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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">X1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">X0</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">X2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/>







<b>assume </b><a NAME="E1:31"/>
( <font color="Maroon">X1</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X0</font> &amp; <font color="Maroon">X2</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X0</font> )
 ;<br/>

<a NAME="E2:31"/><b>then </b>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X2</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> )
 
<b>by </b><i><a class="ref" href="tsep_1.html#T4">TSEP_1:4</a></i>;<br/>
<a NAME="E3:31"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X2</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E4:31"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font>
 
<b>by </b><i><a class="ref" href="tsep_1.html#D2">TSEP_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:31"/>
<font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X0</font>
 <b>by </b><i><a class="ref" href="tsep_1.html#T4">TSEP_1:4</a></i>;<br/>


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