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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="altcat_1.html#L2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_2.html#V1">reflexive</a>  <a href="altcat_1.html#L2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="functor0.html#V8">feasible</a> <a href="functor0.html#V10">Covariant</a>  <a href="functor0.html#L2">FunctorStr</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be  <a href="functor0.html#V8">feasible</a> <a href="functor0.html#V11">Contravariant</a>  <a href="functor0.html#L2">FunctorStr</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>;<br/>















<b>assume </b><a NAME="E1:13"/><i><font color="Green">E5</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<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> 
 ;<br/>

<b>set </b><font color="Maroon">c<sub>9</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K13">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>4</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>12</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="altcat_2.html#K3">**</a> the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>13</sub></font> = <span class="p1">(<span class="default">the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<a NAME="E6:13"/><i><font color="Green">E6</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></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> 
 
<b>by </b><i><a class="txt" href="functor3.html#E1:13"><i><font color="Green">E5</font></i></a>, <a class="ref" href="functor0.html#D19">FUNCTOR0:def 19</a></i>;<br/>
<a NAME="E7:13"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="functor0.html#K5">Morph-Map</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E8:13"/><b>then </b><i><font color="Green">E7</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
;<br/>
<b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>5</sub></font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<i><font color="Green">E8</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="altcat_2.html#K3">**</a> the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default">the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>

;<br/>
<a NAME="E11:13"/><i><font color="Green">E9</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E12:13"/><i><font color="Green">E10</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K13">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K13">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="functor0.html#T34">FUNCTOR0:34</a></i>;<br/>
<a NAME="E13:13"/><i><font color="Green">E11</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E14:13"/><i><font color="Green">E12</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K3">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K3">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></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> 
 
<b>by </b><i><a class="txt" href="functor3.html#E6:13"><i><font color="Green">E6</font></i></a>, <a class="ref" href="functor0.html#D20">FUNCTOR0:def 20</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K13">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>8</sub></font> = 
<span class="p1">(<span class="default"><a href="functor0.html#K7">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K13">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="functor3.html#E1:13"><i><font color="Green">E5</font></i></a>, <a class="txt" href="functor3.html#E12:13"><i><font color="Green">E10</font></i></a>, <a class="ref" href="functor0.html#D17">FUNCTOR0:def 17</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>

<br/>.= 
<font color="Maroon">c<sub>12</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="functor0.html#D37">FUNCTOR0:def 37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="functor3.html#E10:13"><i><font color="Green">E8</font></i></a>, <a class="txt" href="functor3.html#E13:13"><i><font color="Green">E11</font></i></a>, <a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
<br/>.= 
<font color="Maroon">c<sub>13</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E1:13"><i><font color="Green">E5</font></i></a>, <a class="txt" href="functor3.html#E8:13"><i><font color="Green">E7</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">c<sub>13</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor0.html#K5">Morph-Map</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>13</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E1:13"><i><font color="Green">E5</font></i></a>, <a class="txt" href="functor3.html#E6:13"><i><font color="Green">E6</font></i></a>, <a class="ref" href="functor0.html#D16">FUNCTOR0:def 16</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default">the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E11:13"><i><font color="Green">E9</font></i></a>, <a class="txt" href="functor3.html#E13:13"><i><font color="Green">E11</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default">the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">c<sub>4</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default">the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#T23">FUNCTOR0:23</a></i>
<br/>.= 
<font color="Maroon">c<sub>14</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="functor0.html#K7">Morph-Map</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K8">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E6:13"><i><font color="Green">E6</font></i></a>, <a class="txt" href="functor3.html#E14:13"><i><font color="Green">E12</font></i></a>, <a class="ref" href="functor0.html#D17">FUNCTOR0:def 17</a></i>
;<br/><br/>


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