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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_2.html#NM2">subcategory</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_2.html#NM2">subcategory</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V12">with_units</a>  <a href="altcat_2.html#M1">SubCatStr</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="altcat_2.html#T22">ALTCAT_2:22</a></i>;<br/>
<a NAME="E2:41"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="altcat_2.html#V3">id-inheriting</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>4</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:41_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:41_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E3:41_1_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</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>
 <b>by </b><i><a class="ref" href="altcat_2.html#D11">ALTCAT_2:def 11</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="altcat_4.html#E2:41_1_1"><i><font color="Green">E27</font></i></a></i>;<br/> <a href="altcat_1.html#K8">idm</a> <font color="Maroon">c<sub>5</sub></font> = 
 <a href="altcat_1.html#K8">idm</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="altcat_2.html#T35">ALTCAT_2:35</a></i>
<br/>.= 
 <a href="altcat_1.html#K8">idm</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="altcat_4.html#E1:41_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="altcat_2.html#T35">ALTCAT_2:35</a></i>
;<br/><b>hence </b><a NAME="E6:41_1_1"/>
 <a href="altcat_1.html#K8">idm</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:41_1"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="altcat_2.html#V3">id-inheriting</a>
 <b>by </b><i><a class="ref" href="altcat_2.html#D14">ALTCAT_2:def 14</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:41"/>
<font color="Maroon">c<sub>3</sub></font> is  non <a href="struct_0.html#V3">empty</a> <a href="altcat_2.html#NM2">subcategory</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


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