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<b>let </b><font color="Maroon">C1</font> be   <a href="cat_1.html#NM4">Category</a>, <font color="Maroon">C2</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">C1</font>,<font color="Maroon">C2</font>;<br/>



<b>set </b><font color="Maroon">S1</font> =  <a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font>;<br/>
<b>set </b><font color="Maroon">S2</font> =  <a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C2</font>;<br/>
<b>set </b><font color="Maroon">A1</font> =  <a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font>;<br/>
<b>set </b><font color="Maroon">A2</font> =  <a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font>;<br/>
<b>set </b><font color="Maroon">f</font> =  <a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font>;<br/>
<b>set </b><font color="Maroon">g</font> =  <a href="catalg_1.html#K12" target="_self">Psi</a> <font color="Maroon">F</font>;<br/>
<b>set </b><font color="Maroon">B1</font> = <span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font></span>)</span> <a href="instalg1.html#K1">|</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K12" target="_self">Psi</a> <font color="Maroon">F</font></span>)</span>;<br/>
<a NAME="E1:74"/>
 <a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font>, <a href="catalg_1.html#K12" target="_self">Psi</a> <font color="Maroon">F</font> <a href="pua2mss1.html#R3">form_morphism_between</a>  <a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font>, <a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C2</font>
 
<b>by </b><i><a class="ref" href="catalg_1.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E2:74"/><b>then </b><i><font color="Green">E37</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font></span>)</span> <a href="instalg1.html#K1">|</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K12" target="_self">Psi</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="pboole.html#R6">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font></span>)</span> <a href="pboole.html#K7">*</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font></span>)</span>
 
<b>by </b><i><a class="ref" href="instalg1.html#D3">INSTALG1:def 3</a></i>;<br/>
<b>set </b><font color="Maroon">H</font> = <font color="Maroon">F</font> <a href="catalg_1.html#K1" target="_self">-MSF</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font></span>)</span>,the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font></span>)</span>;<br/>
<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D18">PBOOLE:def 18</a><br/>

<b>assume </b><a NAME="E3:74"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">s</font> = <font color="Maroon">i</font> as   <a href="msualg_1.html#NM1">SortSymbol</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font></span>)</span> ;<br/>
<b>consider </b><font color="Maroon">a</font> being   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C1</font>, <font color="Maroon">b</font> being   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C1</font><b> such that </b><br/><a NAME="E6:74"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 <b>by </b><i/>;<br/>
<a NAME="E7:74"/><i><font color="Green">E42</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="catalg_1.html#K1" target="_self">-MSF</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font></span>)</span>,the <a href="msualg_1.html#U4">Sorts</a> of <span class="p2">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <span class="p2">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E8:74"/>
<span class="p1">(<span class="default"><a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="catalg_1.html#K9" target="_self">homsym</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>
 
<b>by </b><i><a class="txt" href="catalg_1.html#E7:74"><i><font color="Green">E42</font></i></a>, </i>;<br/>
<a NAME="E9:74"/><b>then </b><i><font color="Green">E45</font></i>: 
( the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font></span>)</span> <a href="instalg1.html#K1">|</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K12" target="_self">Psi</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="catalg_1.html#E6:74"><i><font color="Green">E41</font></i></a>, <a class="txt" href="catalg_1.html#E7:74"><i><font color="Green">E42</font></i></a>, <a class="txt" href="catalg_1.html#E2:74"><i><font color="Green">E37</font></i></a>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>;<br/>
<a NAME="E10:74"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="catalg_1.html#K1" target="_self">-MSF</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font></span>)</span>,the <a href="msualg_1.html#U4">Sorts</a> of <span class="p2">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K16">hom</a> <font color="Maroon">F</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i>, <a class="ref" href="cat_1.html#D25">CAT_1:def 25</a></i>;<br/>
<b>hence </b><a NAME="E11:74"/>
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="catalg_1.html#K1" target="_self">-MSF</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font></span>)</span>,the <a href="msualg_1.html#U4">Sorts</a> of <span class="p2">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is   <a href="funct_2.html#NM1">Function</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>,the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font></span>)</span> <a href="instalg1.html#K1">|</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K12" target="_self">Psi</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i/>;<br/>


</div>
