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<b>let </b><font color="Maroon" title="c7">F</font>, <font color="Maroon" title="c8">G</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span>,<font color="Maroon" title="c2">Y</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:141_1_2"/><i><font color="Green" title="E104">A9</font></i>: 
( <font color="Maroon" title="c7">F</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c3">X1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">f1</font> &amp; <font color="Maroon" title="c7">F</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c4">X2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c6">f2</font> )
 <b>and </b><br/><a NAME="E2:141_1_2"/><i><font color="Green" title="E105">A10</font></i>: 
( <font color="Maroon" title="c8">G</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c3">X1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">f1</font> &amp; <font color="Maroon" title="c8">G</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c4">X2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c6">f2</font> )
 ;<br/>

<a NAME="E3:141_1_2"/><i><font color="Green" title="E106">A11</font></i>: 
( <font color="Maroon" title="c3">X1</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font> &amp; <font color="Maroon" title="c4">X2</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font> )
 
<b>by </b><i><a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></i>;<br/>
<b>set </b><font color="Maroon" title="c9">A1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">X1</font>;<br/>
<b>set </b><font color="Maroon" title="c10">A2</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">X2</font>;<br/>
<b>set </b><font color="Maroon" title="c11">A</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span>;<br/>
<a NAME="E4:141_1_2"/><i><font color="Green" title="E107">A12</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <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 <font color="Maroon" title="c3">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">X2</font>
 
<b>by </b><i><a class="ref" href="tsep_1.html#D2" title="TSEP_1:def.2">TSEP_1:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="141_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">a</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span>;<br/><div><i><font color="Green" title="E108">A13</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="141_1_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:141_1_2_1_1"/><i><font color="Green" title="E109">A14</font></i>: 
<font color="Maroon" title="c12">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">X1</font>
 ;<br/><b>hence </b><font color="Maroon" title="c7">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">X1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c5">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="tmap_1.html#E1:141_1_2"><i><font color="Green" title="E104">A9</font></i></a>, <a class="txt" href="tmap_1.html#E3:141_1_2"><i><font color="Green" title="E106">A11</font></i></a>, <a class="ref" href="tmap_1.html#D4" target="_self" title="TMAP_1:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">G</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">X1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="tmap_1.html#E2:141_1_2"><i><font color="Green" title="E105">A10</font></i></a>, <a class="txt" href="tmap_1.html#E3:141_1_2"><i><font color="Green" title="E106">A11</font></i></a>, <a class="ref" href="tmap_1.html#D4" target="_self" title="TMAP_1:def.4">Def4</a></i>
<br/>.= 
<font color="Maroon" title="c8">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="tmap_1.html#E1:141_1_2_1_1"><i><font color="Green" title="E109">A14</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="141_1_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:141_1_2_1_2"/><i><font color="Green" title="E109">A15</font></i>: 
<font color="Maroon" title="c12">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">X2</font>
 ;<br/><b>hence </b><font color="Maroon" title="c7">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">X2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c6">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="tmap_1.html#E1:141_1_2"><i><font color="Green" title="E104">A9</font></i></a>, <a class="txt" href="tmap_1.html#E3:141_1_2"><i><font color="Green" title="E106">A11</font></i></a>, <a class="ref" href="tmap_1.html#D4" target="_self" title="TMAP_1:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">G</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">X2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="tmap_1.html#E2:141_1_2"><i><font color="Green" title="E105">A10</font></i></a>, <a class="txt" href="tmap_1.html#E3:141_1_2"><i><font color="Green" title="E106">A11</font></i></a>, <a class="ref" href="tmap_1.html#D4" target="_self" title="TMAP_1:def.4">Def4</a></i>
<br/>.= 
<font color="Maroon" title="c8">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">a</font>
<b>by </b><i><a class="txt" href="tmap_1.html#E1:141_1_2_1_2"><i><font color="Green" title="E109">A15</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><b>hence </b><a NAME="E3:141_1_2_1"/>
<font color="Maroon" title="c7">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">a</font>
 <b>by </b><i><a class="txt" href="tmap_1.html#E4:141_1_2"><i><font color="Green" title="E107">A12</font></i></a>, <a class="txt" href="tmap_1.html#E1:141_1_2_1"><i><font color="Green" title="E108">A13</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:141_1_2"/>
<font color="Maroon" title="c7">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">G</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


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