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<a NAME="E1:87_3_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being <a href="altcat_1.html#V9">semi-functional</a> <a href="yellow18.html#V2" target="_self">para-functional</a> <a href="altcat_1.html#NM4">category</a> st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Olive">b<sub>1</sub></font><br/>for <font color="Olive">b<sub>4</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow18.html#K3" target="_self">the_carrier_of</a> <font color="Olive">b<sub>3</sub></font> iff ( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>3</sub></font>) &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>] ) ) ) &amp; ( for <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>5</sub></font> being  <a href="funct_1.html#NM1">Function</a> holds <br/>( <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Olive">b<sub>1</sub></font> <a href="binop_1.html#K1">.</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> iff ( <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="yellow18.html#K3" target="_self">-carrier_of</a> <font color="Olive">b<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="yellow18.html#K3" target="_self">-carrier_of</a> <font color="Olive">b<sub>4</sub></font></span>)</span> &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font>] ) ) ) &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Olive">b<sub>2</sub></font><br/>for <font color="Olive">b<sub>4</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow18.html#K3" target="_self">the_carrier_of</a> <font color="Olive">b<sub>3</sub></font> iff ( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>3</sub></font>) &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>] ) ) ) &amp; ( for <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>5</sub></font> being  <a href="funct_1.html#NM1">Function</a> holds <br/>( <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Olive">b<sub>2</sub></font> <a href="binop_1.html#K1">.</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> iff ( <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="yellow18.html#K3" target="_self">-carrier_of</a> <font color="Olive">b<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="yellow18.html#K3" target="_self">-carrier_of</a> <font color="Olive">b<sub>4</sub></font></span>)</span> &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font>] ) ) ) holds <br/> <a href="altcat_1.html#G2">AltCatStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font>,the <a href="altcat_1.html#U1">Arrows</a> of <font color="Olive">b<sub>1</sub></font>,the <a href="altcat_1.html#U2">Comp</a> of <font color="Olive">b<sub>1</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="Olive">b<sub>2</sub></font>,the <a href="altcat_1.html#U1">Arrows</a> of <font color="Olive">b<sub>2</sub></font>,the <a href="altcat_1.html#U2">Comp</a> of <font color="Olive">b<sub>2</sub></font> #)
 
<b>from </b><i><a class="ref" href="yellow18.html#S21" target="_self">YELLOW18:sch 21</a>();<br/></i>
<b>hence </b><a NAME="E2:87_3_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being <a href="altcat_1.html#V6">strict</a> <a href="yellow18.html#V4" target="_self">concrete</a> <a href="altcat_1.html#NM4">category</a> st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Olive">b<sub>1</sub></font><br/>for <font color="Olive">b<sub>4</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow18.html#K3" target="_self">the_carrier_of</a> <font color="Olive">b<sub>3</sub></font> iff ( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K3">Union</a> <span class="p1">(<span class="default"><a href="card_3.html#K2">disjoin</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> <a href="mcart_1.html#K20">`22</a>  ) ) ) &amp; ( for <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>5</sub></font> being  <a href="funct_1.html#NM1">Function</a> holds <br/>( <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Olive">b<sub>1</sub></font> <a href="binop_1.html#K1">.</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> iff ( <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="yellow18.html#K3" target="_self">-carrier_of</a> <font color="Olive">b<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="yellow18.html#K3" target="_self">-carrier_of</a> <font color="Olive">b<sub>4</sub></font></span>)</span> &amp; ex <font color="Olive">b<sub>6</sub></font>, <font color="Olive">b<sub>7</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>8</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>6</sub></font>,<font color="Olive">b<sub>7</sub></font> st <br/>( <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>6</sub></font>,<font color="Olive">b<sub>7</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>  &amp; ( for <font color="Olive">b<sub>9</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font> st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</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>10</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font> holds <font color="Olive">b<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>10</sub></font>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>8</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Olive">b<sub>10</sub></font></span>)</span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>7</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> ) ) ) ) ) &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Olive">b<sub>2</sub></font><br/>for <font color="Olive">b<sub>4</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow18.html#K3" target="_self">the_carrier_of</a> <font color="Olive">b<sub>3</sub></font> iff ( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K3">Union</a> <span class="p1">(<span class="default"><a href="card_3.html#K2">disjoin</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> <a href="mcart_1.html#K20">`22</a>  ) ) ) &amp; ( for <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>5</sub></font> being  <a href="funct_1.html#NM1">Function</a> holds <br/>( <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Olive">b<sub>2</sub></font> <a href="binop_1.html#K1">.</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> iff ( <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="yellow18.html#K3" target="_self">-carrier_of</a> <font color="Olive">b<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="yellow18.html#K3" target="_self">-carrier_of</a> <font color="Olive">b<sub>4</sub></font></span>)</span> &amp; ex <font color="Olive">b<sub>6</sub></font>, <font color="Olive">b<sub>7</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>8</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>6</sub></font>,<font color="Olive">b<sub>7</sub></font> st <br/>( <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>6</sub></font>,<font color="Olive">b<sub>7</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>  &amp; ( for <font color="Olive">b<sub>9</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font> st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</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>10</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font> holds <font color="Olive">b<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>10</sub></font>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>8</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Olive">b<sub>10</sub></font></span>)</span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>7</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> ) ) ) ) ) holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font>
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