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<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">I</font> being   <a href="index_1.html#M3" title="INDEX_1:mode.3">Indexing</a> of the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C</font> holds <br/> ( <font color="Olive" title="b1">I</font> is   <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c1">C</font> iff ( ( for <font color="Olive" title="b2">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b2">a</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">I</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Olive" title="b2">a</font></span>)</span> ) &amp; ( for <font color="Olive" title="b2">m1</font>, <font color="Olive" title="b3">m2</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Olive" title="b3">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="Olive" title="b2">m1</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive" title="b2">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b3">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b2">m1</font></span>)</span> ) ) )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c2">D</font> =  <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C</font> #) as   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T1" title="CAT_5:th.1">CAT_5:1</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c3">I</font> be    <a href="index_1.html#M3" title="INDEX_1:mode.3">Indexing</a> of the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">I</font> is   <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c1">C</font> iff ( ( for <font color="Olive" title="b1">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Olive" title="b1">a</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">m1</font>, <font color="Olive" title="b2">m2</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Olive" title="b2">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="Olive" title="b1">m1</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive" title="b1">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b2">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b1">m1</font></span>)</span> ) ) )</span><br/>

<a NAME="E2:40"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c2">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C</font> #)
 
;<br/>
<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Olive" title="b1">a</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">m1</font>, <font color="Olive" title="b2">m2</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Olive" title="b2">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="Olive" title="b1">m1</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive" title="b1">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b2">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b1">m1</font></span>)</span> ) implies <font color="Maroon" title="c3">I</font> is   <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c1">C</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:40_1"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon" title="c3">I</font> is   <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c1">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Olive" title="b1">a</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">m1</font>, <font color="Olive" title="b2">m2</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Olive" title="b2">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="Olive" title="b1">m1</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive" title="b1">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b2">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b1">m1</font></span>)</span> ) )</span><br/><span class="kw">hence </span><a NAME="E2:40_1"/>
for <font color="Olive" title="b1">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Olive" title="b1">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:40"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="index_1.html#D10" target="_self" title="INDEX_1:def.10">Def10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">m1</font>, <font color="Olive" title="b2">m2</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Olive" title="b2">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="Olive" title="b1">m1</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive" title="b1">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b2">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b1">m1</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">m1</font>, <font color="Maroon" title="c5">m2</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c5">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="c4">m1</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c4">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c5">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c4">m1</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E3:40_1"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c5">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="c4">m1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c4">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c5">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c4">m1</font></span>)</span></span><br/><a NAME="E4:40_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <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 <font color="Maroon" title="c1">C</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c5">m2</font>,<font color="Maroon" title="c4">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c5">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c4">m1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:40"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E1:40_1"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="index_1.html#D10" target="_self" title="INDEX_1:def.10">Def10</a></span>;<br/><span class="kw">hence </span><a NAME="E5:40_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c4">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c5">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c4">m1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:40_1"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="cat_1.html#T41" title="CAT_1:th.41">CAT_1:41</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E4:40"/><span class="lab"><font color="Green" title="E16">A4</font></span>: 
for <font color="Olive" title="b1">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Olive" title="b1">a</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:40"/><span class="lab"><font color="Green" title="E17">A5</font></span>: 
for <font color="Olive" title="b1">m1</font>, <font color="Olive" title="b2">m2</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Olive" title="b2">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="Olive" title="b1">m1</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive" title="b1">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b2">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b1">m1</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">I</font> is   <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c1">C</font></span><br/>

<span class="kw">thus </span><a NAME="E6:40"/>
 ex <font color="Olive" title="b1">D</font> being  <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> st <font color="Olive" title="b1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:40"><span class="lab"><font color="Green" title="E15">A1</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="index_1.html#D10" target="_self" title="INDEX_1:def.10">INDEX_1:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">a</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 <font color="Maroon" title="c1">C</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</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">C</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Olive" title="b1">a</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">m1</font>, <font color="Olive" title="b2">m2</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 <font color="Maroon" title="c1">C</font>  st the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">m2</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">C</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">m1</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <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 <font color="Maroon" title="c1">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">m2</font>,<font color="Olive" title="b1">m1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b2">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b1">m1</font></span>)</span> ) )</span><br/>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">m1</font>, <font color="Olive" title="b2">m2</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 <font color="Maroon" title="c1">C</font>  st the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">m2</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">C</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">m1</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <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 <font color="Maroon" title="c1">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">m2</font>,<font color="Olive" title="b1">m1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b2">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b1">m1</font></span>)</span></span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c4">a</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</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">C</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</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">C</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">a</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c4">a</font></span>)</span>

<br/>.= 
 <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Maroon" title="c4">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:40"><span class="lab"><font color="Green" title="E16">A4</font></span></a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c4">m1</font>, <font color="Maroon" title="c5">m2</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">m2</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">C</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">m1</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <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 <font color="Maroon" title="c1">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">m2</font>,<font color="Maroon" title="c4">m1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c5">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c4">m1</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E8:40"/>
the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">m2</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">C</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">m1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <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 <font color="Maroon" title="c1">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">m2</font>,<font color="Maroon" title="c4">m1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c5">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c4">m1</font></span>)</span></span><br/>

<a NAME="E9:40"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A6</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c5">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="c4">m1</font>
 
;<br/>
<a NAME="E10:40"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A7</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c4">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c5">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c4">m1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:40"><span class="lab"><font color="Green" title="E17">A5</font></span></a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <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 <font color="Maroon" title="c1">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c5">m2</font>,<font color="Maroon" title="c4">m1</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <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 <font color="Maroon" title="c1">C</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c5">m2</font>,<font color="Maroon" title="c4">m1</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c5">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c4">m1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:40"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E10:40"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="ref" href="cat_1.html#T41" title="CAT_1:th.41">CAT_1:41</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
