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<span class="kw">let </span><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</font> be   <a href="cat_5.html#V3" title="CAT_5:attr.3">Categorial</a>   <a href="cat_5.html#V4" title="CAT_5:attr.4">full</a>  <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font> implies  <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C1</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">C2</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">C2</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c2">C2</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c2">C2</font> #) )</span><br/>

<span class="kw">assume </span><a NAME="E1:42"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C1</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">C2</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">C2</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c2">C2</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c2">C2</font> #)</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c3">A</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font> as  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="cat_5.html#V2" title="CAT_5:attr.2">categorial</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#D6" target="_self" title="CAT_5:def.6">Def6</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">B</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K11" title="CAT_5:func.11">`2</a> </span>)</span> where <font color="Olive" title="b1">m</font> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C1</font> : verum </span>}</span> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">m</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C1</font>;<br/>
<a NAME="E4:42"/>
<font color="Maroon" title="c5">m</font> <a href="cat_5.html#K11" title="CAT_5:func.11">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K11" title="CAT_5:func.11">`2</a> </span>)</span> where <font color="Olive" title="b1">m</font> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C1</font> : verum </span>}</span> 
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">B</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K11" title="CAT_5:func.11">`2</a> </span>)</span> where <font color="Olive" title="b1">m</font> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C1</font> : verum </span>}</span>  as  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">D1</font> =  <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C1</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> #), <font color="Maroon" title="c8">D2</font> =  <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">C2</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">C2</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c2">C2</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c2">C2</font> #) as   <a href="cat_1.html#V1" title="CAT_1:attr.1">strict</a>  <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T1" target="_self" title="CAT_5:th.1">Th1</a></span>;<br/>
<a NAME="E7:42"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
<font color="Maroon" title="c7">D1</font> is  <a href="cat_5.html#V3" title="CAT_5:attr.3">Categorial</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T10" target="_self" title="CAT_5:th.10">Th10</a></span>;<br/>
<a NAME="E8:42"/><span class="lab"><font color="Green" title="E28">A3</font></span>: 
<font color="Maroon" title="c8">D2</font> is  <a href="cat_5.html#V3" title="CAT_5:attr.3">Categorial</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T10" target="_self" title="CAT_5:th.10">Th10</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E29">A4</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font> be    <a href="cat_5.html#M1" title="CAT_5:mode.1">Element</a> of <font color="Maroon" title="c3">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> holds <br/> ( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Olive" title="b1">F</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C1</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> #) iff <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">B</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c11">F</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Maroon" title="c11">F</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C1</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> #) iff <font color="Maroon" title="c11">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">B</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c12">m</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Maroon" title="c11">F</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#D8" target="_self" title="CAT_5:def.8">Def8</a></span>;<br/><a NAME="E2:42_1"/>
<font color="Maroon" title="c12">m</font> <a href="cat_5.html#K11" title="CAT_5:func.11">`2</a>  <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c11">F</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><span class="kw">hence </span><a NAME="E3:42_1"/>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Maroon" title="c11">F</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C1</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> #) iff <font color="Maroon" title="c11">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">B</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font> be    <a href="cat_5.html#M1" title="CAT_5:mode.1">Element</a> of <font color="Maroon" title="c3">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> holds <br/> ( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Olive" title="b1">F</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">C2</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">C2</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c2">C2</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c2">C2</font> #) iff <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">B</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c11">F</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Maroon" title="c11">F</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">C2</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">C2</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c2">C2</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c2">C2</font> #) iff <font color="Maroon" title="c11">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">B</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c12">a9</font> = <font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c13">b9</font> = <font color="Maroon" title="c10">b</font> as   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">C2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E26">A1</font></span></a></span>;<br/><a NAME="E2:42_2"/><span class="lab"><font color="Green" title="E30">A5</font></span>: 
 <a href="cat_5.html#K10" title="CAT_5:func.10">cat</a> <font color="Maroon" title="c12">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T16" target="_self" title="CAT_5:th.16">Th16</a></span>;<br/><a NAME="E3:42_2"/>
 <a href="cat_5.html#K10" title="CAT_5:func.10">cat</a> <font color="Maroon" title="c13">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T16" target="_self" title="CAT_5:th.16">Th16</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">m2</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Maroon" title="c11">F</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">C2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42_2"><span class="lab"><font color="Green" title="E30">A5</font></span></a>, <a class="ref" href="cat_5.html#D8" target="_self" title="CAT_5:def.8">Def8</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c15">m</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Maroon" title="c11">F</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#D8" target="_self" title="CAT_5:def.8">Def8</a></span>;<br/><a NAME="E6:42_2"/><span class="lab"><font color="Green" title="E31">A6</font></span>: 
<font color="Maroon" title="c15">m</font> <a href="cat_5.html#K11" title="CAT_5:func.11">`2</a>  <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c11">F</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E7:42_2"/>
<font color="Maroon" title="c14">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">m2</font>
 ;<br/><span class="kw">hence </span><a NAME="E8:42_2"/>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Maroon" title="c11">F</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">C2</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">C2</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c2">C2</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c2">C2</font> #) iff <font color="Maroon" title="c11">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">B</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:42_2"><span class="lab"><font color="Green" title="E31">A6</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E11:42"/>
 <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C1</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">C2</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">C2</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c2">C2</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c2">C2</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="txt" href="#E7:42"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="txt" href="#E8:42"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E29">A4</font></span></a>, <a class="ref" href="cat_5.html#T18" target="_self" title="CAT_5:th.18">Th18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
