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<span class="kw">set </span><font color="Maroon" title="c1">C</font> =  <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">C1</font> =  <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">C2</font> =  <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">f</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span><span class="kw"> such that </span><br/><a NAME="E2:89"/>
 not <font color="Maroon" title="c4">f</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a> 
 <span class="kw">and </span><br/><a NAME="E3:89"/>
 <a href="cat_6.html#K5" title="CAT_6:func.5">Ob</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">f</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">and </span><br/><a NAME="E4:89"/><span class="lab"><font color="Green" title="E50">A1</font></span>: 
 <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c4">f</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 <span class="kw">and </span><br/><a NAME="E5:89"/><span class="lab"><font color="Green" title="E51">A2</font></span>: 
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">f</font>, <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c4">f</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_distinct</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T39" target="_self" onmouseover="rs('cat_7/T39')" onmouseout="rh()">Th39</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">g1</font> =  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c6">g2</font> =  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">f</font> as   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:89"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">F1</font> =  <a href="cat_7.html#K7" title="CAT_7:func.7">MORPHISM</a> <font color="Maroon" title="c5">g1</font> as    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of  <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T47" onmouseover="rs('cat_6/T47')" onmouseout="rh()">CAT_6:47</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">F2</font> =  <a href="cat_7.html#K7" title="CAT_7:func.7">MORPHISM</a> <font color="Maroon" title="c6">g2</font> as    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of  <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T47" onmouseover="rs('cat_6/T47')" onmouseout="rh()">CAT_6:47</a></span>;<br/>
<span class="kw">take </span>
 <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">C1</font>, <font color="Olive" title="b2">C2</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> ex <font color="Olive" title="b3">F1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b1">C1</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> ex <font color="Olive" title="b4">F2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b2">C2</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> st <br/> for <font color="Olive" title="b5">D</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a><br/>  for <font color="Olive" title="b6">P1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b5">D</font>,<font color="Olive" title="b1">C1</font><br/>  for <font color="Olive" title="b7">P2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b5">D</font>,<font color="Olive" title="b2">C2</font>  holds <br/>(  not <font color="Olive" title="b3">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b6">P1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b4">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b7">P2</font> or  ex <font color="Olive" title="b8">D1</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> ex <font color="Olive" title="b9">G1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b8">D1</font>,<font color="Olive" title="b1">C1</font> ex <font color="Olive" title="b10">G2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b8">D1</font>,<font color="Olive" title="b2">C2</font> st <br/>( <font color="Olive" title="b3">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b9">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b4">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b10">G2</font> &amp; (  for <font color="Olive" title="b11">H</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b8">D1</font>,<font color="Olive" title="b5">D</font>  holds <br/>(  not <font color="Olive" title="b6">P1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b11">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b9">G1</font> or  not <font color="Olive" title="b7">P2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b11">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b10">G2</font> or  ex <font color="Olive" title="b12">H1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b8">D1</font>,<font color="Olive" title="b5">D</font> st <br/>( <font color="Olive" title="b6">P1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b12">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b9">G1</font> &amp; <font color="Olive" title="b7">P2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b12">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b10">G2</font> &amp;  not <font color="Olive" title="b11">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b12">H1</font> ) ) ) ) )</span><br/>

<span class="kw">take </span>
 <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">C2</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> ex <font color="Olive" title="b2">F1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of  <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> ex <font color="Olive" title="b3">F2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b1">C2</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> st <br/> for <font color="Olive" title="b4">D</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a><br/>  for <font color="Olive" title="b5">P1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b4">D</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span><br/>  for <font color="Olive" title="b6">P2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b4">D</font>,<font color="Olive" title="b1">C2</font>  holds <br/>(  not <font color="Olive" title="b2">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b5">P1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b6">P2</font> or  ex <font color="Olive" title="b7">D1</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> ex <font color="Olive" title="b8">G1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b7">D1</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> ex <font color="Olive" title="b9">G2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b7">D1</font>,<font color="Olive" title="b1">C2</font> st <br/>( <font color="Olive" title="b2">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b8">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b9">G2</font> &amp; (  for <font color="Olive" title="b10">H</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b7">D1</font>,<font color="Olive" title="b4">D</font>  holds <br/>(  not <font color="Olive" title="b5">P1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b10">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b8">G1</font> or  not <font color="Olive" title="b6">P2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b10">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b9">G2</font> or  ex <font color="Olive" title="b11">H1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b7">D1</font>,<font color="Olive" title="b4">D</font> st <br/>( <font color="Olive" title="b5">P1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b11">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b8">G1</font> &amp; <font color="Olive" title="b6">P2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b11">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b9">G2</font> &amp;  not <font color="Olive" title="b10">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b11">H1</font> ) ) ) ) )</span><br/>

<span class="kw">take </span>
 <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">F2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of  <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> st <br/> for <font color="Olive" title="b3">D</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a><br/>  for <font color="Olive" title="b4">P1</font>, <font color="Olive" title="b5">P2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b3">D</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>  holds <br/>(  not <font color="Olive" title="b1">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b4">P1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b5">P2</font> or  ex <font color="Olive" title="b6">D1</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> ex <font color="Olive" title="b7">G1</font>, <font color="Olive" title="b8">G2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b6">D1</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> st <br/>( <font color="Olive" title="b1">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b7">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b8">G2</font> &amp; (  for <font color="Olive" title="b9">H</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b6">D1</font>,<font color="Olive" title="b3">D</font>  holds <br/>(  not <font color="Olive" title="b4">P1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b9">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b7">G1</font> or  not <font color="Olive" title="b5">P2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b9">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b8">G2</font> or  ex <font color="Olive" title="b10">H1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b6">D1</font>,<font color="Olive" title="b3">D</font> st <br/>( <font color="Olive" title="b4">P1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b10">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b7">G1</font> &amp; <font color="Olive" title="b5">P2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b10">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b8">G2</font> &amp;  not <font color="Olive" title="b9">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b10">H1</font> ) ) ) ) )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c7">F1</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">F2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of  <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> st <br/> for <font color="Olive" title="b2">D</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a><br/>  for <font color="Olive" title="b3">P1</font>, <font color="Olive" title="b4">P2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b2">D</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>  holds <br/>(  not <font color="Maroon" title="c7">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b3">P1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b4">P2</font> or  ex <font color="Olive" title="b5">D1</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> ex <font color="Olive" title="b6">G1</font>, <font color="Olive" title="b7">G2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b5">D1</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> st <br/>( <font color="Maroon" title="c7">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b6">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b7">G2</font> &amp; (  for <font color="Olive" title="b8">H</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b5">D1</font>,<font color="Olive" title="b2">D</font>  holds <br/>(  not <font color="Olive" title="b3">P1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b8">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b6">G1</font> or  not <font color="Olive" title="b4">P2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b8">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b7">G2</font> or  ex <font color="Olive" title="b9">H1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b5">D1</font>,<font color="Olive" title="b2">D</font> st <br/>( <font color="Olive" title="b3">P1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b9">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b6">G1</font> &amp; <font color="Olive" title="b4">P2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b9">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b7">G2</font> &amp;  not <font color="Olive" title="b8">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b9">H1</font> ) ) ) ) )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c8">F2</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">D</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a><br/>  for <font color="Olive" title="b2">P1</font>, <font color="Olive" title="b3">P2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b1">D</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>  holds <br/>(  not <font color="Maroon" title="c7">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b2">P1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c8">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b3">P2</font> or  ex <font color="Olive" title="b4">D1</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> ex <font color="Olive" title="b5">G1</font>, <font color="Olive" title="b6">G2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b4">D1</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> st <br/>( <font color="Maroon" title="c7">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b5">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c8">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b6">G2</font> &amp; (  for <font color="Olive" title="b7">H</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b4">D1</font>,<font color="Olive" title="b1">D</font>  holds <br/>(  not <font color="Olive" title="b2">P1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b7">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b5">G1</font> or  not <font color="Olive" title="b3">P2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b7">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b6">G2</font> or  ex <font color="Olive" title="b8">H1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b4">D1</font>,<font color="Olive" title="b1">D</font> st <br/>( <font color="Olive" title="b2">P1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b8">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b5">G1</font> &amp; <font color="Olive" title="b3">P2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b8">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b6">G2</font> &amp;  not <font color="Olive" title="b7">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b8">H1</font> ) ) ) ) )</span><br/>

<span class="kw">assume </span><a NAME="E9:89"/>
 ex <font color="Olive" title="b1">D</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> ex <font color="Olive" title="b2">P1</font>, <font color="Olive" title="b3">P2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b1">D</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> st <br/>( <font color="Maroon" title="c7">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b2">P1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c8">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b3">P2</font> &amp; (  for <font color="Olive" title="b4">D1</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a><br/>  for <font color="Olive" title="b5">G1</font>, <font color="Olive" title="b6">G2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b4">D1</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>  st <font color="Maroon" title="c7">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b5">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c8">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b6">G2</font> holds <br/> ex <font color="Olive" title="b7">H</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b4">D1</font>,<font color="Olive" title="b1">D</font> st <br/>( <font color="Olive" title="b2">P1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b7">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b5">G1</font> &amp; <font color="Olive" title="b3">P2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b7">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b6">G2</font> &amp; (  for <font color="Olive" title="b8">H1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b4">D1</font>,<font color="Olive" title="b1">D</font>  st <font color="Olive" title="b2">P1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b8">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b5">G1</font> &amp; <font color="Olive" title="b3">P2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b8">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b6">G2</font> holds <br/><font color="Olive" title="b7">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b8">H1</font> ) ) ) )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">D</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>, <font color="Maroon" title="c10">P1</font>, <font color="Maroon" title="c11">P2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c9">D</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span><span class="kw"> such that </span><br/><a NAME="E11:89"/><span class="lab"><font color="Green" title="E52">A3</font></span>: 
( <font color="Maroon" title="c7">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c10">P1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c8">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c11">P2</font> &amp; (  for <font color="Olive" title="b1">D1</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a><br/>  for <font color="Olive" title="b2">G1</font>, <font color="Olive" title="b3">G2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b1">D1</font>, <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span>  st <font color="Maroon" title="c7">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b2">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c8">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b3">G2</font> holds <br/> ex <font color="Olive" title="b4">H</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c9">D</font> st <br/>( <font color="Maroon" title="c10">P1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G1</font> &amp; <font color="Maroon" title="c11">P2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">G2</font> &amp; (  for <font color="Olive" title="b5">H1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c9">D</font>  st <font color="Maroon" title="c10">P1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b5">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G1</font> &amp; <font color="Maroon" title="c11">P2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b5">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">G2</font> holds <br/><font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b5">H1</font> ) ) ) )
 ;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">g</font> =  the   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c9">D</font>;<br/>
<a NAME="E12:89"/><span class="lab"><font color="Green" title="E53">A4</font></span>: 
 the   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c9">D</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c9">D</font>
 
;<br/>
<a NAME="E13:89"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A5</font></span>: 
 the   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c9">D</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c10">P1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E14:89"/><span class="lab"><font color="Green" title="E55">A6</font></span>: 
 the   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c9">D</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c11">P2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:89"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E15:89"/><span class="lab"><font color="Green" title="E56">A7</font></span>: 
 <a href="cat_6.html#K17" title="CAT_6:func.17">Alter</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <span class="p1">(<span class="default"><a href="cat_6.html#K5" title="CAT_6:func.5">Ob</a> <span class="p2">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <span class="p2">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="cat_6.html#K14" title="CAT_6:func.14">SourceMap</a> <span class="p2">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="cat_6.html#K15" title="CAT_6:func.15">TargetMap</a> <span class="p2">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="cat_6.html#K13" title="CAT_6:func.13">CompMap</a> <span class="p2">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span></span>)</span> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D33" onmouseover="rs('cat_6/D33')" onmouseout="rh()">CAT_6:def 33</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">f1</font> = <font color="Maroon" title="c10">P1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a>  the   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c9">D</font> as   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:89"><span class="lab"><font color="Green" title="E56">A7</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">f2</font> = <font color="Maroon" title="c11">P2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a>  the   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c9">D</font> as   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:89"><span class="lab"><font color="Green" title="E56">A7</font></span></a></span>;<br/>
<span class="lab"><font color="Green" title="E57">A8</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c7">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c10">P1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a>  the   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c9">D</font> = 
<font color="Maroon" title="c7">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">P1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a>  the   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c9">D</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:89"><span class="lab"><font color="Green" title="E54">A5</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_7.html#K7" title="CAT_7:func.7">MORPHISM</a> <font color="Maroon" title="c5">g1</font></span>)</span> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c13">f1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>
<br/>.= 
<font color="Maroon" title="c5">g1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T40" target="_self" onmouseover="rs('cat_7/T40')" onmouseout="rh()">Th40</a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a></span>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c11">P2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a>  the   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c9">D</font> = 
<font color="Maroon" title="c8">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">P2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a>  the   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c9">D</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:89"><span class="lab"><font color="Green" title="E55">A6</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_7.html#K7" title="CAT_7:func.7">MORPHISM</a> <font color="Maroon" title="c6">g2</font></span>)</span> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c14">f2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>
<br/>.= 
<font color="Maroon" title="c6">g2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T40" target="_self" onmouseover="rs('cat_7/T40')" onmouseout="rh()">Th40</a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E20:89"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:89"><span class="lab"><font color="Green" title="E57">A8</font></span></a>, <a class="txt" href="#E11:89"><span class="lab"><font color="Green" title="E52">A3</font></span></a>, <a class="txt" href="#E5:89"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D5" onmouseover="rs('zfmisc_1/D5')" onmouseout="rh()">ZFMISC_1:def 5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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