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<b>let </b><font color="Maroon">A</font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V2">transitive</a>  <a href="altcat_1.html#L2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon">B</font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V12">with_units</a>  <a href="altcat_1.html#L2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon">F</font> be  <a href="functor0.html#V8">feasible</a>  <a href="functor0.html#L2">FunctorStr</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/>





<i><font color="Green">E31</font></i>: the <a href="functor0.html#U1">ObjectMap</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor0.html#K11">id</a> <font color="Maroon">B</font></span>)</span> <a href="functor0.html#K13">*</a> <font color="Maroon">F</font></span>)</span> = 
the <a href="functor0.html#U1">ObjectMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K11">id</a> <font color="Maroon">B</font></span>)</span> <a href="partfun1.html#K1">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">F</font>
<b>by </b><i><a class="ref" href="functor0.html#D37">FUNCTOR0:def 37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">B</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="partfun1.html#K1">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">F</font>
<b>by </b><i><a class="ref" href="functor0.html#D30">FUNCTOR0:def 30</a></i>
<br/>.= 
the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">F</font>
<b>by </b><i><a class="ref" href="funct_2.html#T23">FUNCT_2:23</a></i>
;<br/>
<a NAME="E2:9"/><i><font color="Green">E32</font></i>: 
the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">F</font> is    <a href="pboole.html#M3">ManySortedFunction</a> of the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font>,the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">B</font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="functor0.html#D5">FUNCTOR0:def 5</a></i>;<br/>
<div><i><font color="Green">E33</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="9_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:9_2"/>
<font color="Maroon">i</font> <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">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/><b>then consider </b><font color="Maroon">i1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">i2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:9_2"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">i1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> &amp; <font color="Maroon">i2</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">i2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><b>reconsider </b><font color="Maroon">i1</font> = <font color="Maroon">i1</font>, <font color="Maroon">i2</font> = <font color="Maroon">i2</font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font> <b>by </b><i/>;<br/><a NAME="E5:9_2"/>
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">i1</font>,<font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">i2</font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 <b>by </b><i><a class="ref" href="altcat_1.html#D2">ALTCAT_1:def 2</a></i>;<br/><a NAME="E6:9_2"/><b>then </b>
( the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">i2</font></span><a href="altcat_1.html#K1">^&gt;</a></span> &amp; the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">i1</font>,<font color="Maroon">i2</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E7:9_2"/>
( the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  implies the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">B</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i><a class="ref" href="functor0.html#D12">FUNCTOR0:def 12</a></i>;<br/></div><b>end;</b></div>
the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor0.html#K11">id</a> <font color="Maroon">B</font></span>)</span> <a href="functor0.html#K13">*</a> <font color="Maroon">F</font></span>)</span> = 
<span class="p1">(<span class="default">the <a href="functor0.html#U2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K11">id</a> <font color="Maroon">B</font></span>)</span> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">F</font></span>)</span> <a href="altcat_2.html#K3">**</a> the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">F</font>
<b>by </b><i><a class="ref" href="functor0.html#D37">FUNCTOR0:def 37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2">id</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">B</font></span>)</span> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">F</font></span>)</span> <a href="altcat_2.html#K3">**</a> the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">F</font>
<b>by </b><i><a class="ref" href="functor0.html#D30">FUNCTOR0:def 30</a></i>
<br/>.= 
the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">F</font>
<b>by </b><i>, , </i>
;<br/>
<b>hence </b><a NAME="E5:9"/>
<span class="p1">(<span class="default"><a href="functor0.html#K11">id</a> <font color="Maroon">B</font></span>)</span> <a href="functor0.html#K13">*</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="functor0.html#G2">FunctorStr</a>(# the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">F</font>,the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">F</font> #)
 <b>by </b><i/>;<br/>


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