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<div class="add">

<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#V1" title="ALTCAT_2:attr.1">reflexive</a>  <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">B</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#V1" title="ALTCAT_2:attr.1">reflexive</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">A</font>;<br/><b>let </b><font color="Maroon" title="c3">C</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">A</font>;<br/><b>let </b><font color="Maroon" title="c4">D</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c2">B</font>;<br/>







<b>assume </b><a NAME="E1:8"/><i><font color="Green" title="E3">A1</font></i>: 
<font color="Maroon" title="c3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">D</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c5">X</font> = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c6">Y</font> = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>
<a NAME="E2:8"/><i><font color="Green" title="E4">A2</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a></i>;<br/>
<a NAME="E3:8"/><b>then </b><i><font color="Green" title="E5">A3</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></i>;<br/>
<i><font color="Green" title="E6">A4</font></i>: the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c3">C</font></span>)</span> = 
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<b>by </b><i><a class="txt" href="functor1.html#E1:8"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="functor0.html#D29" title="FUNCTOR0:def.29">FUNCTOR0:def 29</a></i>
<br/>.= 
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="functor1.html#E2:8"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a>, <a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T43" title="FUNCT_1:th.43">FUNCT_1:43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#D29" title="FUNCTOR0:def.29">FUNCTOR0:def 29</a></i>
<br/>.= 
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#D29" title="FUNCTOR0:def.29">FUNCTOR0:def 29</a></i>
;<br/>
<a NAME="E5:8"/>
for <font color="Olive" title="b1">i</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds <br/>the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c3">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:8_2"/><i><font color="Green" title="E7">A5</font></i>: 
<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 ;<br/>

<a NAME="E2:8_2"/><b>then </b><i><font color="Green" title="E8">A6</font></i>: 
<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#T34" title="FUNCT_1:th.34">FUNCT_1:34</a></i>;<br/>
<b>set </b><font color="Maroon" title="c8">XX</font> = the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font>;<br/>
<b>set </b><font color="Maroon" title="c9">YY</font> = the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">D</font>;<br/>
<a NAME="E3:8_2"/>
the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">D</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a></i>;<br/>
<a NAME="E4:8_2"/><b>then </b><i><font color="Green" title="E9">A7</font></i>: 
the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
 
<b>by </b><i><a class="txt" href="functor1.html#E1:8_2"><i><font color="Green" title="E7">A5</font></i></a>, <a class="ref" href="altcat_2.html#D2" title="ALTCAT_2:def.2">ALTCAT_2:def 2</a></i>;<br/>
<a NAME="E5:8_2"/><i><font color="Green" title="E10">A8</font></i>: 
the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c3">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:8_2_1"/><i><font color="Green" title="E11">A9</font></i>: 
the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
 
<b>by </b><i><a class="ref" href="functor0.html#D29" title="FUNCTOR0:def.29">FUNCTOR0:def 29</a></i>;<br/>
<a NAME="E2:8_2_1"/><i><font color="Green" title="E12">A10</font></i>: 
the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
 
<b>by </b><i><a class="ref" href="functor0.html#D29" title="FUNCTOR0:def.29">FUNCTOR0:def 29</a></i>;<br/>
<a NAME="E3:8_2_1"/><i><font color="Green" title="E13">A11</font></i>: 
the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c3">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c3">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
 
<b>by </b><i><a class="ref" href="functor0.html#D29" title="FUNCTOR0:def.29">FUNCTOR0:def 29</a></i>;<br/>
<span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2">(<span class="default">the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="functor1.html#E1:8_2"><i><font color="Green" title="E7">A5</font></i></a>, <a class="txt" href="functor1.html#E1:8_2_1"><i><font color="Green" title="E11">A9</font></i></a>, <a class="txt" href="functor1.html#E2:8_2_1"><i><font color="Green" title="E12">A10</font></i></a>, <a class="ref" href="msualg_3.html#D1" title="MSUALG_3:def.1">MSUALG_3:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2">(<span class="default">the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2">(<span class="default">the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="functor1.html#E3:8"><i><font color="Green" title="E5">A3</font></i></a>, <a class="txt" href="functor1.html#E1:8_2"><i><font color="Green" title="E7">A5</font></i></a>, <a class="ref" href="msualg_3.html#D1" title="MSUALG_3:def.1">MSUALG_3:def 1</a></i>
<br/>.= 
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2">(<span class="default">the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T43" title="FUNCT_1:th.43">FUNCT_1:43</a></i>
<br/>.= 
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default">the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>
<b>by </b><i><a class="txt" href="functor1.html#E4:8_2"><i><font color="Green" title="E9">A7</font></i></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>
<br/>.= 
the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c3">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
<b>by </b><i><a class="txt" href="functor1.html#E1:8"><i><font color="Green" title="E3">A1</font></i></a>, <a class="txt" href="functor1.html#E1:8_2"><i><font color="Green" title="E7">A5</font></i></a>, <a class="txt" href="functor1.html#E3:8_2_1"><i><font color="Green" title="E13">A11</font></i></a>, <a class="ref" href="msualg_3.html#D1" title="MSUALG_3:def.1">MSUALG_3:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E5:8_2_1"/>
the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c3">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<i><font color="Green" title="E11">A12</font></i>: <span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> = 
<span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
<b>by </b><i><a class="ref" href="functor0.html#D29" title="FUNCTOR0:def.29">FUNCTOR0:def 29</a></i>
<br/>.= 
the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>
<b>by </b><i><a class="txt" href="functor1.html#E2:8_2"><i><font color="Green" title="E8">A6</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
<b>by </b><i><a class="txt" href="functor1.html#E1:8_2"><i><font color="Green" title="E7">A5</font></i></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>
;<br/>
<b>set </b><font color="Maroon" title="c10">dom1</font> =  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c11">dom2</font> =  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span>;<br/>
<a NAME="E7:8_2"/><i><font color="Green" title="E12">A13</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D24" title="PBOOLE:def.24">PBOOLE:def 24</a></i>;<br/>
<a NAME="E8:8_2"/>
<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_3"><b>proof </b></a><div class="add">

<a NAME="E1:8_2_3"/><i><font color="Green" title="E13">A14</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> = 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#D29" title="FUNCTOR0:def.29">FUNCTOR0:def 29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<b>by </b><i><a class="ref" href="funct_1.html#T37" title="FUNCT_1:th.37">FUNCT_1:37</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<b>by </b><i><a class="txt" href="functor1.html#E2:8"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a>, <a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></i>
;<br/>
<b>hence </b><a NAME="E3:8_2_3"/>
<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="functor1.html#E1:8_2"><i><font color="Green" title="E7">A5</font></i></a>, <a class="txt" href="functor1.html#E1:8_2_3"><i><font color="Green" title="E13">A14</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E9:8_2"/>
the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c3">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
 <b>by </b><i><a class="txt" href="functor1.html#E5:8_2"><i><font color="Green" title="E10">A8</font></i></a>, <a class="txt" href="functor1.html#E6:8_2"><i><font color="Green" title="E11">A12</font></i></a>, <a class="txt" href="functor1.html#E7:8_2"><i><font color="Green" title="E12">A13</font></i></a>, <a class="ref" href="pboole.html#D24" title="PBOOLE:def.24">PBOOLE:def 24</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:8"/><b>then </b>
the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c3">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span>
 
<b>by </b><i><a class="txt" href="functor1.html#E1:8"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</a></i>;<br/>
<b>hence </b><a NAME="E7:8"/>
 <a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c4">D</font></span>)</span>
 <b>by </b><i><a class="txt" href="functor1.html#E1:8"><i><font color="Green" title="E3">A1</font></i></a>, <a class="txt" href="functor1.html#E4:8"><i><font color="Green" title="E6">A4</font></i></a>, <a class="ref" href="functor0.html#D37" title="FUNCTOR0:def.37">FUNCTOR0:def 37</a></i>;<br/>


</div>
