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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E68">Th58</font></span>: <a NAME="T68"><span class="comment"><font color="firebrick">:: BORSUK_7:68</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font>, <font color="Olive" title="b4">B1</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>,1)</span>)</span>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span>  st <font color="Olive" title="b3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="valued_2.html#K20" title="VALUED_2:func.20">(-)</a>  &amp; <font color="Olive" title="b4">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="valued_2.html#K80" title="VALUED_2:func.80">&lt;--&gt;</a> <font color="Olive" title="b3">g</font> &amp; <font color="Olive" title="b2">f</font> is  <a href="borsuk_7.html#NV3" title="BORSUK_7:NV.3">without_antipodals</a>  holds <br/> <a href="borsuk_7.html#K15" title="BORSUK_7:func.15">Sn1-&gt;Sn</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">B1</font> <a href="valued_2.html#K70" title="VALUED_2:func.70">&lt;/&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="jgraph_4.html#K1" title="JGRAPH_4:func.1">NormF</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">B1</font></span>)</span></div></div>
