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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="altcat_1.html#L2">AltCatStr</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="yellow20.html#K2" target="_self">Intersect</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>assume </b><a NAME="E1:24"/>
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="yellow20.html#R1" target="_self">have_the_same_composition</a> 
 ;<br/>

<a NAME="E2:24"/><b>then </b>
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" target="_self">Intersect</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" target="_self">Intersect</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow20.html#K1" target="_self">Intersect</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="altcat_1.html#U2">Comp</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" target="_self">Intersect</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow20.html#K1" target="_self">Intersect</a> the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="yellow20.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E3:24"/>
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" target="_self">Intersect</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" target="_self">Intersect</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="altcat_2.html#R2">cc=</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="altcat_1.html#U2">Comp</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" target="_self">Intersect</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="altcat_2.html#R2">cc=</a> the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="yellow20.html#T15" target="_self">Th15</a>, <a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_2.html#D11">ALTCAT_2:def 11</a><br/>


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