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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  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">t</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font>  st <font color="Olive" title="b1">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Olive" title="b2">F2</font> &amp; <font color="Olive" title="b3">t</font> is  <a href="nattra_1.html#V1" title="NATTRA_1:attr.1">invertible</a>  holds <br/><font color="Olive" title="b2">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Olive" title="b1">F1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">F1</font>, <font color="Maroon" title="c4">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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">t</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c3">F1</font>,<font color="Maroon" title="c4">F2</font>  st <font color="Maroon" title="c3">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c4">F2</font> &amp; <font color="Olive" title="b1">t</font> is  <a href="nattra_1.html#V1" title="NATTRA_1:attr.1">invertible</a>  holds <br/><font color="Maroon" title="c4">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c3">F1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">t</font> be    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c3">F1</font>,<font color="Maroon" title="c4">F2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c4">F2</font> &amp; <font color="Maroon" title="c5">t</font> is  <a href="nattra_1.html#V1" title="NATTRA_1:attr.1">invertible</a>  implies <font color="Maroon" title="c4">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c3">F1</font> )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:46"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
<font color="Maroon" title="c3">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c4">F2</font>
 <span class="kw">and </span><br/><a NAME="E2:46"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
for <font color="Olive" title="b1">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c5">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font> is  <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a> 
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="nattra_1.html#D10" target="_self" title="NATTRA_1:def.10">NATTRA_1:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c3">F1</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">a</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="nattra_1.html#D2" target="_self" title="NATTRA_1:def.2">NATTRA_1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">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><br/>

<a NAME="E3:46"/><span class="lab"><font color="Green" title="E39">A3</font></span>: 
<font color="Maroon" title="c5">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font> is  <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46"><span class="lab"><font color="Green" title="E38">A2</font></span></a></span>;<br/>
<a NAME="E4:46"/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">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="#E1:46"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="nattra_1.html#D2" target="_self" title="NATTRA_1:def.2">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:46"/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">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="#E3:46"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="ref" href="cat_1.html#T70" title="CAT_1:th.70">CAT_1:70</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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