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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V6">strict</a> <a href="altcat_2.html#NM2">subcategory</a> of <font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K4" target="_self">-INF_category</a> ;<br/>

<b>assume </b><a NAME="E1:61_3_2"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K4" target="_self">-INF_category</a> </span>)</span> holds <font color="Olive">b<sub>1</sub></font> is   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:61_3_2"/><b>then </b><i><font color="Green">E42</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K4" target="_self">-INF_category</a> </span>)</span> holds <br/>( <font color="Olive">b<sub>1</sub></font> is   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>3</sub></font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] )
 
;<br/>
<b>assume </b><a NAME="E3:61_3_2"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K4" target="_self">-INF_category</a> </span>)</span><br/>for <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>3</sub></font> st <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  holds <br/>for <font color="Olive">b<sub>5</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> holds <br/>( <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> iff <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>5</sub></font>] )
 ;<br/>

<b>assume </b><a NAME="E4:61_3_2"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K4" target="_self">-INF_category</a> </span>)</span> holds <font color="Olive">b<sub>1</sub></font> is   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E5:61_3_2"/><b>then </b><i><font color="Green">E44</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K4" target="_self">-INF_category</a> </span>)</span> holds <br/>( <font color="Olive">b<sub>1</sub></font> is   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>4</sub></font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] )
 
;<br/>
<b>assume </b><a NAME="E6:61_3_2"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K4" target="_self">-INF_category</a> </span>)</span><br/>for <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>4</sub></font> st <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  holds <br/>for <font color="Olive">b<sub>5</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> holds <br/>( <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> iff <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>5</sub></font>] )
 ;<br/>

<a NAME="E7:61_3_2"/>
 <a href="altcat_1.html#G2">AltCatStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>3</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="altcat_1.html#G2">AltCatStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>,the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>4</sub></font>,the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>4</sub></font> #)
 
<b>from </b><i><a class="ref" href="yellow20.html#S1">YELLOW20:sch 1</a>(<a class="txt" href="waybel34.html#E2:61_3_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="waybel34.html#E3:61_3_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="waybel34.html#E5:61_3_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="waybel34.html#E6:61_3_2"><i><font color="Green">E45</font></i></a>);<br/></i>
<b>hence </b><a NAME="E8:61_3_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>


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