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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V2">transitive</a>  <a href="altcat_1.html#L2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="altcat_2.html#V2" target="_self">full</a>  <a href="altcat_2.html#M1" target="_self">SubCatStr</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:64"/><i><font color="Green">E30</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:64"/><i><font color="Green">E31</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>2</sub></font> = 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>1</sub></font> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="altcat_2.html#D13" target="_self">Def13</a></i>
<br/>.= 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="altcat_2.html#E1:64"><i><font color="Green">E30</font></i></a>, <a class="txt" href="altcat_2.html#E2:64"><i><font color="Green">E31</font></i></a>, <a class="ref" href="relat_1.html#T98">RELAT_1:98</a></i>
;<br/>
<b>hence </b><a NAME="E4:64"/>
 <a href="altcat_1.html#G2">AltCatStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>2</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="altcat_1.html#G2">AltCatStr</a>(# the <a href="struct_0.html#U1">carrier</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>1</sub></font>,the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>1</sub></font> #)
 <b>by </b><i><a class="txt" href="altcat_2.html#E1:64"><i><font color="Green">E30</font></i></a>, <a class="ref" href="altcat_2.html#T26" target="_self">Th26</a></i>;<br/>


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