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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:23"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
 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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">AFP</font> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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">c9</font>, <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font>, <font color="Olive" title="b6">a9</font>, <font color="Olive" title="b7">b9</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">c9</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> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_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">a9</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">b9</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">a9</font>,<font color="Olive" title="b7">b9</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">a9</font>,<font color="Olive" title="b3">c9</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">b9</font>,<font color="Olive" title="b3">c9</font></span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">c</font>, <font color="Olive" title="b2">c9</font>, <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">a9</font>, <font color="Olive" title="b6">b9</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">c9</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> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_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">a9</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">b9</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">a9</font>,<font color="Olive" title="b6">b9</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">a9</font>,<font color="Olive" title="b2">c9</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">b9</font>,<font color="Olive" title="b2">c9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">c9</font>, <font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font>, <font color="Maroon" title="c8">a9</font>, <font color="Maroon" title="c9">b9</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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">c9</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> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_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">a9</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">b9</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">a9</font>,<font color="Maroon" title="c9">b9</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">a9</font>,<font color="Maroon" title="c5">c9</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">b9</font>,<font color="Maroon" title="c5">c9</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:23_1"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:23_1"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E3:23_1"/><span class="lab"><font color="Green" title="E27">A4</font></span>: 
<font color="Maroon" title="c5">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font>
 <span class="kw">and </span><br/><a NAME="E4:23_1"/><span class="lab"><font color="Green" title="E28">A5</font></span>: 
<font color="Maroon" title="c3">K</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E5:23_1"/><span class="lab"><font color="Green" title="E29">A6</font></span>: 
 <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">a9</font>
 <span class="kw">and </span><br/><a NAME="E6:23_1"/><span class="lab"><font color="Green" title="E30">A7</font></span>: 
 <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">b9</font>
 <span class="kw">and </span><br/><a NAME="E7:23_1"/><span class="lab"><font color="Green" title="E31">A8</font></span>: 
 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>
 <span class="kw">and </span><br/><a NAME="E8:23_1"/><span class="lab"><font color="Green" title="E32">A9</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E9:23_1"/><span class="lab"><font color="Green" title="E33">A10</font></span>: 
<font color="Maroon" title="c8">a9</font>,<font color="Maroon" title="c9">b9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">K</font>
 <span class="kw">and </span><br/><a NAME="E10:23_1"/><span class="lab"><font color="Green" title="E34">A11</font></span>: 
<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">a9</font>,<font color="Maroon" title="c5">c9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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">b9</font>,<font color="Maroon" title="c5">c9</font></span><br/><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E12:23_1"/><span class="lab"><font color="Green" title="E35">A12</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E13:23_1"/><span class="lab"><font color="Green" title="E36">A13</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E7:23_1"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E8:23_1"><span class="lab"><font color="Green" title="E32">A9</font></span></a></span>;<br/><a NAME="E14:23_1"/><span class="lab"><font color="Green" title="E37">A14</font></span>: 
<font color="Maroon" title="c10">f</font> is  <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:23_1"><span class="lab"><font color="Green" title="E35">A12</font></span></a>, <a class="ref" href="homothet.html#D1" target="_self" title="HOMOTHET:def.1">Def1</a></span>;<br/><a NAME="E15:23_1"/><span class="lab"><font color="Green" title="E38">A15</font></span>: 
<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">a9</font>,<font color="Maroon" title="c9">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:23_1"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E8:23_1"><span class="lab"><font color="Green" title="E32">A9</font></span></a>, <a class="txt" href="#E9:23_1"><span class="lab"><font color="Green" title="E33">A10</font></span></a>, <a class="ref" href="aff_1.html#T31" title="AFF_1:th.31">AFF_1:31</a></span>;<br/><a NAME="E16:23_1"/><span class="lab"><font color="Green" title="E39">A16</font></span>: 
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">set </span><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">a9</font>;<br/>
<div><span class="lab"><font color="Green" title="E40">A17</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:23_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23_1"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E12:23_1"><span class="lab"><font color="Green" title="E35">A12</font></span></a>, <a class="ref" href="homothet.html#D1" target="_self" title="HOMOTHET:def.1">Def1</a></span>;<br/><a NAME="E2:23_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A18</font></span>: 
 <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">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:23_1"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E13:23_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="txt" href="#E14:23_1"><span class="lab"><font color="Green" title="E37">A14</font></span></a>, <a class="ref" href="transgeo.html#T84" title="TRANSGEO:th.84">TRANSGEO:84</a></span>;<br/><a NAME="E3:23_1_1_1"/>
<font color="Maroon" title="c8">a9</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">a9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:23_1"><span class="lab"><font color="Green" title="E35">A12</font></span></a>, <a class="ref" href="homothet.html#D1" target="_self" title="HOMOTHET:def.1">Def1</a></span>;<br/><a NAME="E4:23_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A19</font></span>: 
<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">a9</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">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:23_1"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E8:23_1"><span class="lab"><font color="Green" title="E32">A9</font></span></a>, <a class="ref" href="aff_1.html#T31" title="AFF_1:th.31">AFF_1:31</a></span>;<br/><span class="kw">assume </span><a NAME="E5:23_1_1_1"/>
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b9</font></span><br/><span class="kw">hence </span><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">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23_1"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E5:23_1"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E6:23_1"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E7:23_1"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E8:23_1"><span class="lab"><font color="Green" title="E32">A9</font></span></a>, <a class="txt" href="#E15:23_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E4:23_1_1_1"><span class="lab"><font color="Green" title="E42">A19</font></span></a>, <a class="txt" href="#E2:23_1_1_1"><span class="lab"><font color="Green" title="E41">A18</font></span></a>, <a class="ref" href="aff_1.html#T46" title="AFF_1:th.46">AFF_1:46</a>, <a class="ref" href="aff_1.html#T56" title="AFF_1:th.56">AFF_1:56</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:23_1_1_2"/><span class="lab"><font color="Green" title="E41">A20</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b9</font></span><br/><a NAME="E2:23_1_1_2"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:23_1"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E12:23_1"><span class="lab"><font color="Green" title="E35">A12</font></span></a>, <a class="txt" href="#E13:23_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="ref" href="homothet.html#T5" target="_self" title="HOMOTHET:th.5">Th5</a></span>;<br/><a NAME="E3:23_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T18" title="FUNCT_1:th.18">FUNCT_1:18</a></span>;<br/><span class="kw">hence </span><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">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23_1"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E5:23_1"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E6:23_1"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E7:23_1"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E9:23_1"><span class="lab"><font color="Green" title="E33">A10</font></span></a>, <a class="txt" href="#E1:23_1_1_2"><span class="lab"><font color="Green" title="E41">A20</font></span></a>, <a class="ref" href="aff_1.html#T47" title="AFF_1:th.47">AFF_1:47</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><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">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23_1_1"><span class="lab"><font color="Green" title="E40">A17</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E17:23_1"/><span class="lab"><font color="Green" title="E40">A21</font></span>: 
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">c9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:23_1"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="txt" href="#E12:23_1"><span class="lab"><font color="Green" title="E35">A12</font></span></a>, <a class="ref" href="homothet.html#D1" target="_self" title="HOMOTHET:def.1">Def1</a></span>;<br/><a NAME="E18:23_1"/>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23_1"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E12:23_1"><span class="lab"><font color="Green" title="E35">A12</font></span></a>, <a class="ref" href="homothet.html#D1" target="_self" title="HOMOTHET:def.1">Def1</a></span>;<br/><span class="kw">hence </span><a NAME="E19:23_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">b9</font>,<font color="Maroon" title="c5">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:23_1"><span class="lab"><font color="Green" title="E34">A11</font></span></a>, <a class="txt" href="#E13:23_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="txt" href="#E14:23_1"><span class="lab"><font color="Green" title="E37">A14</font></span></a>, <a class="txt" href="#E17:23_1"><span class="lab"><font color="Green" title="E40">A21</font></span></a>, <a class="txt" href="#E16:23_1"><span class="lab"><font color="Green" title="E39">A16</font></span></a>, <a class="ref" href="transgeo.html#T83" title="TRANSGEO:th.83">TRANSGEO:83</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:23"/>
<font color="Maroon" title="c1">AFP</font> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="homothet.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
