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<div>:: <span class="kw">deftheorem </span>   defines <a href="borsuk_7.html#V2" title="BORSUK_7:attr.2">with_antipodals</a> <a onclick="hs(this)" href="javascript:()">BORSUK_7:def 13 : <br/></a><span> for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">p</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="b1">m</font></span>)</span><br/>  for <font color="Olive" title="b4">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b5">f</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> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">r</font>)</span>)</span>,<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> holds <br/> ( <font color="Olive" title="b5">f</font> is  <a href="borsuk_7.html#V2" title="BORSUK_7:attr.2">with_antipodals</a>  iff  ex <font color="Olive" title="b6">x</font>, <font color="Olive" title="b7">y</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="b1">m</font></span>)</span> st <font color="Olive" title="b6">x</font>,<font color="Olive" title="b7">y</font> <a href="borsuk_7.html#R2" title="BORSUK_7:pred.2">are_antipodals_of</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">r</font>,<font color="Olive" title="b5">f</font> );<br/></span></div>
