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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>, <font color="Maroon" title="c8">Q1</font>, <font color="Maroon" title="c9">Q2</font>, <font color="Maroon" title="c10">Q3</font>, <font color="Maroon" title="c11">Q4</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>  &amp;  not <font color="Maroon" title="c8">Q1</font>,<font color="Maroon" title="c9">Q2</font>,<font color="Maroon" title="c10">Q3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp;  not <font color="Maroon" title="c8">Q1</font>,<font color="Maroon" title="c9">Q2</font>,<font color="Maroon" title="c11">Q4</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp;  not <font color="Maroon" title="c8">Q1</font>,<font color="Maroon" title="c10">Q3</font>,<font color="Maroon" title="c11">Q4</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp;  not <font color="Maroon" title="c9">Q2</font>,<font color="Maroon" title="c10">Q3</font>,<font color="Maroon" title="c11">Q4</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> <font color="Maroon" title="c8">Q1</font> &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> <font color="Maroon" title="c9">Q2</font> &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> <font color="Maroon" title="c10">Q3</font> &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> <font color="Maroon" title="c11">Q4</font> ) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:50"/><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>  &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>  )
 <span class="kw">and </span><br/><a NAME="E2:50"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
(  not <font color="Maroon" title="c8">Q1</font>,<font color="Maroon" title="c9">Q2</font>,<font color="Maroon" title="c10">Q3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp;  not <font color="Maroon" title="c8">Q1</font>,<font color="Maroon" title="c9">Q2</font>,<font color="Maroon" title="c11">Q4</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp;  not <font color="Maroon" title="c8">Q1</font>,<font color="Maroon" title="c10">Q3</font>,<font color="Maroon" title="c11">Q4</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp;  not <font color="Maroon" title="c9">Q2</font>,<font color="Maroon" title="c10">Q3</font>,<font color="Maroon" title="c11">Q4</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> <font color="Maroon" title="c8">Q1</font> &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> <font color="Maroon" title="c9">Q2</font> &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> <font color="Maroon" title="c10">Q3</font> &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> <font color="Maroon" title="c11">Q4</font> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c12">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="E4:50"/><span class="lab"><font color="Green" title="E39">A3</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="c12">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>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c12">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>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c12">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>  &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c12">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="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="#E1:50"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="anproj_9.html#T30" target="_self" onmouseover="rs('anproj_9/T30')" onmouseout="rh()">Th26</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c13">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><span class="kw"> such that </span><br/><a NAME="E6:50"/><span class="lab"><font color="Green" title="E40">A4</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="c13">N2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">Q1</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="c13">N2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">Q2</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="c13">N2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">Q3</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="c13">N2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">Q4</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="ref" href="anproj_9.html#T30" target="_self" onmouseover="rs('anproj_9/T30')" onmouseout="rh()">Th26</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">N</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c13">N2</font> <a href="matrix_6.html#K1" title="MATRIX_6:func.1">~</a></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c12">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="c14">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="c14">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> <font color="Maroon" title="c8">Q1</font> &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c14">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> <font color="Maroon" title="c9">Q2</font> &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c14">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> <font color="Maroon" title="c10">Q3</font> &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c14">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> <font color="Maroon" title="c11">Q4</font> )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c8">Q1</font> = 
<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="c13">N2</font> <a href="matrix_6.html#K1" title="MATRIX_6:func.1">~</a></span>)</span></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="c12">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="#E4:50"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="txt" href="#E6:50"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="ref" href="anproj_9.html#T15" target="_self" onmouseover="rs('anproj_9/T15')" onmouseout="rh()">Th16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c14">N</font></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"> ( <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c14">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> <font color="Maroon" title="c9">Q2</font> &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c14">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> <font color="Maroon" title="c10">Q3</font> &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c14">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> <font color="Maroon" title="c11">Q4</font> )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c9">Q2</font> = 
<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="c13">N2</font> <a href="matrix_6.html#K1" title="MATRIX_6:func.1">~</a></span>)</span></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="c12">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="#E4:50"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="txt" href="#E6:50"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="ref" href="anproj_9.html#T15" target="_self" onmouseover="rs('anproj_9/T15')" onmouseout="rh()">Th16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c14">N</font></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"> ( <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c14">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> <font color="Maroon" title="c10">Q3</font> &amp; <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c14">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> <font color="Maroon" title="c11">Q4</font> )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c10">Q3</font> = 
<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="c13">N2</font> <a href="matrix_6.html#K1" title="MATRIX_6:func.1">~</a></span>)</span></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="c12">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="#E4:50"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="txt" href="#E6:50"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="ref" href="anproj_9.html#T15" target="_self" onmouseover="rs('anproj_9/T15')" onmouseout="rh()">Th16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c14">N</font></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"> <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c14">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> <font color="Maroon" title="c11">Q4</font></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c11">Q4</font> = 
<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="c13">N2</font> <a href="matrix_6.html#K1" title="MATRIX_6:func.1">~</a></span>)</span></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="c12">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="#E4:50"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="txt" href="#E6:50"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="ref" href="anproj_9.html#T15" target="_self" onmouseover="rs('anproj_9/T15')" onmouseout="rh()">Th16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c14">N</font></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/>


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