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<span class="kw">let </span><font color="Maroon" title="c1">UN</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">b</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="ringcat1.html#K18" title="RINGCAT1:func.18">RingCat</a> <font color="Maroon" title="c1">UN</font></span>)</span><br/>  for <font color="Olive" title="b2">b9</font> being    <a href="ringcat1.html#M2" title="RINGCAT1:mode.2">Element</a> of  <a href="ringcat1.html#K9" title="RINGCAT1:func.9">RingObjects</a> <font color="Maroon" title="c1">UN</font>  st <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b9</font> holds <br/> <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ringcat1.html#K13" title="RINGCAT1:func.13">ID</a> <font color="Olive" title="b2">b9</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">C</font> =  <a href="ringcat1.html#K18" title="RINGCAT1:func.18">RingCat</a> <font color="Maroon" title="c1">UN</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">V</font> =  <a href="ringcat1.html#K9" title="RINGCAT1:func.9">RingObjects</a> <font color="Maroon" title="c1">UN</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="ringcat1.html#K18" title="RINGCAT1:func.18">RingCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">b9</font> being    <a href="ringcat1.html#M2" title="RINGCAT1:mode.2">Element</a> of  <a href="ringcat1.html#K9" title="RINGCAT1:func.9">RingObjects</a> <font color="Maroon" title="c1">UN</font>  st <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b9</font> holds <br/> <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ringcat1.html#K13" title="RINGCAT1:func.13">ID</a> <font color="Olive" title="b1">b9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">b9</font> be    <a href="ringcat1.html#M2" title="RINGCAT1:mode.2">Element</a> of  <a href="ringcat1.html#K9" title="RINGCAT1:func.9">RingObjects</a> <font color="Maroon" title="c1">UN</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b9</font> implies  <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ringcat1.html#K13" title="RINGCAT1:func.13">ID</a> <font color="Maroon" title="c5">b9</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:72"/>
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ringcat1.html#K13" title="RINGCAT1:func.13">ID</a> <font color="Maroon" title="c5">b9</font></span><br/>

<span class="kw">hence </span> <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <font color="Maroon" title="c4">b</font> = 
<span class="p1">(<span class="default"><a href="ringcat1.html#K16" title="RINGCAT1:func.16">ID</a> <span class="p2">(<span class="default"><a href="ringcat1.html#K9" title="RINGCAT1:func.9">RingObjects</a> <font color="Maroon" title="c1">UN</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">b9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#D2" title="CAT_1:def.2">CAT_1:def 2</a></span>
<br/>.= 
 <a href="ringcat1.html#K13" title="RINGCAT1:func.13">ID</a> <font color="Maroon" title="c5">b9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ringcat1.html#D21" target="_self" title="RINGCAT1:def.21">Def22</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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