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<b>reconsider </b><font color="Maroon" title="c8">tF</font> = <font color="Maroon" title="c7">t</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12" title="CAT_1:func.12">Obj</a> <font color="Maroon" title="c6">F</font></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">A</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c3">C</font> ;<br/>
<a NAME="E2:26_1_1"/>
<font color="Maroon" title="c8">tF</font> is    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c5">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:26_1_1_1"/>
<font color="Maroon" title="c4">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F</font>
 <b>by </b><i><a class="txt" href="isocat_1.html#E1:26"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="isocat_1.html#T8" target="_self" title="ISOCAT_1:th.8">Th8</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D3" title="NATTRA_1:def.3">NATTRA_1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#M1" title="SUBSET_1:mode.1">M2</a>(the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">A</font>) holds  <font color="Maroon" title="c8">tF</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Olive">b<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Olive">b<sub>1</sub></font></span><br/>

<b>let </b><font color="Maroon" title="c9">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"> <font color="Maroon" title="c8">tF</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">a</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</font></span><br/>

<i><font color="Green" title="E16">A2</font></i>: <font color="Maroon" title="c8">tF</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">a</font> = 
<font color="Maroon" title="c7">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K12" title="CAT_1:func.12">Obj</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">a</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
<font color="Maroon" title="c7">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E1:26"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></i>
;<br/>
<a NAME="E3:26_1_1_1"/>
( <font color="Maroon" title="c4">G1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</font> &amp; <font color="Maroon" title="c5">G2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</font> )
 
<b>by </b><i><a class="ref" href="cat_1.html#T113" title="CAT_1:th.113">CAT_1:113</a></i>;<br/>
<b>hence </b><a NAME="E4:26_1_1_1"/>
<font color="Maroon" title="c8">tF</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">a</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</font>
 <b>by </b><i><a class="txt" href="isocat_1.html#E2:26_1_1_1"><i><font color="Green" title="E16">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:26_1_1"/>
<font color="Maroon" title="c7">t</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12" title="CAT_1:func.12">Obj</a> <font color="Maroon" title="c6">F</font></span>)</span> is    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c5">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F</font>
 ; <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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