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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</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">f</font> being    <a href="topgrp_1.html#M3" title="TOPGRP_1:mode.3">Homeomorphism</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b2">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> holds <br/><font color="Olive" title="b2">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be    <a href="topgrp_1.html#M3" title="TOPGRP_1:mode.3">Homeomorphism</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">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span>  st <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> holds <br/><font color="Olive" title="b1">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a> </span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">G</font> =  <a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font>;<br/>
<a NAME="E1:55"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tops_2.html#D5" onmouseover="rs('tops_2/D5')" onmouseout="rh()">TOPS_2:def 5</a></span>;<br/>
<a NAME="E2:55"/><span class="lab"><font color="Green" title="E32">A2</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a>  is    <a href="topgrp_1.html#M3" title="TOPGRP_1:mode.3">Homeomorphism</a> of <font color="Maroon" title="c1">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D4" target="_self" onmouseover="rs('topgrp_1/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">g</font> = <font color="Maroon" title="c2">f</font> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a>  as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<a NAME="E4:55"/><span class="lab"><font color="Green" title="E33">A3</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tops_2.html#D5" onmouseover="rs('tops_2/D5')" onmouseout="rh()">TOPS_2:def 5</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</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"> ( <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font> implies <font color="Maroon" title="c5">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E5:55"/><span class="lab"><font color="Green" title="E34">A4</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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"> <font color="Maroon" title="c5">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a> </span><br/>

<span class="lab"><font color="Green" title="E35">A5</font></span>: <font color="Maroon" title="c4">g</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">a</font> = 
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:55"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
 <a href="topgrp_1.html#K4" title="TOPGRP_1:func.4">id</a> <font color="Maroon" title="c1">T</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:55"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="tops_2.html#T52" onmouseover="rs('tops_2/T52')" onmouseout="rh()">TOPS_2:52</a></span>
<br/>.= 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#T33" target="_self" onmouseover="rs('topgrp_1/T33')" onmouseout="rh()">Th32</a></span>
;<br/>
<font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">g</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c2">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:55"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
 <a href="topgrp_1.html#K4" title="TOPGRP_1:func.4">id</a> <font color="Maroon" title="c1">T</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E4:55"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="tops_2.html#T52" onmouseover="rs('tops_2/T52')" onmouseout="rh()">TOPS_2:52</a></span>
<br/>.= 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#T33" target="_self" onmouseover="rs('topgrp_1/T33')" onmouseout="rh()">Th32</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:55"/>
<font color="Maroon" title="c5">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:55"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="ref" href="group_1.html#T5" onmouseover="rs('group_1/T5')" onmouseout="rh()">GROUP_1:5</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/>


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