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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F</font>, <font color="Olive" title="b2">F1</font>, <font color="Olive" title="b3">F2</font>, <font color="Olive" title="b4">F3</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>  st <font color="Olive" title="b1">F</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Olive" title="b2">F1</font> &amp; <font color="Olive" title="b2">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Olive" title="b3">F2</font> &amp; <font color="Olive" title="b3">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Olive" title="b4">F3</font> holds <br/>for <font color="Olive" title="b5">t1</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">F1</font><br/> for <font color="Olive" title="b6">t2</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Olive" title="b2">F1</font>,<font color="Olive" title="b3">F2</font><br/> for <font color="Olive" title="b7">t3</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Olive" title="b3">F2</font>,<font color="Olive" title="b4">F3</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b7">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b6">t2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b5">t1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b7">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b5">t1</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">F</font>, <font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">F2</font>, <font color="Maroon" title="c6">F3</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">F</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c4">F1</font> &amp; <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> &amp; <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="c6">F3</font> implies for <font color="Olive" title="b1">t1</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F1</font><br/> for <font color="Olive" title="b2">t2</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font><br/> for <font color="Olive" title="b3">t3</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">F3</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b2">t2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b1">t1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b1">t1</font></span>)</span> )</span><br/>











<b>assume </b><a NAME="E1:30"/><i><font color="Green" title="E25">A1</font></i>: 
( <font color="Maroon" title="c3">F</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c4">F1</font> &amp; <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> &amp; <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="c6">F3</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t1</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F1</font><br/> for <font color="Olive" title="b2">t2</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font><br/> for <font color="Olive" title="b3">t3</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">F3</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b2">t2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b1">t1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b1">t1</font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c7">t1</font> be    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t2</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font><br/> for <font color="Olive" title="b2">t3</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">F3</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b1">t2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t1</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c8">t2</font> be    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t3</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">F3</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c8">t2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t1</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c9">t3</font> be    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">F3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c8">t2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t1</font></span>)</span></span><br/>





<a NAME="E2:30"/><i><font color="Green" title="E26">A2</font></i>: 
( <font color="Maroon" title="c3">F</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp; <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">F3</font> )
 
<b>by </b><i><a class="txt" href="nattra_1.html#E1:30"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="nattra_1.html#T19" target="_self" title="NATTRA_1:th.19">Th19</a></i>;<br/>
<a NAME="E3:30"/><b>then </b><i><font color="Green" title="E27">A3</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c6">F3</font>
 
<b>by </b><i><a class="txt" href="nattra_1.html#E1:30"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="nattra_1.html#T19" target="_self" title="NATTRA_1:th.19">Th19</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">a</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c8">t2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t1</font></span>)</span></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span><br/><a NAME="E1:30_1"/><i><font color="Green" title="E28">A4</font></i>: 
(  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">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>  &amp;  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">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>  &amp;  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">F3</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">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>  )
 <b>by </b><i><a class="txt" href="nattra_1.html#E1:30"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="nattra_1.html#D2" target="_self" title="NATTRA_1:def.2">Def2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c8">t2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c8">t2</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span>
<b>by </b><i><a class="txt" href="nattra_1.html#E1:30"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="nattra_1.html#E2:30"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="nattra_1.html#D6" target="_self" title="NATTRA_1:def.6">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span>
<b>by </b><i><a class="txt" href="nattra_1.html#E1:30"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="nattra_1.html#D6" target="_self" title="NATTRA_1:def.6">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="nattra_1.html#E1:30_1"><i><font color="Green" title="E28">A4</font></i></a>, <a class="ref" href="cat_1.html#T54" title="CAT_1:th.54">CAT_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span>
<b>by </b><i><a class="txt" href="nattra_1.html#E1:30"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="nattra_1.html#D6" target="_self" title="NATTRA_1:def.6">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t1</font></span>)</span></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font>
<b>by </b><i><a class="txt" href="nattra_1.html#E1:30"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="nattra_1.html#E2:30"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="nattra_1.html#D6" target="_self" title="NATTRA_1:def.6">Def6</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:30"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c8">t2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t1</font></span>)</span>
 <b>by </b><i><a class="txt" href="nattra_1.html#E3:30"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="nattra_1.html#T20" target="_self" title="NATTRA_1:th.20">Th20</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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