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<span class="kw">let </span><font color="Maroon" title="c1">C</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="altcat_1.html#V12" title="ALTCAT_1:attr.12">with_units</a>   <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">D</font> being   <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">C</font>  st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <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="Olive" title="b1">D</font> &amp; the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Olive" title="b1">D</font> holds <br/><font color="Olive" title="b1">D</font> is  <a href="altcat_2.html#V3" title="ALTCAT_2:attr.3">id-inheriting</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">D</font> be    <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <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="c2">D</font> &amp; the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">D</font> implies <font color="Maroon" title="c2">D</font> is  <a href="altcat_2.html#V3" title="ALTCAT_2:attr.3">id-inheriting</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:39"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <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="c2">D</font> &amp; the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">D</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">D</font> is  <a href="altcat_2.html#V3" title="ALTCAT_2:attr.3">id-inheriting</a> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">D</font> = <font color="Maroon" title="c2">D</font> as  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="altcat_2.html#V2" title="ALTCAT_2:attr.2">full</a>   <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">C</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_4.html#T34" target="_self" title="ALTCAT_4:th.34">Th34</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">o</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c3">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">o9</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>  st <font color="Maroon" title="c4">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">o9</font> holds <br/> <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Olive" title="b1">o9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c4">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">o9</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o9</font> implies  <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c5">o9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c4">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> )</span><br/><span class="kw">assume </span><a NAME="E1:39_1"/>
<font color="Maroon" title="c4">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c5">o9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c4">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span></span><br/><a NAME="E2:39_1"/><span class="kw">then </span>
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o9</font>,<font color="Maroon" title="c5">o9</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c4">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_2.html#T29" title="ALTCAT_2:th.29">ALTCAT_2:29</a></span>;<br/><span class="kw">hence </span><a NAME="E3:39_1"/>
 <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c5">o9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c4">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:39"/>
<font color="Maroon" title="c2">D</font> is  <a href="altcat_2.html#V3" title="ALTCAT_2:attr.3">id-inheriting</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_2.html#D14" title="ALTCAT_2:def.14">ALTCAT_2:def 14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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