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<div class="add">

<span class="kw">set </span><font color="Maroon" title="c5">DD</font> =  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">CC</font> =  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">Cm</font> =  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">I</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="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">O</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font> 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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E8">A3</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">o2</font> = <font color="Maroon" title="c4">o1</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="#E5:13"><span class="lab"><font color="Green" title="E8">A3</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">o</font> = <font color="Maroon" title="c4">o1</font> as   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c3">C</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="cat_2.html#T6" title="CAT_2:th.6">CAT_2:6</a></span>;<br/>
<a NAME="E4:13_1_1"/><span class="lab"><font color="Green" title="E9">A4</font></span>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c4">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c11">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="cat_2.html#D4" title="CAT_2:def.4">CAT_2:def 4</a></span>;<br/>
<a NAME="E5:13_1_1"/>
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c10">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c11">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="ref" href="cat_2.html#D4" title="CAT_2:def.4">CAT_2:def 4</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">M</font> =  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font> 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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_1_1"><span class="lab"><font color="Green" title="E9">A4</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E7:13_1_1"/><span class="lab"><font color="Green" title="E10">A5</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  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>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E8:13_1_1"/><span class="lab"><font color="Green" title="E11">A6</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</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#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E9:13_1_1"/><span class="lab"><font color="Green" title="E12">A7</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</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#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E10:13_1_1"/><span class="lab"><font color="Green" title="E13">A8</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_1_1"><span class="lab"><font color="Green" title="E11">A6</font></span></a>, <a class="ref" href="relat_1.html#T61" title="RELAT_1:th.61">RELAT_1:61</a></span>;<br/>
<a NAME="E11:13_1_1"/><span class="lab"><font color="Green" title="E14">A9</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13_1_1"><span class="lab"><font color="Green" title="E12">A7</font></span></a>, <a class="ref" href="relat_1.html#T61" title="RELAT_1:th.61">RELAT_1:61</a></span>;<br/>
<a NAME="E12:13_1_1"/><span class="lab"><font color="Green" title="E15">A10</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">O</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13_1_1"><span class="lab"><font color="Green" title="E10">A5</font></span></a>, <a class="ref" href="relat_1.html#T61" title="RELAT_1:th.61">RELAT_1:61</a></span>;<br/>
<a NAME="E13:13_1_1"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">O</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c13">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span> or <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">O</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:13_1_1_1"/>
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">O</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">m</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:13_1_1_1"/><span class="lab"><font color="Green" title="E16">A11</font></span>: 
<font color="Maroon" title="c14">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:13_1_1_1"/><span class="lab"><font color="Green" title="E17">A12</font></span>: 
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" title="FUNCT_1:def.3">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">m1</font> = <font color="Maroon" title="c14">m</font> 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="txt" href="#E3:13_1_1_1"><span class="lab"><font color="Green" title="E16">A11</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">m2</font> = <font color="Maroon" title="c14">m</font> 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="#E10:13_1_1"><span class="lab"><font color="Green" title="E13">A8</font></span></a>, <a class="txt" href="#E3:13_1_1_1"><span class="lab"><font color="Green" title="E16">A11</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">m</font> = <font color="Maroon" title="c15">m1</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">C</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="cat_2.html#T8" title="CAT_2:th.8">CAT_2:8</a></span>;<br/>
<a NAME="E8:13_1_1_1"/><span class="lab"><font color="Green" title="E18">A13</font></span>: 
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c15">m1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_1"><span class="lab"><font color="Green" title="E16">A11</font></span></a>, <a class="txt" href="#E4:13_1_1_1"><span class="lab"><font color="Green" title="E17">A12</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/>
<a NAME="E9:13_1_1_1"/><span class="lab"><font color="Green" title="E19">A14</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c15">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c17">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="cat_2.html#T9" title="CAT_2:th.9">CAT_2:9</a></span>;<br/>
<a NAME="E10:13_1_1_1"/>
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c17">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c16">m2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="ref" href="cat_2.html#T9" title="CAT_2:th.9">CAT_2:9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:13_1_1_1"/>
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">O</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_1_1_1"><span class="lab"><font color="Green" title="E18">A13</font></span></a>, <a class="txt" href="#E9:13_1_1_1"><span class="lab"><font color="Green" title="E19">A14</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">DD</font> =  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c9">O</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1_1"><span class="lab"><font color="Green" title="E13">A8</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T4" title="RELSET_1:th.4">RELSET_1:4</a></span>;<br/>
<a NAME="E15:13_1_1"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">O</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c14">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">O</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:13_1_1_2"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">O</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c15">m</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:13_1_1_2"/><span class="lab"><font color="Green" title="E16">A15</font></span>: 
<font color="Maroon" title="c15">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:13_1_1_2"/><span class="lab"><font color="Green" title="E17">A16</font></span>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" title="FUNCT_1:def.3">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">m1</font> = <font color="Maroon" title="c15">m</font> 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="txt" href="#E3:13_1_1_2"><span class="lab"><font color="Green" title="E16">A15</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">m2</font> = <font color="Maroon" title="c15">m</font> 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="#E11:13_1_1"><span class="lab"><font color="Green" title="E14">A9</font></span></a>, <a class="txt" href="#E3:13_1_1_2"><span class="lab"><font color="Green" title="E16">A15</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">m</font> = <font color="Maroon" title="c16">m1</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">C</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="cat_2.html#T8" title="CAT_2:th.8">CAT_2:8</a></span>;<br/>
<a NAME="E8:13_1_1_2"/><span class="lab"><font color="Green" title="E18">A17</font></span>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c16">m1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_2"><span class="lab"><font color="Green" title="E16">A15</font></span></a>, <a class="txt" href="#E4:13_1_1_2"><span class="lab"><font color="Green" title="E17">A16</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/>
<a NAME="E9:13_1_1_2"/><span class="lab"><font color="Green" title="E19">A18</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c16">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c18">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="cat_2.html#T9" title="CAT_2:th.9">CAT_2:9</a></span>;<br/>
<a NAME="E10:13_1_1_2"/>
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c18">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c17">m2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="ref" href="cat_2.html#T9" title="CAT_2:th.9">CAT_2:9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:13_1_1_2"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">O</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_1_1_2"><span class="lab"><font color="Green" title="E18">A17</font></span></a>, <a class="txt" href="#E9:13_1_1_2"><span class="lab"><font color="Green" title="E19">A18</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">CC</font> =  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c9">O</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1_1"><span class="lab"><font color="Green" title="E14">A9</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T4" title="RELSET_1:th.4">RELSET_1:4</a></span>;<br/>
<a NAME="E17:13_1_1"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">M</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c15">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font></span>)</span> or <font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:13_1_1_3"/>
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">m</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:13_1_1_3"/><span class="lab"><font color="Green" title="E16">A19</font></span>: 
<font color="Maroon" title="c16">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:13_1_1_3"/><span class="lab"><font color="Green" title="E17">A20</font></span>: 
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" title="FUNCT_1:def.3">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">m1</font> = <font color="Maroon" title="c16">m</font> as   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_3"><span class="lab"><font color="Green" title="E16">A19</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">m2</font> = <font color="Maroon" title="c16">m</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="#E12:13_1_1"><span class="lab"><font color="Green" title="E15">A10</font></span></a>, <a class="txt" href="#E3:13_1_1_3"><span class="lab"><font color="Green" title="E16">A19</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c19">m</font> = <font color="Maroon" title="c17">m1</font> as   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c3">C</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="cat_2.html#T6" title="CAT_2:th.6">CAT_2:6</a></span>;<br/>
<a NAME="E8:13_1_1_3"/><span class="lab"><font color="Green" title="E18">A21</font></span>: 
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c17">m1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_3"><span class="lab"><font color="Green" title="E16">A19</font></span></a>, <a class="txt" href="#E4:13_1_1_3"><span class="lab"><font color="Green" title="E17">A20</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/>
<a NAME="E9:13_1_1_3"/><span class="lab"><font color="Green" title="E19">A22</font></span>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c17">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c19">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="cat_2.html#D4" title="CAT_2:def.4">CAT_2:def 4</a></span>;<br/>
<a NAME="E10:13_1_1_3"/>
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c19">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c18">m2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="ref" href="cat_2.html#D4" title="CAT_2:def.4">CAT_2:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:13_1_1_3"/>
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_1_1_3"><span class="lab"><font color="Green" title="E18">A21</font></span></a>, <a class="txt" href="#E9:13_1_1_3"><span class="lab"><font color="Green" title="E19">A22</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">I</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="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:13_1_1"><span class="lab"><font color="Green" title="E15">A10</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T4" title="RELSET_1:th.4">RELSET_1:4</a></span>;<br/>
<a NAME="E19:13_1_1"/><span class="lab"><font color="Green" title="E16">A23</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</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#U4" title="STRUCT_0:sel.4">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></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T61" title="RELAT_1:th.61">RELAT_1:61</a></span>;<br/>
<a NAME="E20:13_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</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#U4" title="STRUCT_0:sel.4">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></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#U4" title="STRUCT_0:sel.4">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></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T26" title="XBOOLE_1:th.26">XBOOLE_1:26</a></span>;<br/>
<a NAME="E21:13_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A24</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</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"><font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c12">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T100" title="ZFMISC_1:th.100">ZFMISC_1:100</a></span>;<br/>
<a NAME="E22:13_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">M</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c16">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span> or <font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:13_1_1_4"/>
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c17">m</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:13_1_1_4"/><span class="lab"><font color="Green" title="E18">A25</font></span>: 
<font color="Maroon" title="c17">m</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"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:13_1_1_4"/><span class="lab"><font color="Green" title="E19">A26</font></span>: 
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" title="FUNCT_1:def.3">FUNCT_1:def 3</a></span>;<br/>
<a NAME="E5:13_1_1_4"/><span class="lab"><font color="Green" title="E20">A27</font></span>: 
<font color="Maroon" title="c17">m</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:13_1_1"><span class="lab"><font color="Green" title="E17">A24</font></span></a>, <a class="txt" href="#E3:13_1_1_4"><span class="lab"><font color="Green" title="E18">A25</font></span></a>, <a class="ref" href="mcart_1.html#T10" title="MCART_1:th.10">MCART_1:10</a></span>;<br/>
<a NAME="E6:13_1_1_4"/><span class="lab"><font color="Green" title="E21">A28</font></span>: 
<font color="Maroon" title="c17">m</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:13_1_1"><span class="lab"><font color="Green" title="E17">A24</font></span></a>, <a class="txt" href="#E3:13_1_1_4"><span class="lab"><font color="Green" title="E18">A25</font></span></a>, <a class="ref" href="mcart_1.html#T10" title="MCART_1:th.10">MCART_1:10</a></span>;<br/>
<a NAME="E7:13_1_1_4"/><span class="lab"><font color="Green" title="E22">A29</font></span>: 
<font color="Maroon" title="c17">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">m</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">m</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:13_1_1"><span class="lab"><font color="Green" title="E17">A24</font></span></a>, <a class="txt" href="#E3:13_1_1_4"><span class="lab"><font color="Green" title="E18">A25</font></span></a>, <a class="ref" href="mcart_1.html#T21" title="MCART_1:th.21">MCART_1:21</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">m1</font> = <font color="Maroon" title="c17">m</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> , <font color="Maroon" title="c19">m2</font> = <font color="Maroon" title="c17">m</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  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="txt" href="#E5:13_1_1_4"><span class="lab"><font color="Green" title="E20">A27</font></span></a>, <a class="txt" href="#E6:13_1_1_4"><span class="lab"><font color="Green" title="E21">A28</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c20">n1</font> = <font color="Maroon" title="c17">m</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> , <font color="Maroon" title="c21">n2</font> = <font color="Maroon" title="c17">m</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  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="#E5:13_1_1_4"><span class="lab"><font color="Green" title="E20">A27</font></span></a>, <a class="txt" href="#E6:13_1_1_4"><span class="lab"><font color="Green" title="E21">A28</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c22">mm</font> = <font color="Maroon" title="c18">m1</font>, <font color="Maroon" title="c23">n</font> = <font color="Maroon" title="c19">m2</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">C</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="cat_2.html#T8" title="CAT_2:th.8">CAT_2:8</a></span>;<br/>
<a NAME="E11:13_1_1_4"/><span class="lab"><font color="Green" title="E23">A30</font></span>: 
<font color="Maroon" title="c17">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:13_1_1"><span class="lab"><font color="Green" title="E16">A23</font></span></a>, <a class="txt" href="#E3:13_1_1_4"><span class="lab"><font color="Green" title="E18">A25</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E12:13_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A31</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c18">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c19">m2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13_1_1_4"><span class="lab"><font color="Green" title="E22">A29</font></span></a>, <a class="ref" href="cat_1.html#T15" title="CAT_1:th.15">CAT_1:15</a></span>;<br/>
<a NAME="E13:13_1_1_4"/><span class="lab"><font color="Green" title="E25">A32</font></span>: 
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c18">m1</font>,<font color="Maroon" title="c19">m2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_4"><span class="lab"><font color="Green" title="E18">A25</font></span></a>, <a class="txt" href="#E4:13_1_1_4"><span class="lab"><font color="Green" title="E19">A26</font></span></a>, <a class="txt" href="#E7:13_1_1_4"><span class="lab"><font color="Green" title="E22">A29</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/>
<a NAME="E14:13_1_1_4"/><span class="lab"><font color="Green" title="E26">A33</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c18">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c22">mm</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="cat_2.html#T9" title="CAT_2:th.9">CAT_2:9</a></span>;<br/>
<a NAME="E15:13_1_1_4"/><span class="lab"><font color="Green" title="E27">A34</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c20">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c22">mm</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="ref" href="cat_2.html#T9" title="CAT_2:th.9">CAT_2:9</a></span>;<br/>
<a NAME="E16:13_1_1_4"/><span class="lab"><font color="Green" title="E28">A35</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c19">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c23">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="cat_2.html#T9" title="CAT_2:th.9">CAT_2:9</a></span>;<br/>
<a NAME="E17:13_1_1_4"/><span class="lab"><font color="Green" title="E29">A36</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c21">n2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c23">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="ref" href="cat_2.html#T9" title="CAT_2:th.9">CAT_2:9</a></span>;<br/>
<a NAME="E18:13_1_1_4"/><span class="lab"><font color="Green" title="E30">A37</font></span>: 
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">m1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c19">m2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13_1_1_4"><span class="lab"><font color="Green" title="E22">A29</font></span></a>, <a class="txt" href="#E11:13_1_1_4"><span class="lab"><font color="Green" title="E23">A30</font></span></a>, <a class="txt" href="#E13:13_1_1_4"><span class="lab"><font color="Green" title="E25">A32</font></span></a>, <a class="ref" href="cat_1.html#D1" title="CAT_1:def.1">CAT_1:def 1</a></span>;<br/>
<a NAME="E19:13_1_1_4"/><span class="lab"><font color="Green" title="E31">A38</font></span>: 
<font color="Maroon" title="c18">m1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c19">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">mm</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c23">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="txt" href="#E12:13_1_1_4"><span class="lab"><font color="Green" title="E24">A31</font></span></a>, <a class="ref" href="cat_2.html#T11" title="CAT_2:th.11">CAT_2:11</a></span>;<br/>
<a NAME="E20:13_1_1_4"/>
<font color="Maroon" title="c22">mm</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c23">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">n1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c21">n2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="txt" href="#E12:13_1_1_4"><span class="lab"><font color="Green" title="E24">A31</font></span></a>, <a class="txt" href="#E14:13_1_1_4"><span class="lab"><font color="Green" title="E26">A33</font></span></a>, <a class="txt" href="#E15:13_1_1_4"><span class="lab"><font color="Green" title="E27">A34</font></span></a>, <a class="txt" href="#E16:13_1_1_4"><span class="lab"><font color="Green" title="E28">A35</font></span></a>, <a class="txt" href="#E17:13_1_1_4"><span class="lab"><font color="Green" title="E29">A36</font></span></a>, <a class="ref" href="cat_2.html#T11" title="CAT_2:th.11">CAT_2:11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E21:13_1_1_4"/>
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:13_1_1_4"><span class="lab"><font color="Green" title="E30">A37</font></span></a>, <a class="txt" href="#E19:13_1_1_4"><span class="lab"><font color="Green" title="E31">A38</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c16">Cm</font> =  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c12">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c12">M</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:13_1_1"><span class="lab"><font color="Green" title="E17">A24</font></span></a>, <a class="ref" href="relset_1.html#T4" title="RELSET_1:th.4">RELSET_1:4</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">CAT</font> =  <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #);<br/>
<a NAME="E24:13_1_1"/>
 <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) is  <a href="cat_1.html#V2" title="CAT_1:attr.2">Category-like</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_5"><span class="kw">proof </span></a><div class="add">

<div><span class="kw">hereby </span> <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> or (  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> &amp;  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> ) ) ) &amp; (  for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> or  not  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>3</sub></font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>2</sub></font>)</span>)</span>,<font color="Olive">b<sub>1</sub></font>) ) ) &amp; (  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) holds <br/> (  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp;  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; (  for <font color="Olive">b<sub>2</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<font color="Olive">b<sub>2</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> ) ) &amp; (  for <font color="Olive">b<sub>2</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>2</sub></font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> ) ) ) ) )</span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c18">f</font>, <font color="Maroon" title="c19">g</font> be   <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>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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"><font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) implies  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font> ) &amp; (  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font> implies <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) ) )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c20">g9</font> = <font color="Maroon" title="c19">g</font>, <font color="Maroon" title="c21">f9</font> = <font color="Maroon" title="c18">f</font> 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="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E2:13_1_1_5_1"/><span class="lab"><font color="Green" title="E19">A40</font></span>: 
<font color="Maroon" title="c19">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E3:13_1_1_5_1"/><span class="lab"><font color="Green" title="E20">A41</font></span>: 
<font color="Maroon" title="c18">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font> implies <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:13_1_1_5_1_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font></span><br/><a NAME="E2:13_1_1_5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A42</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:13_1_1"><span class="lab"><font color="Green" title="E16">A23</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">thus </span> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> = 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">g9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1_1_5_1"><span class="lab"><font color="Green" title="E19">A40</font></span></a>, <a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">f9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1_1_5_1_1"><span class="lab"><font color="Green" title="E21">A42</font></span></a>, <a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_5_1"><span class="lab"><font color="Green" title="E20">A41</font></span></a>, <a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E5:13_1_1_5_1"/><span class="lab"><font color="Green" title="E21">A43</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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"><font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)</span><br/><a NAME="E6:13_1_1_5_1"/><span class="lab"><font color="Green" title="E22">A44</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">g9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1_1"><span class="lab"><font color="Green" title="E13">A8</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><a NAME="E7:13_1_1_5_1"/><span class="lab"><font color="Green" title="E23">A45</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">f9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1_1"><span class="lab"><font color="Green" title="E14">A9</font></span></a>, <a class="txt" href="#E5:13_1_1_5_1"><span class="lab"><font color="Green" title="E21">A43</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><a NAME="E8:13_1_1_5_1"/><span class="lab"><font color="Green" title="E24">A46</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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#U4" title="STRUCT_0:sel.4">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></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1_1_5_1"><span class="lab"><font color="Green" title="E19">A40</font></span></a>, <a class="txt" href="#E3:13_1_1_5_1"><span class="lab"><font color="Green" title="E20">A41</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/><a NAME="E9:13_1_1_5_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_1_1_5_1"><span class="lab"><font color="Green" title="E22">A44</font></span></a>, <a class="txt" href="#E7:13_1_1_5_1"><span class="lab"><font color="Green" title="E23">A45</font></span></a>, <a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E10:13_1_1_5_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:13_1_1"><span class="lab"><font color="Green" title="E16">A23</font></span></a>, <a class="txt" href="#E8:13_1_1_5_1"><span class="lab"><font color="Green" title="E24">A46</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> or  not  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>3</sub></font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>2</sub></font>)</span>)</span>,<font color="Olive">b<sub>1</sub></font>) ) ) &amp; (  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) holds <br/> (  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp;  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; (  for <font color="Olive">b<sub>2</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<font color="Olive">b<sub>2</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> ) ) &amp; (  for <font color="Olive">b<sub>2</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>2</sub></font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> ) ) ) ) )</span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c18">f</font>, <font color="Maroon" title="c19">g</font> be   <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>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font> implies (  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font> &amp;  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> ) )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c20">g9</font> = <font color="Maroon" title="c19">g</font>, <font color="Maroon" title="c21">f9</font> = <font color="Maroon" title="c18">f</font> 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="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">assume </span><a NAME="E2:13_1_1_5_2"/><span class="lab"><font color="Green" title="E20">A48</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font> &amp;  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> )</span><br/><a NAME="E3:13_1_1_5_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A49</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1_1_5"><span class="lab"><font color="Green" title="E18">A39</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c22">h</font> =  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font>) as   <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>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#T4" title="PARTFUN1:th.4">PARTFUN1:4</a></span>;<br/><a NAME="E5:13_1_1_5_2"/><span class="lab"><font color="Green" title="E22">A50</font></span>: 
<font color="Maroon" title="c22">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c20">g9</font>,<font color="Maroon" title="c21">f9</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_5_2"><span class="lab"><font color="Green" title="E21">A49</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><a NAME="E6:13_1_1_5_2"/><span class="lab"><font color="Green" title="E23">A51</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">f9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1_1"><span class="lab"><font color="Green" title="E13">A8</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><a NAME="E7:13_1_1_5_2"/><span class="lab"><font color="Green" title="E24">A52</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">g9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1_1"><span class="lab"><font color="Green" title="E13">A8</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><a NAME="E8:13_1_1_5_2"/><span class="lab"><font color="Green" title="E25">A53</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c22">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">h</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1_1"><span class="lab"><font color="Green" title="E13">A8</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><a NAME="E9:13_1_1_5_2"/><span class="lab"><font color="Green" title="E26">A54</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">f9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1_1"><span class="lab"><font color="Green" title="E14">A9</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><a NAME="E10:13_1_1_5_2"/><span class="lab"><font color="Green" title="E27">A55</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">g9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1_1"><span class="lab"><font color="Green" title="E14">A9</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><a NAME="E11:13_1_1_5_2"/>
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c22">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">h</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1_1"><span class="lab"><font color="Green" title="E14">A9</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><span class="kw">hence </span><a NAME="E12:13_1_1_5_2"/>
(  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font> &amp;  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1_1_5_2"><span class="lab"><font color="Green" title="E20">A48</font></span></a>, <a class="txt" href="#E5:13_1_1_5_2"><span class="lab"><font color="Green" title="E22">A50</font></span></a>, <a class="txt" href="#E6:13_1_1_5_2"><span class="lab"><font color="Green" title="E23">A51</font></span></a>, <a class="txt" href="#E7:13_1_1_5_2"><span class="lab"><font color="Green" title="E24">A52</font></span></a>, <a class="txt" href="#E8:13_1_1_5_2"><span class="lab"><font color="Green" title="E25">A53</font></span></a>, <a class="txt" href="#E9:13_1_1_5_2"><span class="lab"><font color="Green" title="E26">A54</font></span></a>, <a class="txt" href="#E10:13_1_1_5_2"><span class="lab"><font color="Green" title="E27">A55</font></span></a>, <a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) holds <br/> (  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp;  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; (  for <font color="Olive">b<sub>2</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<font color="Olive">b<sub>2</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> ) ) &amp; (  for <font color="Olive">b<sub>2</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>2</sub></font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> ) ) )</span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c18">f</font>, <font color="Maroon" title="c19">g</font>, <font color="Maroon" title="c20">h</font> be   <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>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> &amp;  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font> implies  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c20">h</font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c20">h</font>,<font color="Maroon" title="c19">g</font>)</span>)</span>,<font color="Maroon" title="c18">f</font>) )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c21">h9</font> = <font color="Maroon" title="c20">h</font>, <font color="Maroon" title="c22">g9</font> = <font color="Maroon" title="c19">g</font>, <font color="Maroon" title="c23">f9</font> = <font color="Maroon" title="c18">f</font> 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="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:13_1_1_5_3"/><span class="lab"><font color="Green" title="E20">A56</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font>
 <span class="kw">and </span><br/><a NAME="E3:13_1_1_5_3"/><span class="lab"><font color="Green" title="E21">A57</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c20">h</font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c20">h</font>,<font color="Maroon" title="c19">g</font>)</span>)</span>,<font color="Maroon" title="c18">f</font>)</span><br/><a NAME="E4:13_1_1_5_3"/><span class="lab"><font color="Green" title="E22">A58</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c20">h</font>,<font color="Maroon" title="c19">g</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1_1_5"><span class="lab"><font color="Green" title="E18">A39</font></span></a>, <a class="txt" href="#E2:13_1_1_5_3"><span class="lab"><font color="Green" title="E20">A56</font></span></a></span>;<br/><a NAME="E5:13_1_1_5_3"/><span class="lab"><font color="Green" title="E23">A59</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1_1_5"><span class="lab"><font color="Green" title="E18">A39</font></span></a>, <a class="txt" href="#E3:13_1_1_5_3"><span class="lab"><font color="Green" title="E21">A57</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c24">hg</font> =  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c20">h</font>,<font color="Maroon" title="c19">g</font>), <font color="Maroon" title="c25">gf</font> =  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font>) as   <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>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_1_1_5_3"><span class="lab"><font color="Green" title="E22">A58</font></span></a>, <a class="ref" href="partfun1.html#T4" title="PARTFUN1:th.4">PARTFUN1:4</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c26">hg9</font> = <font color="Maroon" title="c24">hg</font>, <font color="Maroon" title="c27">gf9</font> = <font color="Maroon" title="c25">gf</font> 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="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E8:13_1_1_5_3"/><span class="lab"><font color="Green" title="E24">A60</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">hg</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1_1_5"><span class="lab"><font color="Green" title="E19">A47</font></span></a>, <a class="txt" href="#E2:13_1_1_5_3"><span class="lab"><font color="Green" title="E20">A56</font></span></a></span>;<br/><a NAME="E9:13_1_1_5_3"/><span class="lab"><font color="Green" title="E25">A61</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">gf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1_1_5"><span class="lab"><font color="Green" title="E19">A47</font></span></a>, <a class="txt" href="#E3:13_1_1_5_3"><span class="lab"><font color="Green" title="E21">A57</font></span></a></span>;<br/><a NAME="E10:13_1_1_5_3"/><span class="lab"><font color="Green" title="E26">A62</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c24">hg</font>,<font color="Maroon" title="c18">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1_1_5"><span class="lab"><font color="Green" title="E18">A39</font></span></a>, <a class="txt" href="#E3:13_1_1_5_3"><span class="lab"><font color="Green" title="E21">A57</font></span></a>, <a class="txt" href="#E8:13_1_1_5_3"><span class="lab"><font color="Green" title="E24">A60</font></span></a></span>;<br/><a NAME="E11:13_1_1_5_3"/><span class="lab"><font color="Green" title="E27">A63</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c20">h</font>,<font color="Maroon" title="c25">gf</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1_1_5"><span class="lab"><font color="Green" title="E18">A39</font></span></a>, <a class="txt" href="#E2:13_1_1_5_3"><span class="lab"><font color="Green" title="E20">A56</font></span></a>, <a class="txt" href="#E9:13_1_1_5_3"><span class="lab"><font color="Green" title="E25">A61</font></span></a></span>;<br/><a NAME="E12:13_1_1_5_3"/><span class="lab"><font color="Green" title="E28">A64</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">h9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">h</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1_1"><span class="lab"><font color="Green" title="E13">A8</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><a NAME="E13:13_1_1_5_3"/><span class="lab"><font color="Green" title="E29">A65</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c22">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1_1"><span class="lab"><font color="Green" title="E14">A9</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><a NAME="E14:13_1_1_5_3"/><span class="lab"><font color="Green" title="E30">A66</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c22">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1_1"><span class="lab"><font color="Green" title="E13">A8</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><a NAME="E15:13_1_1_5_3"/><span class="lab"><font color="Green" title="E31">A67</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1_1"><span class="lab"><font color="Green" title="E14">A9</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><span class="kw">thus </span> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c20">h</font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c18">f</font>)</span>)</span>) = 
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">h9</font>,<font color="Maroon" title="c27">gf9</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1_1_5_3"><span class="lab"><font color="Green" title="E27">A63</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>
<br/>.= 
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c21">h9</font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c22">g9</font>,<font color="Maroon" title="c23">f9</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_1_5_3"><span class="lab"><font color="Green" title="E23">A59</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>
<br/>.= 
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c21">h9</font>,<font color="Maroon" title="c22">g9</font>)</span>)</span>,<font color="Maroon" title="c23">f9</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1_1_5_3"><span class="lab"><font color="Green" title="E20">A56</font></span></a>, <a class="txt" href="#E3:13_1_1_5_3"><span class="lab"><font color="Green" title="E21">A57</font></span></a>, <a class="txt" href="#E12:13_1_1_5_3"><span class="lab"><font color="Green" title="E28">A64</font></span></a>, <a class="txt" href="#E13:13_1_1_5_3"><span class="lab"><font color="Green" title="E29">A65</font></span></a>, <a class="txt" href="#E14:13_1_1_5_3"><span class="lab"><font color="Green" title="E30">A66</font></span></a>, <a class="txt" href="#E15:13_1_1_5_3"><span class="lab"><font color="Green" title="E31">A67</font></span></a>, <a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a></span>
<br/>.= 
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c26">hg9</font>,<font color="Maroon" title="c23">f9</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_1_1_5_3"><span class="lab"><font color="Green" title="E22">A58</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>
<br/>.= 
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c20">h</font>,<font color="Maroon" title="c19">g</font>)</span>)</span>,<font color="Maroon" title="c18">f</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1_1_5_3"><span class="lab"><font color="Green" title="E26">A62</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c18">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> &amp;  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> &amp; (  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">b</font></span>)</span>,<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> ) ) &amp; (  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>1</sub></font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> ) ) )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c19">b9</font> = <font color="Maroon" title="c18">b</font> as   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">thus </span> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span> = 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1_1"><span class="lab"><font color="Green" title="E13">A8</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>
<br/>.= 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">b9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:13_1_1"><span class="lab"><font color="Green" title="E15">A10</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>
<br/>.= 
<font color="Maroon" title="c18">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> &amp; (  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">b</font></span>)</span>,<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> ) ) &amp; (  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>1</sub></font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> ) ) )</span><br/>

<span class="kw">thus </span> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span> = 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1_1"><span class="lab"><font color="Green" title="E14">A9</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">b9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:13_1_1"><span class="lab"><font color="Green" title="E15">A10</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>
<br/>.= 
<font color="Maroon" title="c18">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">b</font></span>)</span>,<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> ) ) &amp; (  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>1</sub></font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> ) ) )</span><br/>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)  holds <br/>(  not  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>1</sub></font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> )</span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c20">f</font> be   <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>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> implies  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span>,<font color="Maroon" title="c20">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">f</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c21">f9</font> = <font color="Maroon" title="c20">f</font> 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="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">assume </span><a NAME="E2:13_1_1_5_6"/>
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span>,<font color="Maroon" title="c20">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">f</font></span><br/><a NAME="E3:13_1_1_5_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A68</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1_1"><span class="lab"><font color="Green" title="E14">A9</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><a NAME="E4:13_1_1_5_6"/><span class="lab"><font color="Green" title="E21">A69</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">b9</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a></span>;<br/><a NAME="E5:13_1_1_5_6"/><span class="lab"><font color="Green" title="E22">A70</font></span>: 
 the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:13_1_1"><span class="lab"><font color="Green" title="E15">A10</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><a NAME="E6:13_1_1_5_6"/><span class="lab"><font color="Green" title="E23">A71</font></span>: 
<font color="Maroon" title="c20">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E7:13_1_1_5_6"/><span class="lab"><font color="Green" title="E24">A72</font></span>: 
 the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E8:13_1_1_5_6"/><span class="lab"><font color="Green" title="E25">A73</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span>,<font color="Maroon" title="c20">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_5_6"><span class="lab"><font color="Green" title="E20">A68</font></span></a>, <a class="txt" href="#E4:13_1_1_5_6"><span class="lab"><font color="Green" title="E21">A69</font></span></a>, <a class="txt" href="#E5:13_1_1_5_6"><span class="lab"><font color="Green" title="E22">A70</font></span></a>, <a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a></span>;<br/><a NAME="E9:13_1_1_5_6"/><span class="lab"><font color="Green" title="E26">A74</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span>,<font color="Maroon" title="c20">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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#U4" title="STRUCT_0:sel.4">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></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_1_1_5_6"><span class="lab"><font color="Green" title="E23">A71</font></span></a>, <a class="txt" href="#E7:13_1_1_5_6"><span class="lab"><font color="Green" title="E24">A72</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/><a NAME="E10:13_1_1_5_6"/><span class="lab"><font color="Green" title="E27">A75</font></span>: 
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">b9</font></span>)</span>,<font color="Maroon" title="c21">f9</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">f9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_5_6"><span class="lab"><font color="Green" title="E20">A68</font></span></a>, <a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a></span>;<br/><a NAME="E11:13_1_1_5_6"/><span class="lab"><font color="Green" title="E28">A76</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span>,<font color="Maroon" title="c20">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:13_1_1"><span class="lab"><font color="Green" title="E16">A23</font></span></a>, <a class="txt" href="#E8:13_1_1_5_6"><span class="lab"><font color="Green" title="E25">A73</font></span></a>, <a class="txt" href="#E9:13_1_1_5_6"><span class="lab"><font color="Green" title="E26">A74</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E12:13_1_1_5_6"/>
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span>,<font color="Maroon" title="c20">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:13_1_1"><span class="lab"><font color="Green" title="E15">A10</font></span></a>, <a class="txt" href="#E10:13_1_1_5_6"><span class="lab"><font color="Green" title="E27">A75</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/><span class="kw">hence </span><a NAME="E13:13_1_1_5_6"/>
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span>,<font color="Maroon" title="c20">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1_1_5_6"><span class="lab"><font color="Green" title="E28">A76</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c20">g</font> be   <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>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> or  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c20">g</font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">g</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c21">g9</font> = <font color="Maroon" title="c20">g</font> 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="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">assume </span><a NAME="E9:13_1_1_5"/>
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c20">g</font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">g</font></span><br/>

<a NAME="E10:13_1_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A77</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1_1"><span class="lab"><font color="Green" title="E13">A8</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/>
<a NAME="E11:13_1_1_5"/><span class="lab"><font color="Green" title="E21">A78</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">b9</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a></span>;<br/>
<a NAME="E12:13_1_1_5"/><span class="lab"><font color="Green" title="E22">A79</font></span>: 
 the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:13_1_1"><span class="lab"><font color="Green" title="E15">A10</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/>
<a NAME="E13:13_1_1_5"/><span class="lab"><font color="Green" title="E23">A80</font></span>: 
<font color="Maroon" title="c20">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E14:13_1_1_5"/><span class="lab"><font color="Green" title="E24">A81</font></span>: 
 the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E15:13_1_1_5"/><span class="lab"><font color="Green" title="E25">A82</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c20">g</font>,<span class="p2">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1_1_5"><span class="lab"><font color="Green" title="E20">A77</font></span></a>, <a class="txt" href="#E11:13_1_1_5"><span class="lab"><font color="Green" title="E21">A78</font></span></a>, <a class="txt" href="#E12:13_1_1_5"><span class="lab"><font color="Green" title="E22">A79</font></span></a>, <a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a></span>;<br/>
<a NAME="E16:13_1_1_5"/><span class="lab"><font color="Green" title="E26">A83</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c20">g</font>,<span class="p2">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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#U4" title="STRUCT_0:sel.4">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></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_1_1_5"><span class="lab"><font color="Green" title="E23">A80</font></span></a>, <a class="txt" href="#E14:13_1_1_5"><span class="lab"><font color="Green" title="E24">A81</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<a NAME="E17:13_1_1_5"/><span class="lab"><font color="Green" title="E27">A84</font></span>: 
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c21">g9</font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">b9</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">g9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1_1_5"><span class="lab"><font color="Green" title="E20">A77</font></span></a>, <a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a></span>;<br/>
<a NAME="E18:13_1_1_5"/><span class="lab"><font color="Green" title="E28">A85</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c20">g</font>,<span class="p2">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:13_1_1"><span class="lab"><font color="Green" title="E16">A23</font></span></a>, <a class="txt" href="#E15:13_1_1_5"><span class="lab"><font color="Green" title="E25">A82</font></span></a>, <a class="txt" href="#E16:13_1_1_5"><span class="lab"><font color="Green" title="E26">A83</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E19:13_1_1_5"/>
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c20">g</font>,<span class="p2">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:13_1_1"><span class="lab"><font color="Green" title="E15">A10</font></span></a>, <a class="txt" href="#E17:13_1_1_5"><span class="lab"><font color="Green" title="E27">A84</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/>
<span class="kw">hence </span><a NAME="E20:13_1_1_5"/>
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c20">g</font>,<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <font color="Maroon" title="c9">O</font>,<font color="Maroon" title="c12">M</font>,<font color="Maroon" title="c13">DD</font>,<font color="Maroon" title="c14">CC</font>,<font color="Maroon" title="c16">Cm</font>,<font color="Maroon" title="c15">I</font> #) <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:13_1_1_5"><span class="lab"><font color="Green" title="E28">A85</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E25:13_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <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> st <br/>(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive">b<sub>1</sub></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="c1">C1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font> &amp;  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font> &amp;  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font> &amp;  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font> &amp;  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C1</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C2</font> &amp;  the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</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="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
