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<a NAME="E1:52_1_1"/>
the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="cat_2.html#T33" title="CAT_2:th.33">CAT_2:33</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">t</font> = <span class="p1"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> ;<br/>
<a NAME="E3:52_1_1"/>
<font color="Maroon" title="c10">t</font> is    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span>,<span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:52_1_1_1"/>
<span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span>
 <b>by </b><i><a class="txt" href="#E1:52"><i><font color="Green" title="E43">A1</font></i></a>, <a class="ref" href="isocat_2.html#T44" target="_self" title="ISOCAT_2:th.44">Th44</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">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c10">t</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"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive">b<sub>1</sub></font>,<span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive">b<sub>1</sub></font></span><br/>

<b>let </b><font color="Maroon" title="c11">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="c10">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">a</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font>,<span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span><br/>

<a NAME="E2:52_1_1_1"/>
<font color="Maroon" title="c10">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:52"><i><font color="Green" title="E43">A1</font></i></a>, <a class="txt" href="isocat_2.html#E56"><i><font color="Green" title="E41">Lm3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:52_1_1_1"/>
<font color="Maroon" title="c10">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">a</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font>,<span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font>
 <b>by </b><i><a class="ref" href="cat_1.html#D7" title="CAT_1:def.7">CAT_1:def 7</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="E4:52_1_1"/>
<span class="p1"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span> is    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span>,<span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span>
 ; <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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