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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">z</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="anproj_9.html#K1" title="ANPROJ_9:func.1">EnsHomography3</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="anproj_9.html#K2" title="ANPROJ_9:func.2">(*)</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="anproj_9.html#K2" title="ANPROJ_9:func.2">(*)</a> <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="anproj_9.html#K2" title="ANPROJ_9:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="anproj_9.html#K2" title="ANPROJ_9:func.2">(*)</a> <font color="Maroon" title="c3">z</font></span>)</span></span><br/>

<a NAME="E1:30"/>
<font color="Maroon" title="c1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="anproj_9.html#K1" title="ANPROJ_9:func.1">EnsHomography3</a> 
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">Nx</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="E3:30"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c4">Nx</font>
 ;<br/>
<a NAME="E4:30"/>
<font color="Maroon" title="c2">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="anproj_9.html#K1" title="ANPROJ_9:func.1">EnsHomography3</a> 
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">Ny</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="E6:30"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c5">Ny</font>
 ;<br/>
<a NAME="E7:30"/>
<font color="Maroon" title="c3">z</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="anproj_9.html#K1" title="ANPROJ_9:func.1">EnsHomography3</a> 
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">Nz</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="E9:30"/><span class="lab"><font color="Green" title="E27">A4</font></span>: 
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Maroon" title="c6">Nz</font>
 ;<br/>
<a NAME="E10:30"/><span class="lab"><font color="Green" title="E28">A5</font></span>: 
(  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c4">Nx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">Ny</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp;  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c5">Ny</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">Nz</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#T24" onmouseover="rs('matrix_0/T24')" onmouseout="rh()">MATRIX_0:24</a></span>;<br/>
<a NAME="E11:30"/>
<font color="Maroon" title="c2">y</font> <a href="anproj_9.html#K2" title="ANPROJ_9:func.2">(*)</a> <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Ny</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">Nz</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:30"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E9:30"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="anproj_9.html#T18" target="_self" onmouseover="rs('anproj_9/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E29">A6</font></span>: <font color="Maroon" title="c1">x</font> <a href="anproj_9.html#K2" title="ANPROJ_9:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="anproj_9.html#K2" title="ANPROJ_9:func.2">(*)</a> <font color="Maroon" title="c3">z</font></span>)</span> = 
 <a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Nx</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">Ny</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">Nz</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:30"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="anproj_9.html#T18" target="_self" onmouseover="rs('anproj_9/T18')" onmouseout="rh()">Th18</a></span>
<br/>.= 
 <a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">Nx</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c5">Ny</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">Nz</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:30"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="ref" href="matrix_3.html#T33" onmouseover="rs('matrix_3/T33')" onmouseout="rh()">MATRIX_3:33</a></span>
;<br/>
<a NAME="E13:30"/>
<font color="Maroon" title="c1">x</font> <a href="anproj_9.html#K2" title="ANPROJ_9:func.2">(*)</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Nx</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c5">Ny</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:30"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E6:30"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="ref" href="anproj_9.html#T18" target="_self" onmouseover="rs('anproj_9/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:30"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="anproj_9.html#K2" title="ANPROJ_9:func.2">(*)</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="anproj_9.html#K2" title="ANPROJ_9:func.2">(*)</a> <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="anproj_9.html#K2" title="ANPROJ_9:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="anproj_9.html#K2" title="ANPROJ_9:func.2">(*)</a> <font color="Maroon" title="c3">z</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:30"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E9:30"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="anproj_9.html#T18" target="_self" onmouseover="rs('anproj_9/T18')" onmouseout="rh()">Th18</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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