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<b>let </b><font color="Maroon" title="c1">B</font>, <font color="Maroon" title="c2">A</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> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c1">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> holds <br/>for <font color="Olive" title="b4">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>  st ( for <font color="Olive" title="b5">a</font>, <font color="Olive" title="b6">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b5">a</font>,<font color="Olive" title="b6">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>  holds <br/>for <font color="Olive" title="b7">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b5">a</font>,<font color="Olive" title="b6">b</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b4">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b6">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b7">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b7">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b5">a</font></span>)</span> ) holds <br/>for <font color="Olive" title="b5">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>  st ( for <font color="Olive" title="b6">a</font>, <font color="Olive" title="b7">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b6">a</font>,<font color="Olive" title="b7">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>  holds <br/>for <font color="Olive" title="b8">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b6">a</font>,<font color="Olive" title="b7">b</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b5">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b7">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b8">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b8">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b6">a</font></span>)</span> ) holds <br/>for <font color="Olive" title="b6">a</font>, <font color="Olive" title="b7">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b6">a</font>,<font color="Olive" title="b7">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>  holds <br/>for <font color="Olive" title="b8">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b6">a</font>,<font color="Olive" title="b7">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b4">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b7">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b8">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b8">f</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="Olive" title="b5">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b4">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b6">a</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> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c1">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> 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>  st ( for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">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>  holds <br/>for <font color="Olive" title="b4">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">b</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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">a</font></span>)</span> ) holds <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>  st ( for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">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>  holds <br/>for <font color="Olive" title="b5">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b4">b</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="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b5">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b5">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">a</font></span>)</span> ) holds <br/>for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">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>  holds <br/>for <font color="Olive" title="b5">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<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> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b4">b</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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b5">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b5">f</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="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> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">a</font></span>)</span> )</span><br/>









<b>assume </b><b>that </b><br/><a NAME="E1:33"/><i><font color="Green" title="E28">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>
 <b>and </b><br/><a NAME="E2:33"/><i><font color="Green" title="E29">A2</font></i>: 
<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>
 ; <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>  st ( for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">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>  holds <br/>for <font color="Olive" title="b4">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">b</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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">a</font></span>)</span> ) holds <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>  st ( for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">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>  holds <br/>for <font color="Olive" title="b5">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b4">b</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="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b5">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b5">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">a</font></span>)</span> ) holds <br/>for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">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>  holds <br/>for <font color="Olive" title="b5">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<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> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b4">b</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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b5">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b5">f</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="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> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">a</font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c6">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">a</font>, <font color="Olive" title="b2">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">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>  holds <br/>for <font color="Olive" title="b3">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c6">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">b</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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">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="c6">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font></span>)</span> ) implies 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>  st ( for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">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>  holds <br/>for <font color="Olive" title="b4">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">b</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="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">a</font></span>)</span> ) holds <br/>for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">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>  holds <br/>for <font color="Olive" title="b4">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<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="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">b</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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b4">f</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="Olive" title="b1">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">a</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E3:33"/><i><font color="Green" title="E30">A3</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">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>  holds <br/>for <font color="Olive" title="b3">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c6">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">b</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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">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="c6">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font></span>)</span>
 ; <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>  st ( for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">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>  holds <br/>for <font color="Olive" title="b4">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">b</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="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">a</font></span>)</span> ) holds <br/>for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">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>  holds <br/>for <font color="Olive" title="b4">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<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="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">b</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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b4">f</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="Olive" title="b1">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">a</font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c7">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">a</font>, <font color="Olive" title="b2">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">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>  holds <br/>for <font color="Olive" title="b3">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c7">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">b</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="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">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="c7">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font></span>)</span> ) implies for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">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>  holds <br/>for <font color="Olive" title="b3">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">b</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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">f</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="c7">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E4:33"/><i><font color="Green" title="E31">A4</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">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>  holds <br/>for <font color="Olive" title="b3">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c7">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">b</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="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">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="c7">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font></span>)</span>
 ; <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">a</font>, <font color="Olive" title="b2">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">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>  holds <br/>for <font color="Olive" title="b3">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">b</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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">f</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="c7">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">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>  implies for <font color="Olive" title="b1">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">b</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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b1">f</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="c7">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E5:33"/><i><font color="Green" title="E32">A5</font></i>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">b</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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b1">f</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="c7">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</font></span>)</span></span><br/>

<a NAME="E6:33"/><b>then </b><i><font color="Green" title="E33">A6</font></i>: 
(  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c8">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">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>  &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</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="c9">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>  )
 
<b>by </b><i><a class="txt" href="#E1:33"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="nattra_1.html#D2" target="_self" title="NATTRA_1:def.2">Def2</a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/>
<a NAME="E7:33"/><i><font color="Green" title="E34">A7</font></i>: 
(  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c8">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="c8">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#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="c8">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="c8">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="#E1:33"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E2:33"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="nattra_1.html#D2" target="_self" title="NATTRA_1:def.2">Def2</a></i>;<br/>
<a NAME="E8:33"/><i><font color="Green" title="E35">A8</font></i>: 
 <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="c9">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="c9">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> 
 
<b>by </b><i><a class="txt" href="#E2:33"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="nattra_1.html#D2" target="_self" title="NATTRA_1:def.2">Def2</a></i>;<br/>
<a NAME="E9:33"/><i><font color="Green" title="E36">A9</font></i>: 
 <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="c8">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="c9">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> 
 
<b>by </b><i><a class="txt" href="#E5:33"><i><font color="Green" title="E32">A5</font></i></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/>
<a NAME="E10:33"/><i><font color="Green" title="E37">A10</font></i>: 
 <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="c8">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="c9">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> 
 
<b>by </b><i><a class="txt" href="#E5:33"><i><font color="Green" title="E32">A5</font></i></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/>
<b>let </b><font color="Maroon" title="c10">f</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</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="c7">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">b</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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c10">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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="c10">f</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="c7">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</font></span>)</span></span><br/>

<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">b</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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c10">f</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">b</font></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">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">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="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c10">f</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:33"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E2:33"><i><font color="Green" title="E29">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"><font color="Maroon" title="c7">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">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">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c10">f</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E6:33"><i><font color="Green" title="E33">A6</font></i></a>, <a class="txt" href="#E8:33"><i><font color="Green" title="E35">A8</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="c7">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">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="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c10">f</font></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">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:33"><i><font color="Green" title="E30">A3</font></i></a>, <a class="txt" href="#E5:33"><i><font color="Green" title="E32">A5</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</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="c10">f</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">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</font></span>)</span>
<b>by </b><i><a class="txt" href="#E7:33"><i><font color="Green" title="E34">A7</font></i></a>, <a class="txt" href="#E8:33"><i><font color="Green" title="E35">A8</font></i></a>, <a class="txt" href="#E10:33"><i><font color="Green" title="E37">A10</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"><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="c10">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</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">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</font></span>)</span>
<b>by </b><i><a class="txt" href="#E4:33"><i><font color="Green" title="E31">A4</font></i></a>, <a class="txt" href="#E5:33"><i><font color="Green" title="E32">A5</font></i></a></i>
<br/>.= 
<span class="p1">(<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="c10">f</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="c7">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</font></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">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E7:33"><i><font color="Green" title="E34">A7</font></i></a>, <a class="txt" href="#E9:33"><i><font color="Green" title="E36">A9</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="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c10">f</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="c7">t2</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:33"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E2:33"><i><font color="Green" title="E29">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/>


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