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

<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</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">h</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font><br/> for <font color="Olive" title="b2">g</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">T</font></span>)</span>  st <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> &amp; <font color="Olive" title="b1">h</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a> holds <br/><font color="Olive" title="b2">g</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a></span><br/><b>let </b><font color="Maroon" title="c3">h</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</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">g</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">T</font></span>)</span>  st <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> &amp; <font color="Maroon" title="c3">h</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a> holds <br/><font color="Olive" title="b1">g</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a></span><br/><b>let </b><font color="Maroon" title="c4">g</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">T</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> &amp; <font color="Maroon" title="c3">h</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a> implies <font color="Maroon" title="c4">g</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:34"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font>
 <b>and </b><br/><a NAME="E2:34"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c3">h</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">g</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a></span><br/>

<a NAME="E3:34"/><i><font color="Green" title="E18">A3</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">S</font></span>)</span> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">T</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="waybel25.html#E15"><i><font color="Green" title="E9">Lm1</font></i></a></i>;<br/>
<a NAME="E4:34"/><i><font color="Green" title="E19">A4</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</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">S</font>
 
<b>by </b><i><a class="txt" href="#E2:34"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E5:34"/><i><font color="Green" title="E20">A5</font></i>: 
( <font color="Maroon" title="c3">h</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c3">h</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="c2">T</font> )
 
<b>by </b><i><a class="txt" href="#E2:34"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:34_1"/>
( ( not <font color="Maroon" title="c1">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; not <font color="Maroon" title="c2">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> ) or <font color="Maroon" title="c1">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> or <font color="Maroon" title="c2">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_1"><b>suppose </b></a><a NAME="E1:34_1_1"/><i><font color="Green" title="E21">A6</font></i>: 
( not <font color="Maroon" title="c1">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; not <font color="Maroon" title="c2">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">g</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a></span><br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c5">s</font> = <font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c6">t</font> = <font color="Maroon" title="c2">T</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> ;<br/><b>reconsider </b><font color="Maroon" title="c7">f</font> = <font color="Maroon" title="c4">g</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c5">s</font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c6">t</font></span>)</span> ;<br/><a NAME="E4:34_1_1"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c5">s</font></span>)</span> holds <br/> ( <font color="Olive" title="b1">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">y</font> iff <font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Olive" title="b2">y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font>, <font color="Maroon" title="c9">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c5">s</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">y</font> iff <font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c8">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c9">y</font> )</span><br/>

<a NAME="E1:34_1_1_1"/><i><font color="Green" title="E22">A7</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c5">s</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E4:34"><i><font color="Green" title="E19">A4</font></i></a>, <a class="txt" href="waybel25.html#E15"><i><font color="Green" title="E9">Lm1</font></i></a></i>;<br/>
<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c8">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c9">y</font> implies <font color="Maroon" title="c8">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">y</font> )</span>
<div class="add"><b>assume </b><a NAME="E1:34_1_1_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c8">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c9">y</font></span><br/><b>then consider </b><font color="Maroon" title="c10">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">s</font><b> such that </b><br/><a NAME="E3:34_1_1_1_1"/><i><font color="Green" title="E23">A8</font></i>: 
<font color="Maroon" title="c10">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c9">y</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>and </b><br/><a NAME="E4:34_1_1_1_1"/><i><font color="Green" title="E24">A9</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c10">Y</font>
 <b>by </b><i><a class="ref" href="waybel25.html#D2" target="_self" title="WAYBEL25:def.2">Def2</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c11">Z</font> = <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c9">y</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c6">t</font> <b>by </b><i><a class="txt" href="waybel25.html#E15"><i><font color="Green" title="E9">Lm1</font></i></a></i>;<br/><a NAME="E6:34_1_1_1_1"/>
<font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c10">Y</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:34_1_1_1_1"><i><font color="Green" title="E24">A9</font></i></a>, <a class="ref" href="funct_2.html#T43" title="FUNCT_2:th.43">FUNCT_2:43</a></i>;<br/><a NAME="E7:34_1_1_1_1"/><b>then </b><i><font color="Green" title="E25">A10</font></i>: 
<font color="Maroon" title="c3">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c10">Y</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E2:34"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="tops_2.html#T74" title="TOPS_2:th.74">TOPS_2:74</a></i>;<br/><a NAME="E8:34_1_1_1_1"/>
 <a href="relat_1.html#K11" title="RELAT_1:func.11">Im</a> <font color="Maroon" title="c3">h</font>,<font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Z</font>
 <b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E1:34_1_1_1"><i><font color="Green" title="E22">A7</font></i></a>, <a class="ref" href="funct_1.html#T117" title="FUNCT_1:th.117">FUNCT_1:117</a></i>;<br/><b>hence </b><a NAME="E9:34_1_1_1_1"/>
<font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c8">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c9">y</font>
 <b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E3:34_1_1_1_1"><i><font color="Green" title="E23">A8</font></i></a>, <a class="txt" href="#E7:34_1_1_1_1"><i><font color="Green" title="E25">A10</font></i></a>, <a class="ref" href="waybel25.html#D2" target="_self" title="WAYBEL25:def.2">Def2</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>
<b>end;</b></div>

<b>assume </b><a NAME="E3:34_1_1_1"/>
<font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c8">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c9">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">y</font></span><br/>

<b>then consider </b><font color="Maroon" title="c10">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c6">t</font><b> such that </b><br/><a NAME="E5:34_1_1_1"/><i><font color="Green" title="E23">A11</font></i>: 
<font color="Maroon" title="c10">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c9">y</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>and </b><br/><a NAME="E6:34_1_1_1"/><i><font color="Green" title="E24">A12</font></i>: 
<font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c10">Y</font>
 <b>by </b><i><a class="ref" href="waybel25.html#D2" target="_self" title="WAYBEL25:def.2">Def2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">Z</font> = <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c9">y</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">s</font> <b>by </b><i><a class="txt" href="waybel25.html#E15"><i><font color="Green" title="E9">Lm1</font></i></a></i>;<br/>
<a NAME="E8:34_1_1_1"/><i><font color="Green" title="E25">A13</font></i>: 
<font color="Maroon" title="c3">h</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>
 
<b>by </b><i><a class="txt" href="#E2:34"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="#E1:34_1_1"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="tops_2.html#T70" title="TOPS_2:th.70">TOPS_2:70</a></i>;<br/>
<i><font color="Green" title="E26">A14</font></i>: <font color="Maroon" title="c7">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  = 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
<b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E5:34"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="waybel25.html#E15"><i><font color="Green" title="E9">Lm1</font></i></a>, <a class="ref" href="tops_2.html#D4" title="TOPS_2:def.4">TOPS_2:def 4</a></i>
<br/>.= 
<font color="Maroon" title="c3">h</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> 
<b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E5:34"><i><font color="Green" title="E20">A5</font></i></a>, <a class="ref" href="tops_2.html#D4" title="TOPS_2:def.4">TOPS_2:def 4</a></i>
;<br/>
<a NAME="E10:34_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c10">Y</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E6:34_1_1_1"><i><font color="Green" title="E24">A12</font></i></a>, <a class="ref" href="funct_2.html#T43" title="FUNCT_2:th.43">FUNCT_2:43</a></i>;<br/>
<a NAME="E11:34_1_1_1"/><b>then </b><i><font color="Green" title="E27">A15</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c10">Y</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E8:34_1_1_1"><i><font color="Green" title="E25">A13</font></i></a>, <a class="txt" href="#E9:34_1_1_1"><i><font color="Green" title="E26">A14</font></i></a>, <a class="ref" href="tops_2.html#T74" title="TOPS_2:th.74">TOPS_2:74</a></i>;<br/>
<i><font color="Green" title="E28">A16</font></i>: <font color="Maroon" title="c8">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c8">x</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E5:34"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="#E1:34_1_1_1"><i><font color="Green" title="E22">A7</font></i></a>, <a class="ref" href="funct_1.html#T56" title="FUNCT_1:th.56">FUNCT_1:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c8">x</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E5:34"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="waybel25.html#E15"><i><font color="Green" title="E9">Lm1</font></i></a>, <a class="ref" href="tops_2.html#D4" title="TOPS_2:def.4">TOPS_2:def 4</a></i>
;<br/>
<i><font color="Green" title="E29">A17</font></i>: <font color="Maroon" title="c9">y</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">y</font></span>)</span>
<b>by </b><i><a class="txt" href="#E5:34"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="#E1:34_1_1_1"><i><font color="Green" title="E22">A7</font></i></a>, <a class="ref" href="funct_1.html#T56" title="FUNCT_1:th.56">FUNCT_1:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c9">y</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E5:34"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="waybel25.html#E15"><i><font color="Green" title="E9">Lm1</font></i></a>, <a class="ref" href="tops_2.html#D4" title="TOPS_2:def.4">TOPS_2:def 4</a></i>
;<br/>
<i><font color="Green" title="E30">A18</font></i>:  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c7">f</font> = 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">S</font>
<b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E2:34"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></i>
<br/>.= 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>

;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c10">Y</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <font color="Maroon" title="c10">Y</font>
<b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E5:34"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="waybel25.html#E15"><i><font color="Green" title="E9">Lm1</font></i></a>, <a class="ref" href="tops_2.html#D4" title="TOPS_2:def.4">TOPS_2:def 4</a></i>
<br/>.= 
<font color="Maroon" title="c7">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Maroon" title="c10">Y</font>
<b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E5:34"><i><font color="Green" title="E20">A5</font></i></a>, <a class="ref" href="funct_1.html#T155" title="FUNCT_1:th.155">FUNCT_1:155</a></i>
<br/>.= 
<font color="Maroon" title="c11">Z</font>
<b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E3:34"><i><font color="Green" title="E18">A3</font></i></a>, <a class="txt" href="#E5:34"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="#E5:34_1_1_1"><i><font color="Green" title="E23">A11</font></i></a>, <a class="txt" href="#E13:34_1_1_1"><i><font color="Green" title="E29">A17</font></i></a>, <a class="txt" href="#E14:34_1_1_1"><i><font color="Green" title="E30">A18</font></i></a>, <a class="ref" href="finseq_5.html#T4" title="FINSEQ_5:th.4">FINSEQ_5:4</a></i>
;<br/>
<b>hence </b><a NAME="E16:34_1_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">y</font>
 <b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E9:34_1_1_1"><i><font color="Green" title="E26">A14</font></i></a>, <a class="txt" href="#E11:34_1_1_1"><i><font color="Green" title="E27">A15</font></i></a>, <a class="txt" href="#E12:34_1_1_1"><i><font color="Green" title="E28">A16</font></i></a>, <a class="txt" href="#E13:34_1_1_1"><i><font color="Green" title="E29">A17</font></i></a>, <a class="ref" href="waybel25.html#D2" target="_self" title="WAYBEL25:def.2">Def2</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><b>end;</b></div><b>hence </b><a NAME="E5:34_1_1"/>
<font color="Maroon" title="c4">g</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>
 <b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E3:34"><i><font color="Green" title="E18">A3</font></i></a>, <a class="txt" href="#E5:34"><i><font color="Green" title="E20">A5</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</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><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2"><b>suppose </b></a><a NAME="E1:34_1_2"/>
( <font color="Maroon" title="c1">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> or <font color="Maroon" title="c2">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">g</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a></span><br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c5">s</font> = <font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c6">t</font> = <font color="Maroon" title="c2">T</font> as  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> <b>by </b><i><a class="txt" href="#E4:34"><i><font color="Green" title="E19">A4</font></i></a>, <a class="txt" href="#E5:34"><i><font color="Green" title="E20">A5</font></i></a></i>;<br/><a NAME="E3:34_1_2"/>
(  <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c5">s</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp;  <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c6">t</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 ;<br/><b>hence </b><a NAME="E4:34_1_2"/>
<font color="Maroon" title="c4">g</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>
 <b>by </b><i><a class="ref" href="waybel_0.html#D38" title="WAYBEL_0:def.38">WAYBEL_0:def 38</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><b>end;</b></div></div><b>end;</b></div>

</div>
