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<b>let </b><font color="Maroon">Y1</font> be  <a href="pre_topc.html#V1">strict</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">Y</font>, <font color="Maroon">Y2</font> be  <a href="pre_topc.html#V1">strict</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">Y</font>;<br/>

<b>assume </b><a NAME="E1:102_1_2"/><i><font color="Green">E13</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y1</font> <a href="hidden.html#R1">=</a>  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">x</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y2</font> <a href="hidden.html#R1">=</a>  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">x</font> )
 ;<br/>

<b>set </b><font color="Maroon">A1</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y1</font>;<br/>
<b>set </b><font color="Maroon">A2</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y2</font>;<br/>
<a NAME="E2:102_1_2"/><i><font color="Green">E20</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y1</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">Y1</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y2</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">Y2</font> )
 
;<br/>
<a NAME="E3:102_1_2"/><b>then </b>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y1</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">Y</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y2</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">Y</font> )
 
<b>by </b><i><a class="ref" href="pre_topc.html#D9">PRE_TOPC:def 9</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">A1</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y1</font>, <font color="Maroon">A2</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y2</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font> ;<br/>
<a NAME="E5:102_1_2"/>
( <font color="Maroon">Y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">A1</font> &amp; <font color="Maroon">Y2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">A2</font> )
 
<b>by </b><i><a class="ref" href="tex_4.html#D7" target="_self">Def7</a>, <a class="ref" href="pre_topc.html#D10">PRE_TOPC:def 10</a></i>;<br/>
<b>hence </b><a NAME="E6:102_1_2"/>
<font color="Maroon">Y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y2</font>
 <b>by </b><i><a class="ref" href="tex_4.html#T15" target="_self">Th15</a></i>;<br/>


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