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<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a> <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c2">B</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><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="c2">B</font>,<font color="Maroon" title="c1">A</font>;<br/>





<b>assume </b><a NAME="E1:70"/><i><font color="Green" title="E55">A1</font></i>: 
<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>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">m</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">B</font>;<br/><a NAME="E1:70_1"/><i><font color="Green" title="E56">A2</font></i>: 
<font color="Maroon" title="c5">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">m</font></span>)</span>
 ;<br/><a NAME="E2:70_1"/>
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="nattra_1.html#E1:70"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="nattra_1.html#D2" target="_self" title="NATTRA_1:def.2">Def2</a></i>;<br/><a NAME="E3:70_1"/><b>then </b><i><font color="Green" title="E57">A3</font></i>: 
<font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span>
 <b>by </b><i><a class="ref" href="nattra_1.html#T45" target="_self" title="NATTRA_1:th.45">Th45</a></i>;<br/><a NAME="E4:70_1"/><i><font color="Green" title="E58">A4</font></i>: 
<font color="Maroon" title="c3">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="nattra_1.html#E1:70_1"><i><font color="Green" title="E56">A2</font></i></a>, <a class="ref" href="cat_1.html#T123" title="CAT_1:th.123">CAT_1:123</a></i>;<br/><a NAME="E5:70_1"/>
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="nattra_1.html#E1:70_1"><i><font color="Green" title="E56">A2</font></i></a>, <a class="ref" href="cat_1.html#T123" title="CAT_1:th.123">CAT_1:123</a></i>;<br/><a NAME="E6:70_1"/><b>then </b>
<font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">m</font></span>)</span>
 <b>by </b><i><a class="ref" href="nattra_1.html#T45" target="_self" title="NATTRA_1:th.45">Th45</a></i>;<br/><a NAME="E7:70_1"/><b>then </b>
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="nattra_1.html#T44" target="_self" title="NATTRA_1:th.44">Th44</a></i>;<br/><a NAME="E8:70_1"/><b>then </b><i><font color="Green" title="E59">A5</font></i>: 
<font color="Maroon" title="c3">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="nattra_1.html#E4:70_1"><i><font color="Green" title="E58">A4</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E9:70_1"/><i><font color="Green" title="E60">A6</font></i>: 
<font color="Maroon" title="c4">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="nattra_1.html#E1:70_1"><i><font color="Green" title="E56">A2</font></i></a>, <a class="ref" href="cat_1.html#T123" title="CAT_1:th.123">CAT_1:123</a></i>;<br/><a NAME="E10:70_1"/>
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="nattra_1.html#E1:70_1"><i><font color="Green" title="E56">A2</font></i></a>, <a class="ref" href="cat_1.html#T123" title="CAT_1:th.123">CAT_1:123</a></i>;<br/><a NAME="E11:70_1"/><b>then </b>
<font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">m</font></span>)</span>
 <b>by </b><i><a class="ref" href="nattra_1.html#T45" target="_self" title="NATTRA_1:th.45">Th45</a></i>;<br/><a NAME="E12:70_1"/><b>then </b>
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="nattra_1.html#T44" target="_self" title="NATTRA_1:th.44">Th44</a></i>;<br/><b>hence </b><a NAME="E13:70_1"/>
<font color="Maroon" title="c3">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">m</font>
 <b>by </b><i><a class="txt" href="nattra_1.html#E3:70_1"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="nattra_1.html#E8:70_1"><i><font color="Green" title="E59">A5</font></i></a>, <a class="txt" href="nattra_1.html#E9:70_1"><i><font color="Green" title="E60">A6</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:70"/>
<font color="Maroon" title="c3">F1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">F2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


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