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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="altcat_1.html#L2">AltCatStr</a> ;<br/>





<b>assume </b><a NAME="E1:48"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</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 <font color="Maroon">c<sub>1</sub></font> <a href="altcat_2.html#R2" target="_self">cc=</a> 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 <font color="Maroon">c<sub>1</sub></font> <a href="altcat_2.html#R2" target="_self">cc=</a> the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> &amp; the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>2</sub></font> <a href="altcat_2.html#R2" target="_self">cc=</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>3</sub></font> &amp; the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>2</sub></font> <a href="altcat_2.html#R2" target="_self">cc=</a> the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>3</sub></font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_2.html#D11" target="_self">ALTCAT_2:def 11</a><br/>

<b>hence </b><a NAME="E2:48"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> &amp; the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>1</sub></font> <a href="altcat_2.html#R2" target="_self">cc=</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>3</sub></font> &amp; the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>1</sub></font> <a href="altcat_2.html#R2" target="_self">cc=</a> the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="altcat_2.html#T9" target="_self">Th9</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_2.html#D11" target="_self">ALTCAT_2:def 11</a><br/>


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