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<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</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">o1</font>, <font color="Olive" title="b2">o2</font>, <font color="Olive" title="b3">o3</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font><br/>  for <font color="Olive" title="b4">M1</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font><br/>  for <font color="Olive" title="b5">M2</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b2">o2</font>,<font color="Olive" title="b3">o3</font>  st <font color="Olive" title="b4">M1</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a>  &amp; <font color="Olive" title="b5">M2</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a>  holds <br/><font color="Olive" title="b5">M2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive" title="b4">M1</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">o1</font>, <font color="Maroon" title="c3">o2</font>, <font color="Maroon" title="c4">o3</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M1</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font><br/>  for <font color="Olive" title="b2">M2</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c4">o3</font>  st <font color="Olive" title="b1">M1</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a>  &amp; <font color="Olive" title="b2">M2</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a>  holds <br/><font color="Olive" title="b2">M2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive" title="b1">M1</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">M1</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font>; <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">M2</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c4">o3</font>  st <font color="Maroon" title="c5">M1</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a>  &amp; <font color="Olive" title="b1">M2</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a>  holds <br/><font color="Olive" title="b1">M2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">M1</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c6">M2</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c4">o3</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="c5">M1</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a>  &amp; <font color="Maroon" title="c6">M2</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a>  implies <font color="Maroon" title="c6">M2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">M1</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a>  )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:51"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
<font color="Maroon" title="c5">M1</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a> 
 <span class="kw">and </span><br/><a NAME="E2:51"/><span class="lab"><font color="Green" title="E30">A2</font></span>: 
<font color="Maroon" title="c6">M2</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a> 
 ; <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="c6">M2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">M1</font> is  <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c7">o</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="altcat_3.html#D12" target="_self" title="ALTCAT_3:def.12">ALTCAT_3:def 12</a> <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="c7">o</font> is  <a href="altcat_3.html#V8" title="ALTCAT_3:attr.8">_zero</a>  implies  for <font color="Olive" title="b1">A</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c7">o</font><br/>  for <font color="Olive" title="b2">B</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c4">o3</font> holds  <font color="Maroon" title="c6">M2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">B</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive" title="b1">A</font> )</span><br/>

<span class="kw">assume </span><a NAME="E3:51"/><span class="lab"><font color="Green" title="E31">A3</font></span>: 
<font color="Maroon" title="c7">o</font> is  <a href="altcat_3.html#V8" title="ALTCAT_3:attr.8">_zero</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">A</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c7">o</font><br/>  for <font color="Olive" title="b2">B</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c4">o3</font> holds  <font color="Maroon" title="c6">M2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">B</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive" title="b1">A</font></span><br/>

<a NAME="E4:51"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A4</font></span>: 
<font color="Maroon" title="c7">o</font> is  <a href="altcat_3.html#V6" title="ALTCAT_3:attr.6">initial</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_3.html#D11" target="_self" title="ALTCAT_3:def.11">Def11</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">B1</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c3">o2</font><span class="kw"> such that </span><br/><a NAME="E6:51"/><span class="lab"><font color="Green" title="E33">A5</font></span>: 
<font color="Maroon" title="c8">B1</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="c7">o</font>,<font color="Maroon" title="c3">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <span class="kw">and </span><br/><a NAME="E7:51"/>
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c3">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_3.html#D9" target="_self" title="ALTCAT_3:def.9">Def9</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c9">A</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c7">o</font>; <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="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c4">o3</font> holds  <font color="Maroon" title="c6">M2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">B</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c9">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c10">B</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c4">o3</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="c6">M2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">B</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c9">A</font></span><br/>



<span class="kw">consider </span><font color="Maroon" title="c11">B2</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c4">o3</font><span class="kw"> such that </span><br/><a NAME="E9:51"/><span class="lab"><font color="Green" title="E34">A6</font></span>: 
<font color="Maroon" title="c11">B2</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="c7">o</font>,<font color="Maroon" title="c4">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <span class="kw">and </span><br/><a NAME="E10:51"/><span class="lab"><font color="Green" title="E35">A7</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c4">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:51"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="ref" href="altcat_3.html#D9" target="_self" title="ALTCAT_3:def.9">Def9</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c12">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E12:51"/><span class="lab"><font color="Green" title="E36">A8</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c4">o3</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="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c12">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:51"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E10:51"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="ref" href="zfmisc_1.html#T131" title="ZFMISC_1:th.131">ZFMISC_1:131</a></span>;<br/>
<a NAME="E13:51"/><span class="lab"><font color="Green" title="E37">A9</font></span>: 
<font color="Maroon" title="c7">o</font> is  <a href="altcat_3.html#V7" title="ALTCAT_3:attr.7">terminal</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:51"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="ref" href="altcat_3.html#D11" target="_self" title="ALTCAT_3:def.11">Def11</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">A1</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c7">o</font><span class="kw"> such that </span><br/><a NAME="E15:51"/><span class="lab"><font color="Green" title="E38">A10</font></span>: 
<font color="Maroon" title="c13">A1</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="c2">o1</font>,<font color="Maroon" title="c7">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <span class="kw">and </span><br/><a NAME="E16:51"/><span class="lab"><font color="Green" title="E39">A11</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c7">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_3.html#D10" target="_self" title="ALTCAT_3:def.10">Def10</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c14">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E18:51"/><span class="lab"><font color="Green" title="E40">A12</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c7">o</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="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:51"><span class="lab"><font color="Green" title="E38">A10</font></span></a>, <a class="txt" href="#E16:51"><span class="lab"><font color="Green" title="E39">A11</font></span></a>, <a class="ref" href="zfmisc_1.html#T131" title="ZFMISC_1:th.131">ZFMISC_1:131</a></span>;<br/>
<a NAME="E19:51"/>
 ex <font color="Olive" title="b1">M</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c7">o</font> st <br/>( <font color="Olive" title="b1">M</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="c7">o</font>,<font color="Maroon" title="c7">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c7">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:51"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="altcat_3.html#D10" target="_self" title="ALTCAT_3:def.10">Def10</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c15">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E21:51"/><span class="lab"><font color="Green" title="E41">A13</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c7">o</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="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c15">z</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T131" title="ZFMISC_1:th.131">ZFMISC_1:131</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c16">A2</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c7">o</font><span class="kw"> such that </span><br/><a NAME="E23:51"/><span class="lab"><font color="Green" title="E42">A14</font></span>: 
<font color="Maroon" title="c16">A2</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">o2</font>,<font color="Maroon" title="c7">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <span class="kw">and </span><br/><a NAME="E24:51"/>
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c7">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:51"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="altcat_3.html#D10" target="_self" title="ALTCAT_3:def.10">Def10</a></span>;<br/>
<a NAME="E25:51"/><span class="lab"><font color="Green" title="E43">A15</font></span>: 
(  <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c7">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">z</font> &amp; <font color="Maroon" title="c16">A2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c8">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">z</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:51"><span class="lab"><font color="Green" title="E41">A13</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E26:51"/><span class="lab"><font color="Green" title="E44">A16</font></span>: 
( <font color="Maroon" title="c10">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">y</font> &amp; <font color="Maroon" title="c11">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">y</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:51"><span class="lab"><font color="Green" title="E36">A8</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E27:51"/><span class="lab"><font color="Green" title="E45">A17</font></span>: 
( <font color="Maroon" title="c9">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">x</font> &amp; <font color="Maroon" title="c13">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">x</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:51"><span class="lab"><font color="Green" title="E40">A12</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E28:51"/><span class="lab"><font color="Green" title="E46">A18</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c4">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:51"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E23:51"><span class="lab"><font color="Green" title="E42">A14</font></span></a>, <a class="ref" href="altcat_1.html#D2" title="ALTCAT_1:def.2">ALTCAT_1:def 2</a></span>;<br/>
<a NAME="E29:51"/>
<font color="Maroon" title="c6">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">B2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c16">A2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:51"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E3:51"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="ref" href="altcat_3.html#D12" target="_self" title="ALTCAT_3:def.12">Def12</a></span>;<br/>
<span class="kw">hence </span><font color="Maroon" title="c6">M2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">M1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">B2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c16">A2</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">B1</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c13">A1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E3:51"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="ref" href="altcat_3.html#D12" target="_self" title="ALTCAT_3:def.12">Def12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">B2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c16">A2</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c8">B1</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c13">A1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:51"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E15:51"><span class="lab"><font color="Green" title="E38">A10</font></span></a>, <a class="txt" href="#E28:51"><span class="lab"><font color="Green" title="E46">A18</font></span></a>, <a class="ref" href="altcat_1.html#T21" title="ALTCAT_1:th.21">ALTCAT_1:21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">B</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p2">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c7">o</font></span>)</span></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c9">A</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:51"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E9:51"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E23:51"><span class="lab"><font color="Green" title="E42">A14</font></span></a>, <a class="txt" href="#E27:51"><span class="lab"><font color="Green" title="E45">A17</font></span></a>, <a class="txt" href="#E26:51"><span class="lab"><font color="Green" title="E44">A16</font></span></a>, <a class="txt" href="#E25:51"><span class="lab"><font color="Green" title="E43">A15</font></span></a>, <a class="ref" href="altcat_1.html#T21" title="ALTCAT_1:th.21">ALTCAT_1:21</a></span>
<br/>.= 
<font color="Maroon" title="c10">B</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c9">A</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:51"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="ref" href="altcat_1.html#D17" title="ALTCAT_1:def.17">ALTCAT_1:def 17</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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