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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be    <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ;<br/>

<b>set </b><font color="Maroon" title="c3">AB</font> =  <a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>;<br/>
<b>assume </b><a NAME="E1:24"/>
<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="yellow20.html#R1" title="YELLOW20:pred.1">have_the_same_composition</a> 
 ;<br/>

<a NAME="E2:24"/><b>then </b>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</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="c1">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font> &amp; the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow20.html#K1" title="YELLOW20:func.1">Intersect</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font>,the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> &amp; the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow20.html#K1" title="YELLOW20:func.1">Intersect</a> the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c1">A</font>,the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c2">B</font> )
 
<b>by </b><i><a class="ref" href="yellow20.html#D3" target="_self" title="YELLOW20:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E3:24"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> &amp; the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span>)</span> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font> &amp; the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span>)</span> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c1">A</font> )
 <b>by </b><i><a class="ref" href="yellow20.html#T15" target="_self" title="YELLOW20:th.15">Th15</a>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a><br/>


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