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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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">p</font>, <font color="Olive" title="b5">p9</font>, <font color="Olive" title="b6">y</font>, <font color="Olive" title="b7">q</font>, <font color="Olive" title="b8">q9</font>, <font color="Olive" title="b9">s</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="b10">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="b10">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="b10">K</font> &amp; not <font color="Olive" title="b3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">K</font> &amp; <font color="Maroon" title="c1">AFP</font> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a>  &amp; <font color="Olive" title="b4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">K</font> &amp; <font color="Olive" title="b5">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">K</font> &amp; <font color="Olive" title="b4">p</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">p9</font>,<font color="Olive" title="b3">x</font> &amp; <font color="Olive" title="b4">p</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">p9</font>,<font color="Olive" title="b6">y</font> &amp; <font color="Olive" title="b3">x</font>,<font color="Olive" title="b6">y</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Olive" title="b10">K</font> &amp; <font color="Olive" title="b7">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">K</font> &amp; <font color="Olive" title="b8">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">K</font> &amp; <font color="Olive" title="b7">q</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b8">q9</font>,<font color="Olive" title="b3">x</font> &amp; <font color="Olive" title="b3">x</font>,<font color="Olive" title="b9">s</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Olive" title="b10">K</font> &amp; <font color="Olive" title="b7">q</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b8">q9</font>,<font color="Olive" title="b9">s</font> holds <br/><font color="Olive" title="b9">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">p</font>, <font color="Maroon" title="c6">p9</font>, <font color="Maroon" title="c7">y</font>, <font color="Maroon" title="c8">q</font>, <font color="Maroon" title="c9">q9</font>, <font color="Maroon" title="c10">s</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="Red">::  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>  st <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Olive" title="b1">K</font> &amp; not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c1">AFP</font> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a>  &amp; <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c6">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c7">y</font> &amp; <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c9">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c10">s</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c10">s</font> holds <br/><font color="Maroon" title="c10">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c11">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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c11">K</font> &amp; not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">K</font> &amp; not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c1">AFP</font> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a>  &amp; <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c6">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c7">y</font> &amp; <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c9">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c10">s</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c10">s</font> implies <font color="Maroon" title="c10">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">y</font> )</span><br/>





















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:29"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c11">K</font>
 <span class="kw">and </span><br/><a NAME="E2:29"/><span class="lab"><font color="Green" title="E31">A2</font></span>: 
not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">K</font>
 <span class="kw">and </span><br/><a NAME="E3:29"/><span class="lab"><font color="Green" title="E32">A3</font></span>: 
not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">K</font>
 <span class="kw">and </span><br/><a NAME="E4:29"/><span class="lab"><font color="Green" title="E33">A4</font></span>: 
<font color="Maroon" title="c1">AFP</font> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a> 
 <span class="kw">and </span><br/><a NAME="E5:29"/><span class="lab"><font color="Green" title="E34">A5</font></span>: 
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">K</font>
 <span class="kw">and </span><br/><a NAME="E6:29"/><span class="lab"><font color="Green" title="E35">A6</font></span>: 
<font color="Maroon" title="c6">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">K</font>
 <span class="kw">and </span><br/><a NAME="E7:29"/><span class="lab"><font color="Green" title="E36">A7</font></span>: 
<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c4">x</font>
 <span class="kw">and </span><br/><a NAME="E8:29"/><span class="lab"><font color="Green" title="E37">A8</font></span>: 
<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c7">y</font>
 <span class="kw">and </span><br/><a NAME="E9:29"/><span class="lab"><font color="Green" title="E38">A9</font></span>: 
<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c11">K</font>
 <span class="kw">and </span><br/><a NAME="E10:29"/><span class="lab"><font color="Green" title="E39">A10</font></span>: 
<font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">K</font>
 <span class="kw">and </span><br/><a NAME="E11:29"/><span class="lab"><font color="Green" title="E40">A11</font></span>: 
<font color="Maroon" title="c9">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">K</font>
 <span class="kw">and </span><br/><a NAME="E12:29"/><span class="lab"><font color="Green" title="E41">A12</font></span>: 
<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c4">x</font>
 <span class="kw">and </span><br/><a NAME="E13:29"/><span class="lab"><font color="Green" title="E42">A13</font></span>: 
<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c10">s</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c11">K</font>
 <span class="kw">and </span><br/><a NAME="E14:29"/><span class="lab"><font color="Green" title="E43">A14</font></span>: 
<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c10">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">y</font></span><br/>

<a NAME="E15:29"/><span class="lab"><font color="Green" title="E44">A15</font></span>: 
not <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="ref" href="aff_1.html#T49" title="AFF_1:th.49">AFF_1:49</a></span>;<br/>
<a NAME="E16:29"/>
<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c7">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="txt" href="#E3:29"><span class="lab"><font color="Green" title="E32">A3</font></span></a>, <a class="txt" href="#E4:29"><span class="lab"><font color="Green" title="E33">A4</font></span></a>, <a class="txt" href="#E5:29"><span class="lab"><font color="Green" title="E34">A5</font></span></a>, <a class="txt" href="#E6:29"><span class="lab"><font color="Green" title="E35">A6</font></span></a>, <a class="txt" href="#E7:29"><span class="lab"><font color="Green" title="E36">A7</font></span></a>, <a class="txt" href="#E8:29"><span class="lab"><font color="Green" title="E37">A8</font></span></a>, <a class="txt" href="#E9:29"><span class="lab"><font color="Green" title="E38">A9</font></span></a>, <a class="txt" href="#E10:29"><span class="lab"><font color="Green" title="E39">A10</font></span></a>, <a class="txt" href="#E11:29"><span class="lab"><font color="Green" title="E40">A11</font></span></a>, <a class="txt" href="#E12:29"><span class="lab"><font color="Green" title="E41">A12</font></span></a>, <a class="txt" href="homothet.html#E29"><span class="lab"><font color="Green" title="E28">Lm21</font></span></a></span>;<br/>
<a NAME="E17:29"/><span class="kw">then </span>
<font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c10">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c7">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:29"><span class="lab"><font color="Green" title="E39">A10</font></span></a>, <a class="txt" href="#E14:29"><span class="lab"><font color="Green" title="E43">A14</font></span></a>, <a class="txt" href="#E15:29"><span class="lab"><font color="Green" title="E44">A15</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/>
<a NAME="E18:29"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c7">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E19:29"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A16</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c9">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">assume </span><a NAME="E20:29"/><span class="lab"><font color="Green" title="E46">A17</font></span>: 
not <font color="Maroon" title="c10">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c12">M</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AFP</font><span class="kw"> such that </span><br/><a NAME="E22:29"/><span class="lab"><font color="Green" title="E47">A18</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M</font>
 <span class="kw">and </span><br/><a NAME="E23:29"/><span class="lab"><font color="Green" title="E48">A19</font></span>: 
<font color="Maroon" title="c11">K</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a>, <a class="ref" href="aff_1.html#T63" title="AFF_1:th.63">AFF_1:63</a></span>;<br/>
<a NAME="E24:29"/><span class="lab"><font color="Green" title="E49">A20</font></span>: 
<font color="Maroon" title="c12">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:29"><span class="lab"><font color="Green" title="E48">A19</font></span></a>, <a class="ref" href="aff_1.html#T50" title="AFF_1:th.50">AFF_1:50</a></span>;<br/>
<a NAME="E25:29"/>
<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c10">s</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:29"><span class="lab"><font color="Green" title="E42">A13</font></span></a>, <a class="txt" href="#E23:29"><span class="lab"><font color="Green" title="E48">A19</font></span></a>, <a class="ref" href="aff_1.html#T57" title="AFF_1:th.57">AFF_1:57</a></span>;<br/>
<a NAME="E26:29"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A21</font></span>: 
<font color="Maroon" title="c10">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:29"><span class="lab"><font color="Green" title="E47">A18</font></span></a>, <a class="txt" href="#E24:29"><span class="lab"><font color="Green" title="E49">A20</font></span></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></span>;<br/>
<a NAME="E27:29"/>
<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:29"><span class="lab"><font color="Green" title="E38">A9</font></span></a>, <a class="txt" href="#E23:29"><span class="lab"><font color="Green" title="E48">A19</font></span></a>, <a class="ref" href="aff_1.html#T57" title="AFF_1:th.57">AFF_1:57</a></span>;<br/>
<a NAME="E28:29"/><span class="kw">then </span>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:29"><span class="lab"><font color="Green" title="E47">A18</font></span></a>, <a class="txt" href="#E24:29"><span class="lab"><font color="Green" title="E49">A20</font></span></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></span>;<br/>
<a NAME="E29:29"/><span class="kw">then </span>
<font color="Maroon" title="c12">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c10">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:29"><span class="lab"><font color="Green" title="E46">A17</font></span></a>, <a class="txt" href="#E24:29"><span class="lab"><font color="Green" title="E49">A20</font></span></a>, <a class="txt" href="#E26:29"><span class="lab"><font color="Green" title="E50">A21</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E30:29"/><span class="kw">then </span>
<font color="Maroon" title="c9">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:29"><span class="lab"><font color="Green" title="E45">A16</font></span></a>, <a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E31:29"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:29"><span class="lab"><font color="Green" title="E32">A3</font></span></a>, <a class="txt" href="#E11:29"><span class="lab"><font color="Green" title="E40">A11</font></span></a>, <a class="txt" href="#E22:29"><span class="lab"><font color="Green" title="E47">A18</font></span></a>, <a class="txt" href="#E23:29"><span class="lab"><font color="Green" title="E48">A19</font></span></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
