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<b>consider </b><font color="Maroon">V</font> being  non <a href="realset2.html#V3">trivial</a> <a href="rlvect_1.html#NM2">RealLinearSpace</a><b> such that </b><br/><a NAME="E2:101_2_1"/><i><font color="Green">E62</font></i>: 
 ex <font color="Olive">u</font>, <font color="Olive">v</font>, <font color="Olive">w</font>, <font color="Olive">u1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> st <br/>( ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font> being  <a href="real_1.html#NM1">Real</a>  st <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">a</font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">u</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Olive">b</font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">v</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Olive">c</font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">w</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">d</font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">u1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> holds <br/>( <font color="Olive">a</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">c</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">d</font> <a href="hidden.html#R1">=</a> 0 ) ) &amp; ( for <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>  ex <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">a</font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">u</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Olive">b</font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">v</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Olive">c</font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">w</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">d</font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">u1</font></span>)</span> ) )
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">V</font> = <font color="Maroon">V</font> as  <a href="anproj_2.html#V1" target="_self">up-3-dimensional</a> <a href="rlvect_1.html#NM2">RealLinearSpace</a> <b>by </b><i>, </i>;<br/>
<b>take </b><font color="Maroon">CS</font> =  <a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">V</font>;<br/>

<b>thus </b><a NAME="E4:101_2_1"/>
( <font color="Maroon">CS</font> is <a href="collsp.html#V1">strict</a> &amp; <font color="Maroon">CS</font> is <a href="anproj_2.html#V4" target="_self">Fanoian</a> &amp; <font color="Maroon">CS</font> is <a href="anproj_2.html#V5" target="_self">Desarguesian</a> &amp; <font color="Maroon">CS</font> is <a href="anproj_2.html#V6" target="_self">Pappian</a> )
 ;<br/>

<a NAME="E5:101_2_1"/>
 ex <font color="Olive">CS</font> being  <a href="anproj_2.html#NM1">CollProjectiveSpace</a> st <br/>( <font color="Olive">CS</font> <a href="hidden.html#R1">=</a>  <a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">V</font> &amp; not <font color="Olive">CS</font> is <a href="anproj_2.html#V7" target="_self">2-dimensional</a> &amp; <font color="Olive">CS</font> is <a href="anproj_2.html#V8" target="_self">at_most-3-dimensional</a> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:101_2_1"/>
( <font color="Maroon">CS</font> is <a href="anproj_2.html#V8" target="_self">at_most-3-dimensional</a> &amp; not <font color="Maroon">CS</font> is <a href="anproj_2.html#V7" target="_self">2-dimensional</a> )
 ;<br/>


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