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<b>thus </b><a NAME="E1:53_4_2"/>
for <font color="Olive" title="b1">C1</font>, <font color="Olive" title="b2">C2</font> being <a href="cat_1.html#V1" title="CAT_1:attr.1">strict</a> <a href="cat_5.html#V1" title="CAT_5:attr.1">with_triple-like_morphisms</a> <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>  st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_5.html#K12" title="CAT_5:func.12">Hom</a> <font color="Maroon" title="c2">o</font> &amp; ( for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cat_5.html#K12" title="CAT_5:func.12">Hom</a> <font color="Maroon" title="c2">o</font><br/> for <font color="Olive" title="b5">f</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 <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b5">f</font>] holds <br/><span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Olive" title="b5">f</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">C1</font> ) &amp; ( for <font color="Olive" title="b3">m</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">C1</font>  ex <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cat_5.html#K12" title="CAT_5:func.12">Hom</a> <font color="Maroon" title="c2">o</font> ex <font color="Olive" title="b6">f</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 <br/>( <font color="Olive" title="b3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Olive" title="b6">f</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font>,<font color="Olive" title="b6">f</font>] ) ) &amp; ( for <font color="Olive" title="b3">m1</font>, <font color="Olive" title="b4">m2</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">C1</font><br/> for <font color="Olive" title="b5">a1</font>, <font color="Olive" title="b6">a2</font>, <font color="Olive" title="b7">a3</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cat_5.html#K12" title="CAT_5:func.12">Hom</a> <font color="Maroon" title="c2">o</font><br/> for <font color="Olive" title="b8">f1</font>, <font color="Olive" title="b9">f2</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 <font color="Olive" title="b3">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b5">a1</font>,<font color="Olive" title="b6">a2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Olive" title="b8">f1</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> &amp; <font color="Olive" title="b4">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b6">a2</font>,<font color="Olive" title="b7">a3</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Olive" title="b9">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> holds <br/><font color="Olive" title="b4">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive" title="b3">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b5">a1</font>,<font color="Olive" title="b7">a3</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b9">f2</font>,<font color="Olive" title="b8">f1</font>)</span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> ) &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_5.html#K12" title="CAT_5:func.12">Hom</a> <font color="Maroon" title="c2">o</font> &amp; ( for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cat_5.html#K12" title="CAT_5:func.12">Hom</a> <font color="Maroon" title="c2">o</font><br/> for <font color="Olive" title="b5">f</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 <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b5">f</font>] holds <br/><span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Olive" title="b5">f</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Olive" title="b2">C2</font> ) &amp; ( for <font color="Olive" title="b3">m</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Olive" title="b2">C2</font>  ex <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cat_5.html#K12" title="CAT_5:func.12">Hom</a> <font color="Maroon" title="c2">o</font> ex <font color="Olive" title="b6">f</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 <br/>( <font color="Olive" title="b3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Olive" title="b6">f</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font>,<font color="Olive" title="b6">f</font>] ) ) &amp; ( for <font color="Olive" title="b3">m1</font>, <font color="Olive" title="b4">m2</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Olive" title="b2">C2</font><br/> for <font color="Olive" title="b5">a1</font>, <font color="Olive" title="b6">a2</font>, <font color="Olive" title="b7">a3</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cat_5.html#K12" title="CAT_5:func.12">Hom</a> <font color="Maroon" title="c2">o</font><br/> for <font color="Olive" title="b8">f1</font>, <font color="Olive" title="b9">f2</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 <font color="Olive" title="b3">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b5">a1</font>,<font color="Olive" title="b6">a2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Olive" title="b8">f1</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> &amp; <font color="Olive" title="b4">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b6">a2</font>,<font color="Olive" title="b7">a3</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Olive" title="b9">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> holds <br/><font color="Olive" title="b4">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive" title="b3">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b5">a1</font>,<font color="Olive" title="b7">a3</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b9">f2</font>,<font color="Olive" title="b8">f1</font>)</span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> ) holds <br/><font color="Olive" title="b1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">C2</font>
 <b>from </b><i><a class="ref" href="cat_5.html#S2" target="_self" title="CAT_5:sch.2">CAT_5:sch 2</a>(<a class="txt" href="#E2:53"><i><font color="Green" title="E33">A3</font></i></a>);</i> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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