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<b>let </b><font color="Maroon" title="c1">AFP</font> be   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a>; <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">a</font>, <font color="Olive" title="b2">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font><br/> for <font color="Olive" title="b3">K</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AFP</font>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Olive" title="b3">K</font> &amp; not <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">K</font> holds <br/> ex <font color="Olive" title="b4">f</font> being  <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">AFP</font> st <br/>( <font color="Olive" title="b4">f</font> <a href="homothet.html#R1" title="HOMOTHET:pred.1">is_Sc</a> <font color="Olive" title="b3">K</font> &amp; <font color="Olive" title="b4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> ) ) implies <font color="Maroon" title="c1">AFP</font> <a href="aff_2.html#NR7" title="AFF_2:NR.7">satisfies_TDES</a>  )</span><br/>

<b>assume </b><a NAME="E1:23"/><i><font color="Green" title="E24">A1</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font><br/> for <font color="Olive" title="b3">K</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AFP</font>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Olive" title="b3">K</font> &amp; not <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">K</font> holds <br/> ex <font color="Olive" title="b4">f</font> being  <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">AFP</font> st <br/>( <font color="Olive" title="b4">f</font> <a href="homothet.html#R1" title="HOMOTHET:pred.1">is_Sc</a> <font color="Olive" title="b3">K</font> &amp; <font color="Olive" title="b4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">AFP</font> <a href="aff_2.html#NR7" title="AFF_2:NR.7">satisfies_TDES</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">o</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</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">K</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AFP</font><br/> for <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">c'</font>, <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font>, <font color="Olive" title="b6">a'</font>, <font color="Olive" title="b7">b'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font>  st <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Olive" title="b2">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Olive" title="b3">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Olive" title="b1">K</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b4">a</font>,<font color="Olive" title="b6">a'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b5">b</font>,<font color="Olive" title="b7">b'</font> &amp; not <font color="Olive" title="b4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Olive" title="b1">K</font> &amp; <font color="Olive" title="b6">a'</font>,<font color="Olive" title="b7">b'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Olive" title="b1">K</font> &amp; <font color="Olive" title="b4">a</font>,<font color="Olive" title="b2">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">a'</font>,<font color="Olive" title="b3">c'</font> holds <br/><font color="Olive" title="b5">b</font>,<font color="Olive" title="b2">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b7">b'</font>,<font color="Olive" title="b3">c'</font></span><br/><b>let </b><font color="Maroon" title="c3">K</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AFP</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">c</font>, <font color="Olive" title="b2">c'</font>, <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">a'</font>, <font color="Olive" title="b6">b'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font>  st <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Olive" title="b1">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Olive" title="b2">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c3">K</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b5">a'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b6">b'</font> &amp; not <font color="Olive" title="b3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Olive" title="b5">a'</font>,<font color="Olive" title="b6">b'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a'</font>,<font color="Olive" title="b2">c'</font> holds <br/><font color="Olive" title="b4">b</font>,<font color="Olive" title="b1">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">b'</font>,<font color="Olive" title="b2">c'</font></span><br/><b>let </b><font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">c'</font>, <font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font>, <font color="Maroon" title="c8">a'</font>, <font color="Maroon" title="c9">b'</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c5">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c3">K</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">a'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">b'</font> &amp; not <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c9">b'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c5">c'</font> implies <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c5">c'</font> )</span><br/><b>assume </b><a NAME="E1:23_1"/><i><font color="Green" title="E25">A2</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c5">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c3">K</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">a'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">b'</font> &amp; not <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c9">b'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c5">c'</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c5">c'</font></span><br/><b>then consider </b><font color="Maroon" title="c10">f</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">AFP</font><b> such that </b><br/><a NAME="E3:23_1"/><i><font color="Green" title="E26">A3</font></i>: 
( <font color="Maroon" title="c10">f</font> <a href="homothet.html#R1" title="HOMOTHET:pred.1">is_Sc</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> )
 <b>by </b><i><a class="txt" href="homothet.html#E1:23"><i><font color="Green" title="E24">A1</font></i></a></i>;<br/><a NAME="E4:23_1"/><i><font color="Green" title="E27">A4</font></i>: 
<font color="Maroon" title="c10">f</font> <a href="transgeo.html#NR10" title="TRANSGEO:NR.10">is_Col</a> 
 <b>by </b><i><a class="txt" href="homothet.html#E3:23_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="homothet.html#D1" target="_self" title="HOMOTHET:def.1">Def1</a></i>;<br/><a NAME="E5:23_1"/><i><font color="Green" title="E28">A5</font></i>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c9">b'</font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:23_1"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></i>;<br/><a NAME="E6:23_1"/><i><font color="Green" title="E29">A6</font></i>: 
( <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c'</font> )
 <b>by </b><i><a class="txt" href="homothet.html#E1:23_1"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="homothet.html#E3:23_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="homothet.html#D1" target="_self" title="HOMOTHET:def.1">Def1</a></i>;<br/><a NAME="E7:23_1"/>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c11">x</font> = <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a'</font>;<br/>
<div><i><font color="Green" title="E30">A7</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:23_1_1_1"/><i><font color="Green" title="E31">A8</font></i>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</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">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b'</font></span><br/><a NAME="E2:23_1_1_1"/>
<font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">K</font>
 <b>by </b><i><a class="txt" href="homothet.html#E3:23_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="homothet.html#D1" target="_self" title="HOMOTHET:def.1">Def1</a></i>;<br/><a NAME="E3:23_1_1_1"/><b>then </b><i><font color="Green" title="E32">A9</font></i>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a'</font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:23_1"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></i>;<br/><a NAME="E4:23_1_1_1"/>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:23_1"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="homothet.html#E3:23_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="homothet.html#D1" target="_self" title="HOMOTHET:def.1">Def1</a></i>;<br/><a NAME="E5:23_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a'</font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:23_1"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="homothet.html#E3:23_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="homothet.html#E4:23_1"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="transgeo.html#T108" title="TRANSGEO:th.108">TRANSGEO:108</a></i>;<br/><b>hence </b><a NAME="E6:23_1_1_1"/>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b'</font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:23_1"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="homothet.html#E5:23_1"><i><font color="Green" title="E28">A5</font></i></a>, <a class="txt" href="homothet.html#E1:23_1_1_1"><i><font color="Green" title="E31">A8</font></i></a>, <a class="txt" href="homothet.html#E3:23_1_1_1"><i><font color="Green" title="E32">A9</font></i></a>, <a class="ref" href="aff_1.html#T60" title="AFF_1:th.60">AFF_1:60</a>, <a class="ref" href="aff_1.html#T70" title="AFF_1:th.70">AFF_1:70</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>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:23_1_1_2"/><i><font color="Green" title="E31">A10</font></i>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</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">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b'</font></span><br/><a NAME="E2:23_1_1_2"/><b>then </b>
<font color="Maroon" title="c10">f</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">AFP</font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:23_1"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="homothet.html#E3:23_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="homothet.html#T5" target="_self" title="HOMOTHET:th.5">Th5</a></i>;<br/><a NAME="E3:23_1_1_2"/><b>then </b>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">a'</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>;<br/><b>hence </b><a NAME="E4:23_1_1_2"/>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b'</font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:23_1"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="homothet.html#E1:23_1_1_2"><i><font color="Green" title="E31">A10</font></i></a>, <a class="ref" href="aff_1.html#T61" title="AFF_1:th.61">AFF_1:61</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="E3:23_1_1"/>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b'</font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:23_1_1"><i><font color="Green" title="E30">A7</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="E8:23_1"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c5">c'</font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:23_1"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="homothet.html#E3:23_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="homothet.html#E4:23_1"><i><font color="Green" title="E27">A4</font></i></a>, <a class="txt" href="homothet.html#E6:23_1"><i><font color="Green" title="E29">A6</font></i></a>, <a class="ref" href="transgeo.html#T107" title="TRANSGEO:th.107">TRANSGEO:107</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="E3:23"/>
<font color="Maroon" title="c1">AFP</font> <a href="aff_2.html#NR7" title="AFF_2:NR.7">satisfies_TDES</a> 
 <b>by </b><i><a class="txt" href="homothet.html#E2"><i><font color="Green" title="E2">Lm2</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>
