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<a NAME="E1:59_1_1"/><i><font color="Green" title="E28">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="altcat_2.html#K8" title="ALTCAT_2:func.8">ObCat</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">o</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="altcat_2.html#D12" target="_self" title="ALTCAT_2:def.12">Def12</a></i>;<br/>
<b>thus </b><a NAME="E2:59_1_1"/>
 <a href="altcat_2.html#K8" title="ALTCAT_2:func.8">ObCat</a> <font color="Maroon" title="c2">o</font> is <a href="altcat_2.html#V2" title="ALTCAT_2:attr.2">full</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="altcat_2.html#K8" title="ALTCAT_2:func.8">ObCat</a> <font color="Maroon" title="c2">o</font> is <a href="altcat_2.html#V3" title="ALTCAT_2:attr.3">id-inheriting</a></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b>the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_2.html#K8" title="ALTCAT_2:func.8">ObCat</a> <font color="Maroon" title="c2">o</font></span>)</span> = 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c2">o</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">:-&gt;</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c2">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
<b>by </b><i><a class="ref" href="altcat_2.html#D12" target="_self" title="ALTCAT_2:def.12">Def12</a></i>
<br/>.= 
the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">C</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="altcat_2.html#K8" title="ALTCAT_2:func.8">ObCat</a> <font color="Maroon" title="c2">o</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:59_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="funct_7.html#T8" title="FUNCT_7:th.8">FUNCT_7:8</a></i>
; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_2.html#D13" target="_self" title="ALTCAT_2:def.13">ALTCAT_2:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">o1</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <span class="p1">(<span class="default"><a href="altcat_2.html#K8" title="ALTCAT_2:func.8">ObCat</a> <font color="Maroon" title="c2">o</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">o2</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="c3">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">o2</font> holds <br/> <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Olive" title="b1">o2</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="c3">o1</font>,<font color="Maroon" title="c3">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c4">o2</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">o2</font> implies  <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c4">o2</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="c3">o1</font>,<font color="Maroon" title="c3">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> )</span><br/><a NAME="E1:59_1_1_2"/><i><font color="Green" title="E29">A2</font></i>: 
<font color="Maroon" title="c3">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font>
 <b>by </b><i><a class="ref" href="altcat_2.html#T24" target="_self" title="ALTCAT_2:th.24">Th24</a></i>;<br/><b>assume </b><a NAME="E2:59_1_1_2"/><i><font color="Green" title="E30">A3</font></i>: 
<font color="Maroon" title="c3">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">o2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c4">o2</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="c3">o1</font>,<font color="Maroon" title="c3">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span></span><br/><span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c3">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c2">o</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">:-&gt;</a> <span class="p2"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c2">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c2">o</font>
<b>by </b><i><a class="txt" href="#E1:59_1_1_2"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="altcat_2.html#D12" target="_self" title="ALTCAT_2:def.12">Def12</a></i>
<br/>.= 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c4">o2</font>,<font color="Maroon" title="c4">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
<b>by </b><i><a class="txt" href="#E1:59_1_1_2"><i><font color="Green" title="E29">A2</font></i></a>, <a class="txt" href="#E2:59_1_1_2"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="altcat_1.html#T12" title="ALTCAT_1:th.12">ALTCAT_1:12</a></i>
;<br/><b>hence </b><a NAME="E4:59_1_1_2"/>
 <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c4">o2</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="c3">o1</font>,<font color="Maroon" title="c3">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <b>by </b><i><a class="ref" href="altcat_1.html#T23" title="ALTCAT_1:th.23">ALTCAT_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:59_1_1"/>
 <a href="altcat_2.html#K8" title="ALTCAT_2:func.8">ObCat</a> <font color="Maroon" title="c2">o</font> is <a href="altcat_2.html#V3" title="ALTCAT_2:attr.3">id-inheriting</a>
 <b>by </b><i><a class="ref" href="altcat_2.html#D14" target="_self" title="ALTCAT_2:def.14">Def14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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