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

<b>let </b><font color="Maroon" title="c4">T1</font>, <font color="Maroon" title="c5">T2</font> be  <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:51_1_2"/><i><font color="Green" title="E39">A8</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font>
 <b>and </b><br/><a NAME="E2:51_1_2"/><i><font color="Green" title="E40">A9</font></i>: 
for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">T1</font> holds   <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">IFEQ</a> <font color="Olive" title="b1">A</font>,<a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> ,<font color="Olive" title="b1">A</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x0</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">X</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E3:51_1_2"/><i><font color="Green" title="E41">A10</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">T2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font>
 <b>and </b><br/><a NAME="E4:51_1_2"/><i><font color="Green" title="E42">A11</font></i>: 
for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">T2</font> holds   <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">IFEQ</a> <font color="Olive" title="b1">A</font>,<a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> ,<font color="Olive" title="b1">A</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x0</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">X</font></span>)</span></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">A1</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">T1</font>;<br/><b>let </b><font color="Maroon" title="c7">A2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">T2</font>;<br/><b>assume </b><a NAME="E1:51_1_2_1"/>
<font color="Maroon" title="c6">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">A2</font>
 ;<br/><b>hence </b> <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c6">A1</font> = 
 <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">IFEQ</a> <font color="Maroon" title="c7">A2</font>,<a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> ,<font color="Maroon" title="c7">A2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">A2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x0</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">X</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="topgen_3.html#E2:51_1_2"><i><font color="Green" title="E40">A9</font></i></a></i>
<br/>.= 
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c7">A2</font>
<b>by </b><i><a class="txt" href="topgen_3.html#E4:51_1_2"><i><font color="Green" title="E42">A11</font></i></a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:51_1_2"/>
<font color="Maroon" title="c4">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">T2</font>
 <b>by </b><i><a class="txt" href="topgen_3.html#E1:51_1_2"><i><font color="Green" title="E39">A8</font></i></a>, <a class="txt" href="topgen_3.html#E3:51_1_2"><i><font color="Green" title="E41">A10</font></i></a>, <a class="ref" href="topgen_3.html#T8" target="_self" title="TOPGEN_3:th.8">Th8</a></i>;<br/>


</div>
