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<b>set </b><font color="Maroon" title="c4">X</font> =  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c2">a</font>;<br/>
<b>set </b><font color="Maroon" title="c5">Y</font> =  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c2">a</font>;<br/>
<b>let </b><font color="Maroon" title="c6">h1</font>, <font color="Maroon" title="c7">h2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c2">a</font>, <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c3">f</font></span>)</span>,<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"> ( ( for <font color="Olive" title="b1">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c2">a</font> holds <br/><font color="Maroon" title="c6">h1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font> ) &amp; ( for <font color="Olive" title="b1">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c2">a</font> holds <br/><font color="Maroon" title="c7">h2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font> ) implies <font color="Maroon" title="c6">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">h2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:61_2_2"/><i><font color="Green" title="E35">A12</font></i>: 
for <font color="Olive" title="b1">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c2">a</font> holds <br/><font color="Maroon" title="c6">h1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font>
 <b>and </b><br/><a NAME="E2:61_2_2"/><i><font color="Green" title="E36">A13</font></i>: 
for <font color="Olive" title="b1">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c2">a</font> holds <br/><font color="Maroon" title="c7">h2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">h2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_2_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_2_2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c6">h1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">h2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> )</span><br/><b>assume </b><a NAME="E1:61_2_2_1_1"/><i><font color="Green" title="E37">A14</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font></span>)</span>,<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"> <font color="Maroon" title="c6">h1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">h2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/><b>then reconsider </b><font color="Maroon" title="c9">g</font> = <font color="Maroon" title="c8">x</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> ;<br/><b>thus </b><font color="Maroon" title="c6">h1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> = 
<font color="Maroon" title="c9">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font>
<b>by </b><i><a class="txt" href="ens_1.html#E1:61_2_2"><i><font color="Green" title="E35">A12</font></i></a>, <a class="txt" href="ens_1.html#E1:61_2_2_1_1"><i><font color="Green" title="E37">A14</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c7">h2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
<b>by </b><i><a class="txt" href="ens_1.html#E2:61_2_2"><i><font color="Green" title="E36">A13</font></i></a>, <a class="txt" href="ens_1.html#E1:61_2_2_1_1"><i><font color="Green" title="E37">A14</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="E2:61_2_2_1"/>
<font color="Maroon" title="c6">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">h2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18" title="FUNCT_2:th.18">FUNCT_2:18</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="E4:61_2_2"/>
<font color="Maroon" title="c6">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">h2</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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