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<span class="kw">set </span><font color="Maroon" title="c1">A</font> =  <a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c2">C</font> =  <a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span>)</span>,<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as   <a href="cat_1.html#V1" title="CAT_1:attr.1">strict</a>   <a href="cat_5.html#V3" title="CAT_5:attr.3">Categorial</a>  <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T11" target="_self" title="CAT_5:th.11">Th11</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">C</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">C</font> is  <a href="cat_5.html#V4" title="CAT_5:attr.4">full</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="cat_5.html#D8" target="_self" title="CAT_5:def.8">CAT_5:def 8</a> <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">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">C</font> &amp; <font color="Maroon" title="c4">b</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">C</font> implies for <font color="Olive" title="b1">F</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> holds  <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b1">F</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">C</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:41_1_1"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
<font color="Maroon" title="c3">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">C</font>
 <span class="kw">and </span><br/><a NAME="E3:41_1_1"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
<font color="Maroon" title="c4">b</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> holds  <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b1">F</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">C</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">F</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c5">F</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">C</font></span><br/>

<a NAME="E4:41_1_1"/><span class="lab"><font color="Green" title="E28">A3</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:41_1_1"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E5:41_1_1"/><span class="lab"><font color="Green" title="E29">A4</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:41_1_1"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E6:41_1_1"/><span class="kw">then </span>
 <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c5">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:41_1_1"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="ref" href="funct_2.html#T66" title="FUNCT_2:th.66">FUNCT_2:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:41_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c5">F</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:41_1_1"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="txt" href="#E5:41_1_1"><span class="lab"><font color="Green" title="E29">A4</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</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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