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<span class="kw">let </span><font color="Maroon" title="c2">B</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A</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">B</font> is  <a href="yellow21.html#V1" title="YELLOW21:attr.1">carrier-underlaid</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">b</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">B</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="yellow21.html#D3" target="_self" title="YELLOW21:def.3">YELLOW21:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">S</font> being   <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a>  st <br/>( <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">S</font> &amp;  <a href="yellow18.html#K3" title="YELLOW18:func.3">the_carrier_of</a> <font color="Maroon" title="c3">b</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">S</font> )</span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c4">a</font> = <font color="Maroon" title="c3">b</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_2.html#T30" title="ALTCAT_2:th.30">ALTCAT_2:30</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">S</font> being    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> <span class="kw"> such that </span><br/><a NAME="E3:57_1_1"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font>
 <span class="kw">and </span><br/><a NAME="E4:57_1_1"/><span class="lab"><font color="Green" title="E24">A2</font></span>: 
 <a href="yellow18.html#K3" title="YELLOW18:func.3">the_carrier_of</a> <font color="Maroon" title="c4">a</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="c5">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow21.html#D3" target="_self" title="YELLOW21:def.3">Def3</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">S</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="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> &amp;  <a href="yellow18.html#K3" title="YELLOW18:func.3">the_carrier_of</a> <font color="Maroon" title="c3">b</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="c5">S</font> )</span><br/>

<span class="kw">thus </span><a NAME="E5:57_1_1"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:57_1_1"><span class="lab"><font color="Green" title="E23">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="yellow18.html#K3" title="YELLOW18:func.3">the_carrier_of</a> <font color="Maroon" title="c3">b</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="c5">S</font></span><br/>

<span class="kw">thus </span><a NAME="E6:57_1_1"/>
 <a href="yellow18.html#K3" title="YELLOW18:func.3">the_carrier_of</a> <font color="Maroon" title="c3">b</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="c5">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57_1_1"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="ref" href="altcat_2.html#T35" title="ALTCAT_2:th.35">ALTCAT_2:35</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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