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<span class="kw">let </span><font color="Maroon" title="c1">N</font> be   <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>; <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">  for <font color="Olive" title="b1">P</font> being   <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> holds <br/> ( <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c1">N</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> <span class="p3">(<span class="default"><font color="Maroon" title="c1">N</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> <font color="Olive" title="b1">P</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">P</font> &amp; <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="c1">N</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="c1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">P</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">P</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">P</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"> ( <span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c1">N</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> <span class="p3">(<span class="default"><font color="Maroon" title="c1">N</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> <font color="Maroon" title="c2">P</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font> &amp; <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="c1">N</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="c1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">P</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font> )</span><br/>



<a NAME="E1:22"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
<font color="Maroon" title="c1">N</font> <a href="matrix_6.html#K1" title="MATRIX_6:func.1">~</a>  <a href="matrix_6.html#R2" title="MATRIX_6:pred.2">is_reverse_of</a> <font color="Maroon" title="c1">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_6.html#D4" onmouseover="rs('matrix_6/D4')" onmouseout="rh()">MATRIX_6:def 4</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c1">N</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> <span class="p3">(<span class="default"><font color="Maroon" title="c1">N</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> <font color="Maroon" title="c2">P</font></span>)</span> = 
<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="c1">N</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">N</font> <a href="matrix_6.html#K1" title="MATRIX_6:func.1">~</a></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">P</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>
<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"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>,3)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">P</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="matrix_6.html#D2" onmouseover="rs('matrix_6/D2')" onmouseout="rh()">MATRIX_6:def 2</a></span>
<br/>.= 
<font color="Maroon" title="c2">P</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_9.html#T14" target="_self" onmouseover="rs('anproj_9/T14')" onmouseout="rh()">Th15</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> <span class="p2">(<span class="default"><font color="Maroon" title="c1">N</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="c1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">P</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font></span><br/>

<span class="kw">thus </span><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="c1">N</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="c1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">P</font></span>)</span> = 
<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"><span class="p3">(<span class="default"><font color="Maroon" title="c1">N</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="c1">N</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">P</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>
<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"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>,3)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">P</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="matrix_6.html#D2" onmouseover="rs('matrix_6/D2')" onmouseout="rh()">MATRIX_6:def 2</a></span>
<br/>.= 
<font color="Maroon" title="c2">P</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_9.html#T14" target="_self" onmouseover="rs('anproj_9/T14')" onmouseout="rh()">Th15</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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