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<div><span class="kw">theorem </span><a NAME="T12"><span class="comment"><font color="firebrick">:: BROUWER:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">r</font> being   non  <a href="xxreal_0.html#V3" title="XXREAL_0:attr.3">negative</a>  <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b2">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b3">o</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b2">n</font></span>)</span><br/>  for <font color="Olive" title="b4">f</font> being   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2" title="BROUWER:func.2">Tdisk</a> (<font color="Olive" title="b3">o</font>,<font color="Olive" title="b1">r</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="brouwer.html#K2" title="BROUWER:func.2">Tdisk</a> (<font color="Olive" title="b3">o</font>,<font color="Olive" title="b1">r</font>)</span>)</span>  st <font color="Olive" title="b4">f</font> is  <a href="abian.html#NV5" title="ABIAN:NV.5">without_fixpoints</a>  holds <br/><span class="p1">(<span class="default"><a href="brouwer.html#K5" title="BROUWER:func.5">BR-map</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> (<font color="Olive" title="b3">o</font>,<font color="Olive" title="b1">r</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> (<font color="Olive" title="b3">o</font>,<font color="Olive" title="b1">r</font>)</span>)</span></div></div>
