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<span class="kw">let </span><font color="Maroon" title="c4">P1</font>, <font color="Maroon" title="c5">P2</font>, <font color="Maroon" title="c6">P3</font>, <font color="Maroon" title="c7">P4</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3</span>)</span></span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">P1</font>,<font color="Maroon" title="c5">P2</font>,<font color="Maroon" title="c6">P3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp;  not <font color="Maroon" title="c4">P1</font>,<font color="Maroon" title="c5">P2</font>,<font color="Maroon" title="c7">P4</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp;  not <font color="Maroon" title="c4">P1</font>,<font color="Maroon" title="c6">P3</font>,<font color="Maroon" title="c7">P4</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp;  not <font color="Maroon" title="c5">P2</font>,<font color="Maroon" title="c6">P3</font>,<font color="Maroon" title="c7">P4</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  implies  ex <font color="Olive" title="b1">N</font> being   <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of 3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> st <br/>( <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K5" title="ANPROJ_9:func.5">Dir100</a>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K6" title="ANPROJ_9:func.6">Dir010</a>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">P3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K7" title="ANPROJ_9:func.7">Dir001</a>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K8" title="ANPROJ_9:func.8">Dir111</a>  ) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:49"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
 not <font color="Maroon" title="c4">P1</font>,<font color="Maroon" title="c5">P2</font>,<font color="Maroon" title="c6">P3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E2:49"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
 not <font color="Maroon" title="c4">P1</font>,<font color="Maroon" title="c5">P2</font>,<font color="Maroon" title="c7">P4</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E3:49"/><span class="lab"><font color="Green" title="E39">A3</font></span>: 
 not <font color="Maroon" title="c4">P1</font>,<font color="Maroon" title="c6">P3</font>,<font color="Maroon" title="c7">P4</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E4:49"/><span class="lab"><font color="Green" title="E40">A4</font></span>: 
 not <font color="Maroon" title="c5">P2</font>,<font color="Maroon" title="c6">P3</font>,<font color="Maroon" title="c7">P4</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">N</font> being   <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of 3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> st <br/>( <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K5" title="ANPROJ_9:func.5">Dir100</a>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K6" title="ANPROJ_9:func.6">Dir010</a>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">P3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K7" title="ANPROJ_9:func.7">Dir001</a>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K8" title="ANPROJ_9:func.8">Dir111</a>  )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c8">N1</font> being   <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of 3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a><span class="kw"> such that </span><br/><a NAME="E6:49"/><span class="lab"><font color="Green" title="E41">A5</font></span>: 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K5" title="ANPROJ_9:func.5">Dir100</a> 
 <span class="kw">and </span><br/><a NAME="E7:49"/><span class="lab"><font color="Green" title="E42">A6</font></span>: 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K6" title="ANPROJ_9:func.6">Dir010</a> 
 <span class="kw">and </span><br/><a NAME="E8:49"/><span class="lab"><font color="Green" title="E43">A7</font></span>: 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">P3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K7" title="ANPROJ_9:func.7">Dir001</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="anproj_9.html#T24" target="_self" onmouseover="rs('anproj_9/T24')" onmouseout="rh()">Th20</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">Q1</font> = <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">Q2</font> = <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">P2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">Q3</font> = <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">P3</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">Q4</font> = <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font>;<br/>
<a NAME="E9:49"/>
(  not <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P1</font>,<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">P2</font>,<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">P3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp;  not <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P1</font>,<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">P2</font>,<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp;  not <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P1</font>,<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">P3</font>,<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp;  not <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">P2</font>,<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">P3</font>,<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="txt" href="#E2:49"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="txt" href="#E3:49"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="txt" href="#E4:49"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="ref" href="anproj_8.html#T102" onmouseover="rs('anproj_8/T102')" onmouseout="rh()">ANPROJ_8:102</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">a</font>, <font color="Maroon" title="c14">b</font>, <font color="Maroon" title="c15">c</font> being   non  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a><span class="kw"> such that </span><br/><a NAME="E11:49"/><span class="lab"><font color="Green" title="E44">A8</font></span>: 
 for <font color="Olive" title="b1">N2</font> being   <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of 3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st <font color="Olive" title="b1">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c13">a</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c14">b</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c15">c</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> holds <br/><span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Olive" title="b1">N2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K8" title="ANPROJ_9:func.8">Dir111</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:49"><span class="lab"><font color="Green" title="E41">A5</font></span></a>, <a class="txt" href="#E7:49"><span class="lab"><font color="Green" title="E42">A6</font></span></a>, <a class="txt" href="#E8:49"><span class="lab"><font color="Green" title="E43">A7</font></span></a>, <a class="ref" href="anproj_9.html#T29" target="_self" onmouseover="rs('anproj_9/T29')" onmouseout="rh()">Th25</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">N2</font> = <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c13">a</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c14">b</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c15">c</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> as   <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of 3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_9.html#T9" target="_self" onmouseover="rs('anproj_9/T9')" onmouseout="rh()">Th10</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">N</font> = <font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font> as   <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of 3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c17">N</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c17">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K5" title="ANPROJ_9:func.5">Dir100</a>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c17">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K6" title="ANPROJ_9:func.6">Dir010</a>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c17">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">P3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K7" title="ANPROJ_9:func.7">Dir001</a>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c17">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K8" title="ANPROJ_9:func.8">Dir111</a>  )</span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="49_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="anproj_9.html#K5" title="ANPROJ_9:func.5">Dir100</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P1</font> &amp;  <a href="anproj_9.html#K6" title="ANPROJ_9:func.6">Dir010</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">P2</font> &amp;  <a href="anproj_9.html#K7" title="ANPROJ_9:func.7">Dir001</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">P3</font> &amp;  <a href="anproj_9.html#K8" title="ANPROJ_9:func.8">Dir111</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font> )</span></a><div class="add"><span class="kw">thus </span> <a href="anproj_9.html#K5" title="ANPROJ_9:func.5">Dir100</a>  = 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c16">N2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:49"><span class="lab"><font color="Green" title="E41">A5</font></span></a>, <a class="ref" href="anproj_9.html#T25" target="_self" onmouseover="rs('anproj_9/T25')" onmouseout="rh()">Th21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_9.html#T13" target="_self" onmouseover="rs('anproj_9/T13')" onmouseout="rh()">Th14</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="anproj_9.html#K6" title="ANPROJ_9:func.6">Dir010</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">P2</font> &amp;  <a href="anproj_9.html#K7" title="ANPROJ_9:func.7">Dir001</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">P3</font> &amp;  <a href="anproj_9.html#K8" title="ANPROJ_9:func.8">Dir111</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font> )</span><br/><span class="kw">thus </span> <a href="anproj_9.html#K6" title="ANPROJ_9:func.6">Dir010</a>  = 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c16">N2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">P2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:49"><span class="lab"><font color="Green" title="E42">A6</font></span></a>, <a class="ref" href="anproj_9.html#T25" target="_self" onmouseover="rs('anproj_9/T25')" onmouseout="rh()">Th21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">P2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_9.html#T13" target="_self" onmouseover="rs('anproj_9/T13')" onmouseout="rh()">Th14</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="anproj_9.html#K7" title="ANPROJ_9:func.7">Dir001</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">P3</font> &amp;  <a href="anproj_9.html#K8" title="ANPROJ_9:func.8">Dir111</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font> )</span><br/><span class="kw">thus </span> <a href="anproj_9.html#K7" title="ANPROJ_9:func.7">Dir001</a>  = 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c16">N2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">P3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:49"><span class="lab"><font color="Green" title="E43">A7</font></span></a>, <a class="ref" href="anproj_9.html#T25" target="_self" onmouseover="rs('anproj_9/T25')" onmouseout="rh()">Th21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">P3</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_9.html#T13" target="_self" onmouseover="rs('anproj_9/T13')" onmouseout="rh()">Th14</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="anproj_9.html#K8" title="ANPROJ_9:func.8">Dir111</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font></span><br/><span class="kw">thus </span> <a href="anproj_9.html#K8" title="ANPROJ_9:func.8">Dir111</a>  = 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c16">N2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c8">N1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:49"><span class="lab"><font color="Green" title="E44">A8</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">N2</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c8">N1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_9.html#T13" target="_self" onmouseover="rs('anproj_9/T13')" onmouseout="rh()">Th14</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="E15:49"/>
( <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c17">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K5" title="ANPROJ_9:func.5">Dir100</a>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c17">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K6" title="ANPROJ_9:func.6">Dir010</a>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c17">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">P3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K7" title="ANPROJ_9:func.7">Dir001</a>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c17">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">P4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_9.html#K8" title="ANPROJ_9:func.8">Dir111</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
