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<b>let </b><font color="Maroon">Y1</font> be  non <a href="struct_0.html#V3">empty</a> <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  non <a href="struct_0.html#V3">empty</a> <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="E1:41_1_2"/><i><font color="Green">E17</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">y</font></span><a href="domain_1.html#K6">}</a></span> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">y</font></span><a href="domain_1.html#K6">}</a></span> )
 ;<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="E2:41_1_2"/><i><font color="Green">E22</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="E3:41_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="E5:41_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="pre_topc.html#D10">PRE_TOPC:def 10</a></i>;<br/>
<b>hence </b><a NAME="E6:41_1_2"/>
<font color="Maroon">Y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y2</font>
 <b>by </b><i/>;<br/>


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