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<div><span class="kw">theorem </span><a NAME="T43"><span class="comment"><font color="firebrick">:: GTARSKI2:43</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="gtarski2.html#K1" title="GTARSKI2:func.1">TarskiEuclidSpace</a> <font color="Olive" title="b1">n</font></span>)</span>  st  <a href="gtarski2.html#K3" title="GTARSKI2:func.3">Tn2TR</a> <font color="Olive" title="b3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><a href="gtarski2.html#K3" title="GTARSKI2:func.3">Tn2TR</a> <font color="Olive" title="b2">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="gtarski2.html#K3" title="GTARSKI2:func.3">Tn2TR</a> <font color="Olive" title="b4">c</font></span>)</span>) holds <br/> ex <font color="Olive" title="b5">jj</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>(  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b5">jj</font> &amp; <font color="Olive" title="b5">jj</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 &amp; <span class="p1">(<span class="default"><a href="gtarski2.html#K3" title="GTARSKI2:func.3">Tn2TR</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><a href="gtarski2.html#K3" title="GTARSKI2:func.3">Tn2TR</a> <font color="Olive" title="b2">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">jj</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gtarski2.html#K3" title="GTARSKI2:func.3">Tn2TR</a> <font color="Olive" title="b4">c</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><a href="gtarski2.html#K3" title="GTARSKI2:func.3">Tn2TR</a> <font color="Olive" title="b2">a</font></span>)</span></span>)</span> )</div></div>
