title="b5">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">W</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="77_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">W</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">b</font>  ex <font color="Olive" title="b2">A</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font> ex <font color="Olive" title="b3">B</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c3">b</font> st <font color="Olive" title="b2">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Olive" title="b3">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">W</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">W</font> be    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">b</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">A</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font> ex <font color="Olive" title="b2">B</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c3">b</font> st <font color="Olive" title="b1">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Olive" title="b2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">W</font></span><br/>



<a NAME="E1:77_2"/>
<font color="Maroon" title="c4">W</font> is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span>
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">A</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c6">B</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c3">b</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> <span class="kw"> such that </span><br/><a NAME="E3:77_2"/><span class="lab"><font color="Green" title="E42">A6</font></span>: 
<font color="Maroon" title="c5">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">B</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">W</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:77"><span class="lab"><font color="Green" title="E40">A1</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">B1</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c3">b</font><span class="kw"> such that </span><br/><a NAME="E5:77_2"/><span class="lab"><font color="Green" title="E43">A7</font></span>: 
<font color="Maroon" title="c7">B1</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:77"><span class="lab"><font color="Green" title="E41">A2</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">A</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">B</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c3">b</font> st <font color="Maroon" title="c5">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">W</font></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c7">B1</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Maroon" title="c7">B1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">W</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Maroon" title="c7">B1</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">W</font> )</span><br/>

<span class="kw">assume </span><a NAME="E6:77_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Maroon" title="c7">B1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">W</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">g</font>, <font color="Maroon" title="c10">h</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font><span class="kw"> such that </span><br/><a NAME="E8:77_2"/><span class="lab"><font color="Green" title="E44">A8</font></span>: 
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">h</font> &amp; <font color="Maroon" title="c9">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">A</font> )
 <span class="kw">and </span><br/><a NAME="E9:77_2"/><span class="lab"><font color="Green" title="E45">A9</font></span>: 
<font color="Maroon" title="c10">h</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c7">B1</font>
 ;<br/>
<a NAME="E10:77_2"/>
<font color="Maroon" title="c10">h</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c7">B1</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:77_2"><span class="lab"><font color="Green" title="E45">A9</font></span></a></span>;<br/>
<a NAME="E11:77_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">h</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">B</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:77_2"><span class="lab"><font color="Green" title="E43">A7</font></span></a>, <a class="ref" href="topgrp_1.html#T7" target="_self" onmouseover="rs('topgrp_1/T7')" onmouseout="rh()">Th7</a></span>;<br/>
<a NAME="E12:77_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">B</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:77_2"><span class="lab"><font color="Green" title="E44">A8</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:77_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">W</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:77_2"><span class="lab"><font color="Green" title="E42">A6</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:77"/>
<font color="Maroon" title="c1">T</font> is   <a href="topgrp_1.html#NM5" title="TOPGRP_1:NM.5">TopologicalGroup</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:77"><span class="lab"><font color="Green" title="E41">A2</font></span></a>, <a class="ref" href="topgrp_1.html#T38" target="_self" onmouseover="rs('topgrp_1/T38')" onmouseout="rh()">Th37</a>, <a class="ref" href="topgrp_1.html#T40" target="_self" onmouseover="rs('topgrp_1/T40')" onmouseout="rh()">Th39</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
