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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">F2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font><br/>  for <font color="Olive" title="b3">G1</font>, <font color="Olive" title="b4">G2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>  st <font color="Olive" title="b1">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b2">F2</font> &amp; <font color="Olive" title="b3">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b4">G2</font> holds <br/><font color="Olive" title="b3">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Olive" title="b1">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b4">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Olive" title="b2">F2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">F2</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>; <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" title="b1">G1</font>, <font color="Olive" title="b2">G2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>  st <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp; <font color="Olive" title="b1">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b2">G2</font> holds <br/><font color="Olive" title="b1">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b2">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">G1</font>, <font color="Maroon" title="c7">G2</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>; <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="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp; <font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c7">G2</font> implies <font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font> )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:28"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font>
 <span class="kw">and </span><br/><a NAME="E2:28"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
<font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c7">G2</font>
 ; <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="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">t1</font> =  the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">t2</font> =  the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font>;<br/>
<a NAME="E3:28"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
<font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c7">G2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></span>;<br/>
<a NAME="E4:28"/><span class="lab"><font color="Green" title="E22">A4</font></span>: 
<font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">F2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:28"/><span class="lab"><font color="Green" title="E23">A5</font></span>: 
<font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="isocat_1.html#T5" target="_self" title="ISOCAT_1:th.5">Th8</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font> st <br/> for <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">M2</a>( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>)  holds <br/>(  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  for <font color="Olive">b<sub>4</sub></font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> holds  <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive">b<sub>4</sub></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="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> )</span><br/>

<span class="kw">take </span><font color="Maroon" title="c10">t</font> = <span class="p1">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="isocat_1.html#K3" title="ISOCAT_1:func.3">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="isocat_1.html#K2" title="ISOCAT_1:func.2">*</a>  the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span>)</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> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">M2</a>( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>)  holds <br/>(  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  for <font color="Olive">b<sub>3</sub></font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive">b<sub>3</sub></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="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c11">a</font>, <font color="Maroon" title="c12">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  for <font color="Olive">b<sub>1</sub></font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive">b<sub>1</sub></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="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span> )</span><br/>

<a NAME="E6:28"/><span class="lab"><font color="Green" title="E24">A6</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/>
<a NAME="E7:28"/><span class="lab"><font color="Green" title="E25">A7</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:28"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/>
<a NAME="E8:28"/><span class="lab"><font color="Green" title="E26">A8</font></span>: 
<font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="isocat_1.html#T5" target="_self" title="ISOCAT_1:th.5">Th8</a></span>;<br/>
<a NAME="E9:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A9</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/>
<a NAME="E10:28"/><span class="lab"><font color="Green" title="E28">A10</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:28"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E11:28"/><span class="lab"><font color="Green" title="E29">A11</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive">b<sub>1</sub></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="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span><br/>

<a NAME="E12:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A12</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T84" title="CAT_1:th.84">CAT_1:84</a></span>;<br/>
<a NAME="E13:28"/><span class="lab"><font color="Green" title="E31">A13</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/>
<a NAME="E14:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A14</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T84" title="CAT_1:th.84">CAT_1:84</a></span>;<br/>
<a NAME="E15:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A15</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:28"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="ref" href="cat_1.html#T24" title="CAT_1:th.24">CAT_1:24</a></span>;<br/>
<a NAME="E16:28"/><span class="lab"><font color="Green" title="E34">A16</font></span>: 
<font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="isocat_1.html#T5" target="_self" title="ISOCAT_1:th.5">Th8</a></span>;<br/>
<a NAME="E17:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A17</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/>
<a NAME="E18:28"/><span class="lab"><font color="Green" title="E36">A18</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:28"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/>
<a NAME="E19:28"/><span class="lab"><font color="Green" title="E37">A19</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:28"><span class="lab"><font color="Green" title="E34">A16</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/>
<a NAME="E20:28"/><span class="lab"><font color="Green" title="E38">A20</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/>
<a NAME="E21:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A21</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T84" title="CAT_1:th.84">CAT_1:84</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c13">f</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</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">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</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="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span><br/>

<a NAME="E22:28"/><span class="lab"><font color="Green" title="E40">A22</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:28"><span class="lab"><font color="Green" title="E29">A11</font></span></a>, <a class="ref" href="cat_1.html#T84" title="CAT_1:th.84">CAT_1:84</a></span>;<br/>
<a NAME="E23:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A23</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T84" title="CAT_1:th.84">CAT_1:84</a></span>;<br/>
<a NAME="E24:28"/><span class="lab"><font color="Green" title="E42">A24</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:28"><span class="lab"><font color="Green" title="E29">A11</font></span></a>, <a class="ref" href="cat_1.html#T84" title="CAT_1:th.84">CAT_1:84</a></span>;<br/>
<a NAME="E25:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A25</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T84" title="CAT_1:th.84">CAT_1:84</a></span>;<br/>
<a NAME="E26:28"/><span class="lab"><font color="Green" title="E44">A26</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/>
<a NAME="E27:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A27</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:28"><span class="lab"><font color="Green" title="E39">A21</font></span></a>, <a class="ref" href="cat_1.html#T24" title="CAT_1:th.24">CAT_1:24</a></span>;<br/>
<a NAME="E28:28"/><span class="lab"><font color="Green" title="E46">A28</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:28"><span class="lab"><font color="Green" title="E40">A22</font></span></a>, <a class="ref" href="cat_1.html#T84" title="CAT_1:th.84">CAT_1:84</a></span>;<br/>
<a NAME="E29:28"/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:28"><span class="lab"><font color="Green" title="E29">A11</font></span></a>, <a class="ref" href="cat_1.html#T84" title="CAT_1:th.84">CAT_1:84</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:28"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:28"><span class="lab"><font color="Green" title="E29">A11</font></span></a>, <a class="ref" href="nattra_1.html#T11" title="NATTRA_1:th.11">NATTRA_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="isocat_1.html#K3" title="ISOCAT_1:func.3">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="isocat_1.html#K2" title="ISOCAT_1:func.2">*</a>  the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:28"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E16:28"><span class="lab"><font color="Green" title="E34">A16</font></span></a>, <a class="ref" href="nattra_1.html#D6" title="NATTRA_1:def.6">NATTRA_1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="isocat_1.html#K3" title="ISOCAT_1:func.3">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="isocat_1.html#K2" title="ISOCAT_1:func.2">*</a>  the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:28"><span class="lab"><font color="Green" title="E35">A17</font></span></a>, <a class="txt" href="#E9:28"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="isocat_1.html#K3" title="ISOCAT_1:func.3">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="isocat_1.html#T21" target="_self" title="ISOCAT_1:th.21">Th26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="isocat_1.html#T20" target="_self" title="ISOCAT_1:th.20">Th25</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:28"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E14:28"><span class="lab"><font color="Green" title="E32">A14</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:28"><span class="lab"><font color="Green" title="E43">A25</font></span></a>, <a class="txt" href="#E15:28"><span class="lab"><font color="Green" title="E33">A15</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:28"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E14:28"><span class="lab"><font color="Green" title="E32">A14</font></span></a>, <a class="txt" href="#E25:28"><span class="lab"><font color="Green" title="E43">A25</font></span></a>, <a class="ref" href="cat_1.html#T25" title="CAT_1:th.25">CAT_1:25</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:28"><span class="lab"><font color="Green" title="E31">A13</font></span></a>, <a class="txt" href="#E24:28"><span class="lab"><font color="Green" title="E42">A24</font></span></a>, <a class="ref" href="nattra_1.html#T13" title="NATTRA_1:th.13">NATTRA_1:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E11:28"><span class="lab"><font color="Green" title="E29">A11</font></span></a>, <a class="ref" href="nattra_1.html#D8" title="NATTRA_1:def.8">NATTRA_1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:28"><span class="lab"><font color="Green" title="E40">A22</font></span></a>, <a class="txt" href="#E20:28"><span class="lab"><font color="Green" title="E38">A20</font></span></a>, <a class="ref" href="nattra_1.html#T13" title="NATTRA_1:th.13">NATTRA_1:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:28"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E23:28"><span class="lab"><font color="Green" title="E41">A23</font></span></a>, <a class="txt" href="#E21:28"><span class="lab"><font color="Green" title="E39">A21</font></span></a>, <a class="ref" href="cat_1.html#T25" title="CAT_1:th.25">CAT_1:25</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E22:28"><span class="lab"><font color="Green" title="E40">A22</font></span></a>, <a class="ref" href="nattra_1.html#D8" title="NATTRA_1:def.8">NATTRA_1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:28"><span class="lab"><font color="Green" title="E39">A21</font></span></a>, <a class="txt" href="#E28:28"><span class="lab"><font color="Green" title="E46">A28</font></span></a>, <a class="txt" href="#E26:28"><span class="lab"><font color="Green" title="E44">A26</font></span></a>, <a class="ref" href="cat_1.html#T25" title="CAT_1:th.25">CAT_1:25</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:28"><span class="lab"><font color="Green" title="E46">A28</font></span></a>, <a class="txt" href="#E27:28"><span class="lab"><font color="Green" title="E45">A27</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:28"><span class="lab"><font color="Green" title="E39">A21</font></span></a>, <a class="txt" href="#E26:28"><span class="lab"><font color="Green" title="E44">A26</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="isocat_1.html#K3" title="ISOCAT_1:func.3">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="isocat_1.html#T20" target="_self" title="ISOCAT_1:th.20">Th25</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="isocat_1.html#K3" title="ISOCAT_1:func.3">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="isocat_1.html#K2" title="ISOCAT_1:func.2">*</a>  the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="isocat_1.html#T21" target="_self" title="ISOCAT_1:th.21">Th26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"> the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c7">G2</font> <a href="isocat_1.html#K3" title="ISOCAT_1:func.3">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="isocat_1.html#K2" title="ISOCAT_1:func.2">*</a>  the    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:28"><span class="lab"><font color="Green" title="E37">A19</font></span></a>, <a class="txt" href="#E18:28"><span class="lab"><font color="Green" title="E36">A18</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:28"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E16:28"><span class="lab"><font color="Green" title="E34">A16</font></span></a>, <a class="ref" href="nattra_1.html#D6" title="NATTRA_1:def.6">NATTRA_1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:28"><span class="lab"><font color="Green" title="E29">A11</font></span></a>, <a class="ref" href="nattra_1.html#T11" title="NATTRA_1:th.11">NATTRA_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="txt" href="#E12:28"><span class="lab"><font color="Green" title="E30">A12</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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