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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th21</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: ANPROJ11:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font> being   non  <a href="anproj11.html#V1" title="ANPROJ11:attr.1">zero_proj1</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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><br/>  for <font color="Olive" title="b2">u</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 <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3</span>)</span><br/>  for <font color="Olive" title="b3">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3</span>)</span>  st <font color="Olive" title="b2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj11.html#K1" title="ANPROJ11:func.1">normalize_proj1</a> <font color="Olive" title="b1">P</font> holds <br/><span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><span class="p2">(<span class="default"><a href="anproj11.html#K4" title="ANPROJ11:func.4">dir1a</a> <font color="Olive" title="b1">P</font></span>)</span>,<span class="p2">(<span class="default"><a href="anproj11.html#K6" title="ANPROJ11:func.6">dir1b</a> <font color="Olive" title="b1">P</font></span>)</span>,<font color="Olive" title="b3">v</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|(</a><span class="default"><font color="Olive" title="b2">u</font>,<font color="Olive" title="b3">v</font></span><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">)|</a></span></div></div>
