<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon">c<sub>1</sub></font> =  <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #);<br/>
<a NAME="E1:25_1_1"/>
( ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="cat_1.html#U2" target="_self">Morphisms</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) holds <br/>( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> the <a href="cat_1.html#U5" target="_self">Comp</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) iff the <a href="cat_1.html#U3" target="_self">Dom</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U4" target="_self">Cod</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> ) ) &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="cat_1.html#U2" target="_self">Morphisms</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) st the <a href="cat_1.html#U3" target="_self">Dom</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U4" target="_self">Cod</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> holds <br/>( the <a href="cat_1.html#U3" target="_self">Dom</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">the <a href="cat_1.html#U5" target="_self">Comp</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_1.html#K1">.</a> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U3" target="_self">Dom</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> &amp; the <a href="cat_1.html#U4" target="_self">Cod</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">the <a href="cat_1.html#U5" target="_self">Comp</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_1.html#K1">.</a> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U4" target="_self">Cod</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> ) ) &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="cat_1.html#U2" target="_self">Morphisms</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) st the <a href="cat_1.html#U3" target="_self">Dom</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U4" target="_self">Cod</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> &amp; the <a href="cat_1.html#U3" target="_self">Dom</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U4" target="_self">Cod</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> holds <br/>the <a href="cat_1.html#U5" target="_self">Comp</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>3</sub></font>,<span class="p2">(<span class="default">the <a href="cat_1.html#U5" target="_self">Comp</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U5" target="_self">Comp</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default">the <a href="cat_1.html#U5" target="_self">Comp</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="cat_1.html#U1" target="_self">Objects</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) holds <br/>( the <a href="cat_1.html#U3" target="_self">Dom</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default">the <a href="cat_1.html#U6" target="_self">Id</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; the <a href="cat_1.html#U4" target="_self">Cod</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default">the <a href="cat_1.html#U6" target="_self">Id</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="cat_1.html#U2" target="_self">Morphisms</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) st the <a href="cat_1.html#U4" target="_self">Cod</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> holds <br/>the <a href="cat_1.html#U5" target="_self">Comp</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default">the <a href="cat_1.html#U6" target="_self">Id</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<font color="Olive">b<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="cat_1.html#U2" target="_self">Morphisms</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) st the <a href="cat_1.html#U3" target="_self">Dom</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> holds <br/>the <a href="cat_1.html#U5" target="_self">Comp</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<span class="p2">(<span class="default">the <a href="cat_1.html#U6" target="_self">Id</a> of <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) ) ) )
 
<b>by </b><i><a class="txt" href="cat_1.html#E35"><i><font color="Green">Lemma12</font></i></a></i>;<br/>
<a NAME="E2:25_1_1"/><b>then </b>
 <a href="cat_1.html#G1" target="_self">CatStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 0</span>)</span>,<span class="p1">(<span class="default">1,1 <a href="cat_1.html#K1" target="_self">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default">0 <a href="cat_1.html#K7" target="_self">.--&gt;</a> 1</span>)</span> #) is   <a href="cat_1.html#NM4">Category</a>
 
<b>by </b><i><a class="ref" href="cat_1.html#D8" target="_self">Def8</a></i>;<br/>
<b>hence </b><a NAME="E3:25_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="cat_1.html#NM4">Category</a> st <font color="Olive">b<sub>1</sub></font> is <a href="cat_1.html#V1" target="_self">strict</a>
 ;<br/>


</div>
