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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E30">Th32</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: COMBGRAS:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3 <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b2">X</font> holds <br/> for <font color="Olive" title="b3">F</font> being    <a href="combgras.html#L1" title="COMBGRAS:struct.1">IncProjMap</a> over  <a href="combgras.html#K1" title="COMBGRAS:func.1">G_</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Olive" title="b2">X</font>), <a href="combgras.html#K1" title="COMBGRAS:func.1">G_</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Olive" title="b2">X</font>)  st <font color="Olive" title="b3">F</font> is  <a href="combgras.html#V7" title="COMBGRAS:attr.7">automorphism</a>  holds <br/> for <font color="Olive" title="b4">H</font> being    <a href="combgras.html#L1" title="COMBGRAS:struct.1">IncProjMap</a> over  <a href="combgras.html#K1" title="COMBGRAS:func.1">G_</a> (<font color="Olive" title="b1">k</font>,<font color="Olive" title="b2">X</font>), <a href="combgras.html#K1" title="COMBGRAS:func.1">G_</a> (<font color="Olive" title="b1">k</font>,<font color="Olive" title="b2">X</font>)  st  the <a href="combgras.html#U2" title="COMBGRAS:sel.2">line-map</a> of <font color="Olive" title="b4">H</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  the <a href="combgras.html#U1" title="COMBGRAS:sel.1">point-map</a> of <font color="Olive" title="b3">F</font> holds <br/> for <font color="Olive" title="b5">f</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <font color="Olive" title="b2">X</font>  st  <a href="combgras.html#G1" title="COMBGRAS:aggr.1">IncProjMap</a>(#  the <a href="combgras.html#U1" title="COMBGRAS:sel.1">point-map</a> of <font color="Olive" title="b4">H</font>, the <a href="combgras.html#U2" title="COMBGRAS:sel.2">line-map</a> of <font color="Olive" title="b4">H</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="combgras.html#K8" title="COMBGRAS:func.8">incprojmap</a> (<font color="Olive" title="b1">k</font>,<font color="Olive" title="b5">f</font>) holds <br/> <a href="combgras.html#G1" title="COMBGRAS:aggr.1">IncProjMap</a>(#  the <a href="combgras.html#U1" title="COMBGRAS:sel.1">point-map</a> of <font color="Olive" title="b3">F</font>, the <a href="combgras.html#U2" title="COMBGRAS:sel.2">line-map</a> of <font color="Olive" title="b3">F</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="combgras.html#K8" title="COMBGRAS:func.8">incprojmap</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Olive" title="b5">f</font>)</div></div>
